{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":53975,"title":"Compute the effective conductivity of more heterogeneous aquifers","description":"Cody Problem 52070 asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single value of conductivity set such that the aquifer produces the same flow under the same total change in head. In that problem, the aquifer had soil units either in series only or in parallel only. \r\nWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided.  \r\nFor example, if in the aquifer below  = 0.1 m/d,  = 0.2 m/d,  = 0.01 m/d, and  = 20 m/d, then the effective conductivity is 0.092 m/d.  \r\nHint: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \r\n   and   \r\nThen conservation of mass leads to \r\n\r\nSolve this equation for the head , compute the flow through the aquifer, and get the effective conductivity from the definition.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 725.117px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 362.558px; transform-origin: 407px 362.558px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.25px 7.79167px; transform-origin: 318.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.017px 7.79167px; transform-origin: 331.017px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.79167px; transform-origin: 25.2667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.933px 7.79167px; transform-origin: 359.933px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.858px 7.79167px; transform-origin: 110.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if in the aquifer below \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.1 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.2 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K3\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7px 7.79167px; transform-origin: 52.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.01 m/d, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K4\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.35px 7.79167px; transform-origin: 88.35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.79167px; transform-origin: 13.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.683px 7.79167px; transform-origin: 342.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"vx = -Kdh/dx\" style=\"width: 72px; height: 35px;\" width=\"72\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 7.79167px; transform-origin: 23.325px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   and   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v_y = -Kdh/dy\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.408px 7.79167px; transform-origin: 112.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen conservation of mass leads to \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\" style=\"width: 173.5px; height: 35px;\" width=\"173.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.358px 7.79167px; transform-origin: 100.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSolve this equation for the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.9px 7.79167px; transform-origin: 251.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 246.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 123.233px; text-align: left; transform-origin: 384px 123.233px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 513px;height: 241px\" 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\" data-image-state=\"image-loaded\" width=\"513\" height=\"241\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity2(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 0.1; K2 = 0.2; K3 = 0.01; K4 = 20;\r\no = ones(50,50);\r\nK = [K1*o K2*o; K3*o K4*o];\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.0916;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 5; K2 = 3; K3 = 8; K4 = 6;\r\nK = K3*ones(50,110);\r\nK(1:20,1:50) = K1;\r\nK(21:end,1:30) = K2;\r\nK(1:20,51:end) = K4;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 2.5471;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 0.1; K2 = 1;\r\nK = diag(K2*ones(50,1));\r\nfor j = 1:9\r\n    K = K+diag(K2*ones(1,50-j),j)+diag(K2*ones(1,50-j),-j);\r\nend\r\nK(K==0) = K1;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.2945;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 1; K2 = randi(9)/10;\r\nw1 = 10*randi(9); w2 = 100-w1;\r\nK = K2*ones(100); K(1:w1,:) = K1; \r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = (K1*w1+K2*w2)/(w1+w2);\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-02-02T15:06:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-28T03:19:00.000Z","updated_at":"2026-04-05T08:16:36.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55825,"title":"Measure the hydraulic conductivity with a constant-head permeameter","description":"A constant-head permeameter is a device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . By supplying a flow  to a standpipe, water is maintained at a constant level so that the head difference , or the difference in water levels between the standpipe and outlet, is constant. \r\nThe hydraulic conductivity can then be determined from Darcy’s law\r\n\r\nwhere the head gradient  is simply . Darcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\r\n\r\nwhere  is the acceleration of gravity and  is the porosity of the soil \r\nWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use  and .\r\n\r\n                              ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.2px; transform-origin: 407px 419.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.342px 8px; transform-origin: 256.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 8px; transform-origin: 65.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. By supplying a flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8417px 8px; transform-origin: 75.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah\" style=\"width: 21.5px; height: 18px;\" width=\"21.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.533px 8px; transform-origin: 188.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.533px 8px; transform-origin: 209.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4167px 8px; transform-origin: 77.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 18.5px;\" width=\"39.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 8px; transform-origin: 30.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is simply \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAlCAYAAAAHrmSHAAAEZUlEQVRoQ+1ZOa9NURR+7wcQU6U0FKIgQjQUCkNQaASJQiExFDqzRGMIalOiUEgQnSAoKJAQJHQSQyUqQ8QP4Ptkr5d199vnrLXXPa+4N/ckX8579+5h7W9/ew37jo+NnmoGxqt7jDqMjUgLiGDYSJsNDi4C2wNcuLsMG2l7sPKDwAI3A4GGw0baa3BwDbga4MLdJUraEszwFfjhnqnccBU+Xgy8BN73OdY89P8MzAe+tIxF26e1fP/HsiVK2k8MfBk4Hlgo/c0WYJvqu9Qy1DHPabRZB6ww2pK0RcAlYKZqS8IPAB8M0kPRk4u+mSabg3dUbTxKy4FfwCwHKVaTT2hwArhlNUzfH8L7nGrrXktEaTSOR4DPXiDqP6hW7jQVu9+50KZmVM87wL3wRK6ovcqGWtLog54pyynplQG1ySI51I4KdTSRxqNGtdakGnrzq2yoJe0hDJNw3o/a9NGoUUcTaVTtTuCBU7F609jFCh49w9aQJtGJR/I3IH7tDf62nG++FpK/Hoj0zcfaiA9uJKU5ORtjPnclNa62oYY0HgHKf2Ga7CPeEn02Vewyu/9NYxzG+7xaKTdmLvANaEsbNDl0/FRajV9kH/FnZ/B3VRbgJU1UpifQR6xmt6iM+2nVq/F+Dkj5IwthRF0DWLkb+30HalMWCUI0Q2zwqtSdcpCgIwBTBFGAECmTeSdnPnUsdeKm0b88BRjBXihCPQqg8k8BNWVTHsy8wpkg1dOBu8mj+BjIoxOP7L402u3C96Xdk/yM7c8mwkRV2kF70hmOdQfQR9xSjD4hj9B4g9Uh/95DmiSzpSOQRyHrmMhxoh30Z1uBk4BEPb0gS7nesilfs2ya2FBD+P+xPKQxnyGadkQiIcezkkRdTVBpzPO0E9ZjWbaRYJJeE7n1ptFea5OLIrQME6fdFh1zH9GWd+njXAoeElU9R722bCIBOgiFyzeLNO48d8faTZ1dtzlw3S7fZU2+5c8iZRNJ00HIszHVSpNFWAvgwPrY8f+S2rT/Kxms/ZmVoUfKJtoVKZ04F+vrifSnTWlszKsWb22pc58S0ToLLzl58WeeiCbJrPdGg4TlKZK1MexD4dwFem5hmkiTCfKMvSjX9KFWSqmQlyy8yZeIPxPCuWn3gLyejJRN+WmgfVZuR7f0CmCq1VNtNJGmz34bUW3f5WpruwrS/owKWAvwOJdKI5LJp6ZsYntdOlkVDEVDF8JkftINSIk0SWb1rWaEOG2YJqV0DZOXZFRC6ZpHUgYrh8vtzfNJqp2k88peP9Pxz+Y0t6x/Ekcl0ih/Xvt28fB404GSgF1pwFK+x0UdBWYA15MqSvNHyiZuyLI0du2anqDDpOTXSjlqJ5nq9gwWb4GqW4mujRok0qJlU9ecucqozicNDsiUZTdgJdrB4f3dBklpTEwvANEfcvysGC0HhbRo2dQZUXqgQSFNImDNr01TQhgHHRTSGAT4Y070h+lOCRwU0jpddL+DjUgLMDgiLUDaP98z9CZZXgwsAAAAAElFTkSuQmCC\" alt=\"Deltah/L\" style=\"width: 38.5px; height: 18.5px;\" width=\"38.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 214.6px 8px; transform-origin: 214.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.025px 8px; transform-origin: 91.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.417px 8px; transform-origin: 175.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAABGCAYAAAA96C05AAAHyElEQVR4Xu2d2+s2UxTHvX8AcriSXDhcuCLHEheU85Uo5EaR04USObtyKCQl5ygXyjkSQsoFybEo5cLhQrhyiH+A9cleb6vdnpk9M2uemXmeNbWa931mn+a7v3uvvdbas3979okrEJgBgT0z1BlVBgL7BPGCBLMgEMSbBfaoNIgXHJgFgSDeLLBHpUG8ZXHgIGnO0SLnirws8s2ymufXmiCeH5ZjSrpEMt8ockIq5Ee5HzmmwKXnDeItq4f+Tc15Qu7XLatpvq0J4vniOaY01OzvqYBL5f7imMKWnjeIt5weOk+a8nZqzsFy/2M5TfNvSRDPH9OhJT4uGa8V+VLkxKGFrCVfEG85PfWDNOUIkftE7lhOs6ZpSRBvGK6nSrbvCurwcPntkIZneU2a9jd5sK/I1ynBaXL/eFiz1pMriFfXV8dIsrNFrkqzErlKBPlTfj9ABKv0rgIxyYfr5B6Rv0ReSWW+L3fULNdO9MlOvGQdt6pSMUvhY+O6ReSBLJeu0/g5NxCwWt8VwVdnrVZrVLwnz86pasnKEwXx+nfgF4k8L6XZKy+B51zWQGDG/FCE2fAakadMJtT2R+n/+bP+rVtJjiBe/466V7LcLoL1yeyUuz0wEh405LIzXckxbGe8YyXf1obJLNQ1xGNEnlLRP99Kmncq0q09yc3yAvenl8jVKVi9KXKgeUlVv6zpjioQVYm8LWEy1rCfi/zU1tE1xCM/quIZEY0l8hsjnsXx/iIsjFEjgMuo3mZ3gFWN+QyFmn1IRKMONWpUVffaw2RqNOES6py5a4kH0exIh2B2VFt1Qtq1g9g2WC2ZzpeEOsuDz3EidIBe1tigQ/JZgAGtbpS1hsnA4zkR3k8vV+KpSqDw0sLarlVI01l5W+8u+Jm1bJV4EOg1kZNF7JpPg/5N0Yg2K3jBEOxtGn3O9ZnIYyIXp/939n2fGU8965TdZH0p0KRZ6wiu6XB9T3D4VASL9XQRaxjY2awUjbAz55xhMrTVRSLW0q7BIE9jNaIb8ewop8KS2uB3Szyrhoa8yJLz2O1LuE2uzEhH2y2xcuLR2cwSqp70+dXppceSoAY72nCFyK0psV061eTfCPFYt7yQamqyvnJV20TOIS+1tDw1A8xuc7KuFzXUiFbgluFikO4nwmbQqTcIWMJhEHJ5xIcnmfHsWqRkOOTGRc2LWDfNJ/Lya4pPKvG6lhMWNwYsyxVCb+T7RUQdxzzDYCv5Bb0GXRPhnpUKWl0flQ2YhHgag9TRaf11qGGMDXW1NHn0yWtfnhH/qMjDKW8NWRWDWt9iF2avDgQdQ6v2mwjU5wWpIV/J3XY0xETFvSEy1cZP+geVqi4vmgLWXoRTjN2JZxfJ2ui/5R/4784yhEOd4OtrWp9YX6CdKbTBfRbY9iW7yNX2vHMRPKbwmfNCuJsS4bQpUxBuMuIxYp9MpaMSnhY5QwSVwUVgm+8D2qbrtlilOlDnmPEY9du203fThJuMeOyoUJKpG8VabJAx91/ZwW7Xf/mspqRmfYOq9lhrzDzRzFb9XISbjHjWgrOqyfr12hbZVi1aF4uSDuJeKLITwfEJaMnAvnuDKrXpFVzXeHZmy8NktqImg8K6FCAYa8KTRNgIyWV3cUzQJztTpI2T8tJoFhsz3gQQrsRrC5PVOJXt+pC1INfrInj7x8xwc1u1m+jIIXXMSUBX4unCHxBKYbLS+s8C1hUkHwIueTZt1R4/tKEj8uF6GXrNQUA34lk1CQClSISNaJTcIZaYnt+Kes14NVYtH+/8OpQBI/J9IHnPHJGfrPnRGFOqYDfi1YTJIOf3Ihp6yf1idsYr+cx0YfyWlLHkTaR85LPpC+J5WfkM1DtF1DsxBQHdiGdJ0+bctelyX1y+A4NtMwomsd1HRMLA2BylpySgtQc6HfNN26KsUQAsbS4PSy7S5rtSbIN4jpHBSUhYyTeIrClGuzmKTFtTiYBDNyegtVgSMAGp5sPLwQaIxhm7RDymzKbrZ3lQiinmefJ0WMC4UQ4T4VnnnvxpcY/SEwJElJhkWFYN2RZFv7KXr+kitFoMofbZCBq9tb0IQCCv9WQVSkG8KpgikTcCQTxvRKO8KgSCeFUwRSJvBIJ43ohGeVUIBPGqYIpE3ggE8bwRjfKqEAjiVcEUibwRCOJ5I/p/eUQGDhX5R6QpBo3zdszWsGlavqFSg3h+QOP9v1xEA/GU3PRRO6S7TcSes+LXkhWUFMTz7yTdw9h0LBk1Er8mdLiJEwP839ChxCCeA4hZEfoNctuxsqTJz1rxb8mCSwzi+XaO/Qa56WAj3R281X+rrAvWIF4XQv2ed+1J08N6dn4PYhCvH7G6Uuv6rulgI4jJURJDtiB11b2q50E8v+6yX921nYe3Mye7t0EbxPMjnv1GJf/jK3qEBzPh0J2+fi1dQElBPL9OYGc235TkbhS+LXk+VVM69d2vBSsqKYjn11nqRtFTFSDc9SI4lOOYjgznIJ4P8fJDjDAe9MMX/HmXiWzbqVSjkAvijYJvb+b8SzrUrR48GV/RFTAO4vkQT7+24q8bsTEgyNaBaxDPh3hRSk8Egng9AYvkPggE8XxwjFJ6IhDE6wlYJPdBIIjng2OU0hOBIF5PwCK5DwJBPB8co5SeCATxegIWyX0QCOL54Bil9ETgP9ZvqFabH15tAAAAAElFTkSuQmCC\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.733px 8px; transform-origin: 114.733px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.492px 8px; transform-origin: 371.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.55px; text-align: left; transform-origin: 384px 18.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K = (gd^2/(180nu))(n^3/(1-n)^2)\" style=\"width: 114px; height: 37px;\" width=\"114\" height=\"37\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.95px 8px; transform-origin: 78.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the porosity of the soil \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.683px 8px; transform-origin: 363.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-6} m^2/s\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 338.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.35px; text-align: left; transform-origin: 384px 169.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 494px;height: 333px\" 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\" 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margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = CHP(Q,L,D,dh,n)\r\n   K = f(Q,L,D,dh);\r\n   isDLvalid = true;","test_suite":"%% Coarse sand #1\r\nQ  = 8.92e-6;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #1--larger cylinder area\r\nQ  = 3.57e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.1;                   %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #2\r\nQ  = 2.44e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 9.69e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1\r\nQ  = 1.52e-5;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.1;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1--reduced head difference\r\nQ  = 7.61e-6;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Medium sand #2\r\nQ  = 7.08e-7;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.3;                   %  Porosity\r\nK_correct = 1.2e-4;         %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Fine sand \r\nQ  = 3.57e-7;               %  Flow (m3/s) \r\nL  = 0.075;                 %  Sample length (m)\r\nD  = 0.075;                 %  Diameter of cylinder holding sample (m)\r\ndh = 0.4;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-5;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Silt \r\nQ  = 1.17e-7;               %  Flow (m3/s) \r\nL  = 0.05;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 3.88e-6;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nfiletext = fileread('CHP.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-08-18T23:24:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T14:41:04.000Z","updated_at":"2025-12-01T14:29:21.000Z","published_at":"2022-09-17T14:42:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. By supplying a flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is simply \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah/L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h/L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = (gd^2/(180nu))(n^3/(1-n)^2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = \\\\frac{g d^2}{180 \\\\nu}\\\\frac{n^3}{(1-n)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the porosity of the soil \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\rm\\\\,m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-6} m^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57620,"title":"Compute frequency factors for the normal distribution","description":"In frequency analysis in hydrology, the streamflow  corresponding to a specified exceedance probability  (or return period ) can be computed as\r\n\r\nwhere  and  are the mean and standard deviation of the streamflow series, respectively, and  is the frequency factor. \r\nWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.242px 8px; transform-origin: 156.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn frequency analysis in hydrology, the streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.95px 8px; transform-origin: 164.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to a specified exceedance probability \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.6667px 8px; transform-origin: 32.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or return period \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = 1/p\" style=\"width: 55.5px; height: 18.5px;\" width=\"55.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT = mu + KT sigma\" style=\"width: 89.5px; height: 20px;\" width=\"89.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eμ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eσ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.592px 8px; transform-origin: 249.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"KT\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.275px 8px; transform-origin: 74.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the frequency factor. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 8px; transform-origin: 373.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function KT = normFreqFactor(p)\r\n  KT = trapz(QT:inf,exp(-Q.^2));\r\nend","test_suite":"%%\r\np = 0.001;\r\nKT_correct = 3.090;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.002;\r\nKT_correct = 2.878;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.01;\r\nKT_correct = 2.326;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.02;\r\nKT_correct = 2.054;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.04;\r\nKT_correct = 1.751;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.1;\r\nKT_correct = 1.282;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.2;\r\nKT_correct = 0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.3;\r\nKT_correct = 0.524;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.5;\r\nKT_correct = 0;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.8;\r\nKT_correct = -0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\nT = [5 10 20 25 50 100 250 500 1000];\r\nKT_correct = [0.842 1.282 1.645 1.751 2.054 2.326 2.652 2.878 3.090];\r\nassert(all(abs(normFreqFactor(1./T)-KT_correct)\u003c1e-3))\r\n\r\n%%\r\np = rand(1,randi(15));\r\nK1 = normFreqFactor(p);\r\nK2 = normFreqFactor(1-p);\r\nassert(all(abs(K1+K2)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('normFreqFactor.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp') || contains(filetext, 'interp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-29T19:23:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-29T19:23:11.000Z","updated_at":"2026-01-04T12:13:24.000Z","published_at":"2023-01-29T19:23:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn frequency analysis in hydrology, the streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to a specified exceedance probability \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or return period \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = 1/p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = 1/p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT = mu + KT sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T = \\\\mu + K_T \\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"mu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"KT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the frequency factor. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59034,"title":"Compute the maximum length of a contaminant plume in groundwater","description":"Problem statement \r\nWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of , and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s maximum contaminant level, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity , the magnitude of the head gradient , effective porosity , bulk density , and soil organic fraction . Along with the MCLs, the properties of the contaminants provided to the function are the half life  and the octanol-water partition coefficient .\r\nCompute the longitudinal dispersion coefficient as , where  is the average linear velocity and  is the longitudinal dispersivity. The variable aL will be specified as either a number or ‘X\u0026E’. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026 Eckstein (1995):\r\n\r\nwhere  is in meters if the flow length  is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\r\nBackground\r\nContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration  of the contaminant in time  and spatial coordinate  can be computed with\r\n\r\nThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where . Retardation is included in the retardation coefficient . The maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a second-order linear ordinary differential equation with constant coefficients, which can be solved with the boundary conditions  and . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 605.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 302.95px; transform-origin: 407px 302.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 151px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75.5px; text-align: left; transform-origin: 384px 75.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 350.983px 8px; transform-origin: 350.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"C0\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.525px 8px; transform-origin: 157.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.967px 8px; transform-origin: 325.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.358px 8px; transform-origin: 114.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the magnitude of the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18.5\" alt=\"|dh/dx|\" style=\"width: 49.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.2083px 8px; transform-origin: 58.2083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, effective porosity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"ne\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, bulk density \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rhob\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.125px 8px; transform-origin: 29.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and soil organic fraction \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"20\" alt=\"phio\" style=\"width: 17.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.217px 8px; transform-origin: 302.217px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" alt=\"T_1/2\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the octanol-water partition coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"22.5\" height=\"20\" alt=\"Koc\" style=\"width: 22.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.875px 8px; transform-origin: 155.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the longitudinal dispersion coefficient as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAAAoCAYAAADdRklLAAAFm0lEQVR4Xu2bTcgWVRTHc1+bWtXCwFoECbrRAqldBRFECzVdhCBYrSKiyBbRqqKPRStTSiRCy0UQSFCBSSL0sYkIcmFRLmpVFLWv/0/mPJzmvR9n5tXpGZ87cJhH587MPef8zzn/e+68G65pR7NAZ4ENzRLNAmaBBoaGhYUFGhgaGBoYGgbWWqBlhoaKlhkaBoZnhld0y92SOyrG+1XXz0relnzSDD1PC0TLxPdS77ZORRx/l+SH7t/bdN4pedpdf1C/v56nSVZ31lEw/CIT3diZ6VWdn0mYDFCcllzbXdveADEvYEXAcItUuuDUuq9QCh7TtUNu7A36/fu8TLK6s42AwTuYErG54mCfRY5o7KOra955aR4Bw/tSaVenFuSQzFA6DuvigW7A3zpfNy+TrO5sI2D4y/GA5/T7pYq5+qXiVo03srm6lp6B5jUwQAq/cnpEHHuvxn/s7nlYv8kuV/OBzk9JNkr+7OSozk9KWJaXeFbJLtfr4rOSmzu5XecXEwFp2TiSubPvq4HhYPdyHnBeskNSI4T9zHAlwdAH3ljARTJe6tk464SEefAMnIJ9fBBRKnFmzW6luUPiv5GwUks53Jfm0faugYEIR1GOk5LdAWvTqLKeA8PHRkXgVZfm5rNQ5J7UmDFgAAjnJPRfUvf/071oXdHqJmvcDRJ/U0IJ81UkeyftVAODKcTNUcR5AHHf1bi89EDIrZjMdmOAlnKWz7gpm5Idtkjul4zKQiUw9KMu6lRPOL/UxO4cG65LfJ8BPrfU9rYbHak9/f0zU4HJkh6OMpqflcDg033UqZSR95wSlysqlgkX3ik5/ayGR3lWRD+y0W/dwMd1ftPdBLdjCyCaFcgyD0nOSBarwxIY/H5ErgXdV+IL/YdtapWiZr/GWe+Cce9KXh6b3iKWvIxjTMecfjjtZwlkL8ezIIQ044xbQTKPS96SlPZ0rPT40sSz2CSM7AcZ4f1D4wHyKcliUZADg0chdozsMwxZUnq2HeUiKX9OTSB9az7naJ9R+xHc18FKarRTmxoPOI9JfKZI2cp4zre6yLzgFdy7yCY5MPh0H2lB86LvJLaZVVPOyFB/B3RoAE8NBk/iUo72S0B0KfEsD6zoisuykgHR+EFklQfPoQ/ygIQmIKD90YMoB4YhLWjPrDEAQKCGlRitPT/KRYaC5EqN91Hfz2hmB5pOlErjCzh9k6RP7MYEhIGBZ78j2eqivKSzzdtAB6f5SfKfbnIODJEta15OZB7rMgJ1L9UdS03Snj83gukzg5+7AQEHPSKh90D0vib5UJKq5xYQQ/oQnpNx355C0FGK4R+WPRl/ppsLPltTVlJg6KfefvSC9Hsk+yRGFk3xyActni9EuEgJ8VNf8+SQd5MFOfa6QDCSRwnkwE6pr7+s/g8JCJ8ZLN3nbEDpeEECMAnUjyQfSD6VJLO2BwNOJrKN5ZcMDUBgzJ91Dx+yEWUt7lwnbWoHD30fwfJGz8hkAAsE60EAgNczQPABMaQPQTZhJVArw6aTLXFrRPbS+FoHcqihIuPNWNH2duSZcxszRUAYQSVwQ/2H/wMMlkbXs6Scm/P787V0X1t1rUdP4yThUjw1GGzJSg2DCafKC2OydW091lmSe30PJxcQlBGOCAdLqWXv8OSU/2P1kP3ybGowWA3LLSlJbXTFauRoSfw6ahoWEKUeC93fJyQp4hl5qb3DlpIAAQL5fOmZU4PBlpQpvmBAuKgJ1z6tixhkWceUtqJxGh8U86cItW9NS/oZJ6HpxVEFAoOmAkO/F8+7AQQrEg62Xu27iWg3blmdnZsXjmalxj6P/TkBGfLz7gY+gIHocS26F1R6FwCgAcbqw692snabCgxzc9xKzreBYSXdnla6gaGBYWGBBoYGhgaGhoG1FmiZoaGiZYaGgbUW+Bf20VM4+con7wAAAABJRU5ErkJggg==\" width=\"65.5\" height=\"20\" alt=\"DL = aLvL\" style=\"width: 65.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"20\" alt=\"vL = (K/ne)|dh/dx|\" style=\"width: 123.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.808px 8px; transform-origin: 105.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the average linear velocity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.417px 8px; transform-origin: 136.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal dispersivity. The variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eaL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.367px 8px; transform-origin: 121.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be specified as either a number or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e‘X\u0026amp;E’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.275px 8px; transform-origin: 88.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"138.5\" height=\"21\" alt=\"aL = 0.83(log10(L))^2.414\" style=\"width: 138.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters if the flow length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 8px; transform-origin: 250.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8px; transform-origin: 383.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.0083px 8px; transform-origin: 84.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the contaminant in time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 8px; transform-origin: 72.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and spatial coordinate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.1667px 8px; transform-origin: 15.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.95px; text-align: left; transform-origin: 384px 19.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"170\" height=\"40\" alt=\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\" style=\"width: 170px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 108px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 54px; text-align: left; transform-origin: 384px 54px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.05px 8px; transform-origin: 311.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"81.5\" height=\"20\" alt=\"lam = ln(2)/T_1/2\" style=\"width: 81.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Retardation is included in the retardation coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"20\" alt=\"R = 1+rhobKoc phio/ne\" style=\"width: 122px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 8px; transform-origin: 151.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which can be solved with the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" alt=\"C(0) = C0\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18.5\" alt=\"C(infinity) = 0\" style=\"width: 66px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Lp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\n%  See the text suite for the definitions of the parameters\r\n   v  = K*dhdx/ne;\r\n   Lp = (C0-Clim)/v;\r\nend","test_suite":"%%  Dieldrin and styrene\r\nC0   = [1 15];                  %  Source concentrations (mg/L)\r\nClim = [2e-4 0.1];              %  Maximum contaminant levels (mg/L)\r\nK    = 87.5;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.002;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.25;                    %  Effective porosity\r\nrhob = 2.5;                     %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [25120 380];             %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [1825 182];              %  Half lives (d)\r\nLp_correct = [20.76 58.95];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene, toluene, ethylbenzene, and p-xylene\r\nC0   = 30;                      %  Source concentration (mg/L)\r\nClim = [0.005 1 0.7 10];        %  Maximum contaminant levels (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.04;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.22;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [97 242 622 552];        %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [300 20 120 190];        %  Half lives (d)\r\nLp_correct = [1501.21 20.69 54.12 24.98];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Glyphosate\r\nC0   = 13.9;                    %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 30;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0005;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.18;                    %  Effective porosity\r\nrhob = 1.9;                     %  Bulk density (g/cm3)\r\nphio = 0.001;                   %  Soil organic fraction\r\nKoc  = 4e-5;                    %  Octanol-water partition coefficient (mL/g)\r\naL   = 2.8;                     %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 115.59;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  1,4-dioxane\r\nC0   = 10;                      %  Source concentrations (mg/L)\r\nClim = 3e-4;                    %  Limit set by Massachusetts (mg/L)\r\nK    = 7.77;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.01;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.21;                    %  Effective porosity\r\nrhob = 1.8;                     %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = 1;                       %  Octanol-water partition coefficient (mL/g)\r\naL   = 3;                       %  Dispersivity method\r\nTh   = 1;                       %  Half life (d)\r\nLp_correct = 16;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene\r\nC0   = 2;                       %  Source concentrations (mg/L)\r\nClim = 0.005;                   %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 97;                      %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 263.93;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  p-xylene\r\nC0   = 200;                     %  Source concentrations (mg/L)\r\nClim = 10;                      %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 552;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 190;                     %  Half life (d)\r\nLp_correct = 26.74;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Ethylbenzene\r\nC0   = 100;                     %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 622;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 120;                     %  Half life (d)\r\nLp_correct = 29.83;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Nastene, phylthene, siccanol (fictitious chemicals)\r\nC0   = [10 10 20];              %  Source concentrations (mg/L)\r\nClim = [1 2 0.1];               %  Limits (mg/L)\r\nK    = 0.2;                     %  Hydraulic conductivity (m/d)\r\ndhdx = 0.008;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.08;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = [15 80 2];               %  Octanol-water partition coefficient (mL/g)\r\naL   = 2;                       %  Dispersivity method\r\nTh   = [30 100 475];            %  Half lives (d)\r\nLp_correct = [2.6 1.83 72.39];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-01T15:59:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-01T15:47:36.000Z","updated_at":"2026-02-12T14:03:58.000Z","published_at":"2023-10-01T15:59:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the magnitude of the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, effective porosity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, bulk density \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rhob\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho_b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and soil organic fraction \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phio\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the octanol-water partition coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Koc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{oc}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the longitudinal dispersion coefficient as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"DL = aLvL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_L = a_L v_\\\\ell\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vL = (K/ne)|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_\\\\ell = (K/n_e)|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the average linear velocity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal dispersivity. The variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be specified as either a number or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘X\u0026amp;E’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL = 0.83(log10(L))^2.414\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L = 0.83(\\\\log_{10}L)^{2.414}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters if the flow length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the contaminant in time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and spatial coordinate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t}+\\\\frac{v_\\\\ell}{R}\\\\frac{\\\\partial C}{\\\\partial x}=\\\\frac{D_L}{R}\\\\frac{\\\\partial^2 C}{\\\\partial x^2} - \\\\lambda C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"lam = ln(2)/T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda = \\\\ln2/T_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Retardation is included in the retardation coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = 1+rhobKoc phio/ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = 1+\\\\rho_b K_{oc} \\\\phi_o/n_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which can be solved with the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(0) = C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(0) = C_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(infinity) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57452,"title":"Design a well field in an infinite aquifer","description":"A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand  (i.e., volume of water per time) with the constraint of lowering the water table by no more than , the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity , the specific yield , and the initial saturated thickness ) and the radius  of the well. \r\nThe Gupta/Chin method for designing a well field has the following steps:\r\nCompute , an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance ) is . Compute the transmissivity to be . Evaluate the drawdown at a time  1 year. Realize that for small values of  the unconfined well function* can be approximated and compute the pumping rate from  where  and . \r\nCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \r\nSet the pumping rate to . \r\nArrange the wells so that they are equidistant from the central well.\r\nDetermine the distance  between the central well and others so that the total drawdown at the central well is . In other words, add the drawdown from the central well to the drawdown from the other wells. If , then \r\n            \r\n Write a function to design a well field using this method.\r\n\r\n\r\n*http://www.aqtesolv.com/neuman.htm","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 895.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 447.692px; transform-origin: 407px 447.692px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 43.5px; text-align: left; transform-origin: 384px 43.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.242px 8px; transform-origin: 375.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA well field provides water for a community. The design of a well field involves a goal to meet a specified service demand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_d\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292.875px 8px; transform-origin: 292.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., volume of water per time) with the constraint of lowering the water table by no more than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max\" style=\"width: 25.5px; height: 20px;\" width=\"25.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8333px 8px; transform-origin: 47.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 8px; transform-origin: 57.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the specific yield \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S_y\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 8px; transform-origin: 50.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"r_w\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the well. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.008px 8px; transform-origin: 226.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Gupta/Chin method for designing a well field has the following steps:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 231.783px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 115.892px; transform-origin: 391px 115.892px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 104.05px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 52.025px; text-align: left; transform-origin: 363px 52.025px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 30.3417px 8px; transform-origin: 30.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_w\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292.492px 8px; transform-origin: 292.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"r = r_w\" style=\"width: 40.5px; height: 20px;\" width=\"40.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max/2\" style=\"width: 40.5px; height: 20px;\" width=\"40.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.342px 8px; transform-origin: 107.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the transmissivity to be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = K(b-s_{max}/2)\" style=\"width: 116.5px; height: 20px;\" width=\"116.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.35px 8px; transform-origin: 107.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Evaluate the drawdown at a time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"t = \" style=\"width: 22px; height: 18px;\" width=\"22\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.175px 8px; transform-origin: 50.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1 year. Realize that for small values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u = S_y r^2/4Tt\" style=\"width: 81.5px; height: 21px;\" width=\"81.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 243.133px 8px; transform-origin: 243.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the unconfined well function* can be approximated and compute the pumping rate from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max/2 = (Q_w/4 pi T) W(u_w)\" style=\"width: 111.5px; height: 38px;\" width=\"111.5\" height=\"38\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 22.95px 8px; transform-origin: 22.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"W(u) = integral(exp(-x)/x,{x,0,infinity})\" style=\"width: 112px; height: 35.5px;\" width=\"112\" height=\"35.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u_w = S_y r_w^2/4Tt\" style=\"width: 89.5px; height: 22px;\" width=\"89.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.15px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.075px; text-align: left; transform-origin: 363px 21.075px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 356.708px 8px; transform-origin: 356.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ceil(Q_d/Q_w)\" style=\"width: 88.5px; height: 20px;\" width=\"88.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.7167px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSet the pumping rate to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_0 = Q_d/N\" style=\"width: 73.5px; height: 20px;\" width=\"73.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eArrange the wells so that they are equidistant from the central well.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 43.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.7167px; text-align: left; transform-origin: 363px 21.7167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 73.9083px 8px; transform-origin: 73.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 261px 8px; transform-origin: 261px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between the central well and others so that the total drawdown at the central well is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max\" style=\"width: 25.5px; height: 20px;\" width=\"25.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In other words, add the drawdown from the central well to the drawdown from the other wells. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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alt=\"u_R = S_y R^2/4Tt\" style=\"width: 91px; height: 21px;\" width=\"91\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3px 8px; transform-origin: 23.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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style=\"width: 227px; height: 38px;\" width=\"227\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.133px 8px; transform-origin: 174.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Write a function to design a well field using this 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\" 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style=\"\"\u003e*http://www.aqtesolv.com/neuman.htm\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b)\r\n  % Q0 = pumping rate (m3/d)\r\n  % N = number of wells\r\n  % R = distance between central well and other wells (m)\r\n  N = randi(10);\r\n  Q0 = round(Qd/N,'up');\r\n  R = b;\r\nend","test_suite":"%%\r\nQd   = 7000;          %  Demand (m3/d)\r\nsmax = 3;             %  Maximum drawdown (m)\r\nK    = 50;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.2;           %  Specific yield \r\nb    = 30;            %  Initial saturated thickness (m)\r\nrw   = 0.3;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 1400;\r\nN_correct = 5;\r\nR_correct = 189.4;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 6000;          %  Demand (m3/d)\r\nsmax = 2.5;           %  Maximum drawdown (m)\r\nK    = 60;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.22;          %  Specific yield \r\nb    = 20;            %  Initial saturated thickness (m)\r\nrw   = 0.25;          %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 857.1;\r\nN_correct = 7;\r\nR_correct = 297.6;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 10000;         %  Demand (m3/d)\r\nsmax = 4;             %  Maximum drawdown (m)\r\nK    = 80;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.18;          %  Specific yield \r\nb    = 25;            %  Initial saturated thickness (m)\r\nrw   = 0.4;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 2500;\r\nN_correct = 4;\r\nR_correct = 117.6;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 12000;         %  Demand (m3/d)\r\nsmax = 3;             %  Maximum drawdown (m)\r\nK    = 140;           %  Hydraulic conductivity (m/d)\r\nSy   = 0.2;           %  Specific yield \r\nb    = 25;            %  Initial saturated thickness (m)\r\nrw   = 0.4;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 3000;\r\nN_correct = 4;\r\nR_correct = 78.2;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-23T22:33:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-23T00:54:17.000Z","updated_at":"2026-02-12T15:43:55.000Z","published_at":"2022-12-23T00:58:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA well field provides water for a community. The design of a well field involves a goal to meet a specified service demand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., volume of water per time) with the constraint of lowering the water table by no more than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the specific yield \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S_y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the well. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Gupta/Chin method for designing a well field has the following steps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r = r_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er = r_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the transmissivity to be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = K(b-s_{max}/2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = K(b-s_{max}/2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Evaluate the drawdown at a time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = \\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 1 year. Realize that for small values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = S_y r^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = S_y r^2/4Tt\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the unconfined well function* can be approximated and compute the pumping rate from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max/2 = (Q_w/4 pi T) W(u_w)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{s_{max}}{2} = \\\\frac{Q_w}{4\\\\pi T} W(u_w)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"W(u) = integral(exp(-x)/x,{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW(u) = \\\\int_u^\\\\infty \\\\frac{e^{-x}}{x} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u_w = S_y r_w^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_w = S_y r_w^2/4 T t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ceil(Q_d/Q_w)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = \\\\lceil Q_d/Q_w\\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSet the pumping rate to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_0 = Q_d/N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0 = Q_d/N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the wells so that they are equidistant from the central well.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between the central well and others so that the total drawdown at the central well is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In other words, add the drawdown from the central well to the drawdown from the other wells. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u_R = S_y R^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_R = S_y R^2/4Tt\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max} = \\\\frac{Q_0}{4\\\\pi T}\\\\left[W(u_w) + (N-1) W(u_R)\\\\right]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Write a function to design a well field using this method.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"374\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"389\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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the head for steady 1D flow in a homogeneous aquifer","description":"Problem statement\r\nWrite a function that computes the head  (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations . The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length  of the aquifer, hydraulic conductivity , aquifer thickness  (set to [] for unconfined aquifers), width , and a vector BC, which contains two of three of the head  at , the head  at , and the flow . The function should also return the flow.\r\nBackground\r\nThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\r\n\r\nwhere  is the flow area. For a confined aquifer, the flow area is , whereas for an unconfined aquifer .\r\nThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 738.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 369.25px; transform-origin: 407px 369.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.392px 8px; transform-origin: 247.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.433px 8px; transform-origin: 175.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, aquifer thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (set to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.6333px 8px; transform-origin: 97.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for unconfined aquifers), width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eBC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.183px 8px; transform-origin: 127.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains two of three of the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0583px 8px; transform-origin: 33.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5583px 8px; transform-origin: 43.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.575px 8px; transform-origin: 127.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should also return the flow.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.442px 8px; transform-origin: 381.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"35\" style=\"width: 85px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.467px 8px; transform-origin: 173.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area. For a confined aquifer, the flow area is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18\" style=\"width: 49.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, whereas for an unconfined aquifer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"18\" style=\"width: 50px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.85px; text-align: left; transform-origin: 384px 182.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"640\" height=\"360\" style=\"vertical-align: baseline;width: 640px;height: 360px\" 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data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Q] = homogAq(x,confined,L,K,b,w,BC)\r\n% h = head at position x\r\n% Q = flow\r\n% x = position at which head is requested\r\n% L = length of aquifer\r\n% K = hydraulic conductivity\r\n% b = thickness of confined aquifer ([] if unconfined)\r\n% w = width of aquifer\r\n% BC = [h0 hL Q]--one of which is NaN\r\n\r\n  h = conservation of mass + Darcy's law;\r\n  Q = -K*dhdx*A\r\nend","test_suite":"%%  Confined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nb = 2.5;                %  Thickness (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = 3.25;\r\nQ_correct = 31.25;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nb = 31;                 %  Thickness (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [43.4 41.4];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nb = 25;                 %  Thickness (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [164 158 152 146 140 134];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = 3.3354;\r\nQ_correct = 40.625;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [43.8839 42.4476];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [138.7047 137.6190 136.5247 135.4216 134.3093 133.1878];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nb = 34;                 %  Thickness (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 193.545];   %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [53.4 52.8 52.2 51.6];\r\nQ_correct = 193.545;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))\r\n\r\n%%  Unconfined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 298.85625]; %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [53.4135 52.8205 52.2207 51.6140];\r\nQ_correct = 298.85625;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-09T15:47:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2023-09-09T15:42:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-09T15:33:16.000Z","updated_at":"2026-02-10T14:45:49.000Z","published_at":"2023-09-09T15:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, aquifer thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (set to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for unconfined aquifers), width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains two of three of the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should also return the flow.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area. For a confined aquifer, the flow area is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, whereas for an unconfined aquifer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"640\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation  above the bottom of the aquifer and the position of a groundwater divide  given the water table elevations  at ,  at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere  is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position  is \r\n\r\nwhere  is the (unknown) flow at . Using Darcy’s law to replace  provides a differential equation that can be integrated using the water table elevations at the boundaries to determine  and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x  = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAACPUlEQVRYR+1XOy9FQRC+t1fpaBQUEgqNkAgRERKJ1uMPeFQqEgolCZXKI0rx6pSUNB6thIKWioYf4PtkRsaxe/bknrvuLc4mX/Ym59yZ78x8M7NbLtXJKtcJj1JBJJmJIiJ5ItIqf36OIfC01IzA4TAwAHQADcAmsPTfROivETgCSIprFLioBRH6PAEmgFegE3ivFZEXOG6SSDAiUVaofLvh9VY8z2PficICRkNElvHOmjhvwx6lYmg/RORchPqIvS+WPrIQ+cBLLNs9YFYiwwraAtqBT2AIuMubslAfYUS4pgBWzy4wDhwA1AxJ3gC9MYlswPiifHUL9m1xtoKdWtFqik7kGs565IvPsA8C0wD7iK0mm7aKA+NLDTvqm1g9xd4v0Kqx1aRpq5gE/+gjMolnx8ZysrVrNVGsTFvubusjQlHOCBFX6LWafPrgpGaVUWNcJHwI7APOCvMRUSHSQBdgG5nVB4W7npITV/k7X3cR4dc8GX0wTXZl7bbWTnBqu4jMwauWqsuA6kPTwgjx3JKMjNrh1KbYU8eDi0ho7Gu4mRZq6d7jSO3w/BKc2i4i6shlwOqDEeFaBVyHJUs4TUffRpJEQmOfeb8CeD4hER8JayfT1A5N35SCSH2kgqY+mrMYiUVEx0Pm9h+DiB0PvvbP1HH9NLcYRHQ8pJXtA0gsWJHHIGLLP6kPRos9in3l142gmkTohNcOXsJ4YOJiZV3Kbw7HMXn256JWTSJZisP7TkEkGZoiIkVEQiX1BQjHeSlahDCkAAAAAElFTkSuQmCC\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n  h = (h0+hL)/2;\r\n  xd = x;\r\nend","test_suite":"%%\r\nL = 10;                                       %  Length (m)    \r\nx = L/2;                                      %  Position where WTE is desired (m)\r\nh0 = 19.11;                                   %  Water table elevation at x = 0 (m)\r\nhL = 19.11;                                   %  Water table elevation at x = L (m)\r\nK = 5e-7;                                     %  Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8;                                  %  Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 2e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 8e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 50;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 60;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.5;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.1;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand;                                  %  Length (m)                                                   \r\nx = L/17;                                       %  Positions where WTE is desired (m)\r\nh0 = randi(100);                                %  Water table elevation at x = 0 (m)\r\nhL = h0;                                        %  Water table elevation at x = L (m)\r\nK = 5;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x  = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58314,"title":"Compute the normal depth of a channel","description":"For steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \r\nAs described in Cody Problem 57969, the normal depth, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) ):\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel, and  is the cross-sectional area of the flow. The coefficient  is 1 for SI units and 1.49 for U.S. customary units.\r\nWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure channelStruct with the following fields and possible values:\r\n\r\nThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 850.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 425.1px; transform-origin: 407px 425.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.017px 8px; transform-origin: 380.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57969\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 57969\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.85px 8px; transform-origin: 40.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.833px 8px; transform-origin: 197.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n) R^(2/3) S0^(1/2) A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow. The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.942px 8px; transform-origin: 155.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the following fields and possible values:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.85px; text-align: left; transform-origin: 384px 64.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 435px;height: 124px\" 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\" data-image-state=\"image-loaded\" width=\"435\" height=\"124\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.15px 8px; transform-origin: 376.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.85px; text-align: left; transform-origin: 384px 169.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 725px;height: 334px\" 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\" data-image-state=\"image-loaded\" width=\"725\" height=\"334\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yn = normalDepth(Q,n,S0,units,channelStruct)\r\n%  yn = normal depth\r\n%  Q = discharge (or flow)\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = 'SI' for metric, 'USCS' for U.S. Customary System\r\n%  channelStruct = structure with with fields 'type', 'size1', and (for trapezoidal) 'size2'\r\n\r\n   C = switch(units,[1 1.49]);\r\n   yn = solve(Q-(C/n)*R^(2/3)*sqrt(S0)*A,0);   ","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 0.61;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.04;                                   %  Manning coefficient \r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 1.12;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyn_correct = 3.58;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 0.72;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.034;                                  %  Manning coefficient (rock)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 1.16;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 2.80;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyn_correct = 3.33;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\nyn_correct = 4.52;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyn_correct = 7.28;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 9.76;                                   %  Discharge (cfs)\r\nn = 0.015;                                  %  Manning coefficient (concrete pipe)\r\nS0 = 1e-2;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyn_correct = 1.36;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T12:36:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-05-17T14:01:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T13:54:07.000Z","updated_at":"2023-05-18T12:36:47.000Z","published_at":"2023-05-17T14:01:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57969\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 57969\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n) R^(2/3) S0^(1/2) A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n} R^{2/3} S_0^{1/2} A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow. The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the following fields and possible values:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"124\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"435\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"725\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/docu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water surface profiles","description":"Problem statement\r\nWrite a function to classify the water surface profile starting at depth  in a channel with longitudinal slope , discharge , Manning roughness coefficient , and cross section specified by a structure channelStruct as in Cody Problem 58314. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \r\nBackground\r\nSections of channels are classifying by the relationship between the critical depth  and the normal depth . Slopes with  are steep—that is, normal flow is supercritical (fast and shallow), whereas slopes with  are mild—that is, normal flow is subcritical (slow and deep). \r\nThe type of water surface profile in gradually varied flow then depends on the water depth  relative to these two depths, as shown in the figure below. Profile S1 has ; profile S2 has ; and profile S3 has . Profile M1 has ; profile M2 has ; and profile M3 has .  \r\n\r\nFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390.35px; transform-origin: 407px 390.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53px; text-align: left; transform-origin: 384px 53px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.842px 8px; transform-origin: 211.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the water surface profile starting at depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.05px 8px; transform-origin: 112.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel with longitudinal slope \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.175px 8px; transform-origin: 36.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Manning roughness coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.183px 8px; transform-origin: 134.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cross section specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eunits\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.408px 8px; transform-origin: 252.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s^2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s^2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.808px 8px; transform-origin: 258.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.617px 8px; transform-origin: 211.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSections of channels are classifying by the relationship between the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58324\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecritical depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 8px; transform-origin: 41.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003c yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1167px 8px; transform-origin: 17.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003esteep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.275px 8px; transform-origin: 237.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003emild\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.55px 8px; transform-origin: 29.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is subcritical (slow and deep). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.292px 8px; transform-origin: 279.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.35px 8px; transform-origin: 99.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yc \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.6167px 8px; transform-origin: 48.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile S2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e y \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 8px; transform-origin: 62.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile S3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e yn \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Profile M1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yn \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7833px 8px; transform-origin: 49.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile M2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e y \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.4px 8px; transform-origin: 63.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile M3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 427.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213.85px; text-align: left; transform-origin: 384px 213.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 440px;height: 422px\" 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\" data-image-state=\"image-loaded\" width=\"440\" height=\"422\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 353.142px 8px; transform-origin: 353.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function profType = classifyGVF(y,Q,n,S0,units,channelStruct)\r\n%  profType = character string--one of S1, S2, S3, M1, M2, or M3\r\n%  y = water depth\r\n%  Q = discharge\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = either 'SI' or 'USCS' (i.e., lengths in m or ft)\r\n%  channelStruct = structure describing the cross section--see CP 58314\r\n\r\n  y = 'S1';\r\nend","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 1.2;                                    %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.7;                                    %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.34;                                   %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 4;                                      %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 2;                                      %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 1;                                      %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 1;                                      %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.75;                                   %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.6;                                    %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 4.7;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 3.5;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 2.0;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.3;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.2;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 3.7;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nfiletext = fileread('classifyGVF.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T21:56:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-23T01:31:32.000Z","updated_at":"2025-07-09T21:56:13.000Z","published_at":"2023-05-23T01:34:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the water surface profile starting at depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel with longitudinal slope \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, Manning roughness coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and cross section specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunits\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSections of channels are classifying by the relationship between the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58324\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026lt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026lt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esteep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emild\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is subcritical (slow and deep). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yc \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_c \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile S2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; y \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile S3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; yn \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y_n \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Profile M1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile M2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; y \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile M3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"422\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"440\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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9ovku8bQMbYkj29efuZzx1/PUt4YbaCOC2iSGGMbUjRdqqPQAcAVz48d+FO2vWWP+ulA8d+FMf8AIfsz9ZKAG3nh97r4h2OvTJbi3srNooiCfNaViRzxgqFLY5zkmr0GnXFnfaldWtwCLxvOEEiYxN5YTO7+7hF4xnOTk9BTHjvwn212y/77oHjvwp312y/7+UAW/CGjvoXhiz06aYz3Ealp5S27fIxLOc8EjLHGecYzW1XNf8J34U/6D9n/AN/KP+E78Kf9B+z/AO/lAHS0VzX/AAnfhT/oP2f/AH8pf+E78Kf9B+z/AO/lAHSUVzX/AAnfhT/oP2f/AH8o/wCE78Kf9B+z/wC/lAHS0Vzf/Cd+FP8AoP2f/fyk/wCE78Kf9B+z/wC/lAHS0VzX/Cd+FP8AoP2f/fyl/wCE78Kf9B+z/wC/lAHSUVzX/Cd+FP8AoP2f/fyj/hO/Cn/Qfs/+/lAHS0Vzf/Cd+FP+g/Z/9/KT/hO/Cn/Qfs/+/lAHS0VzX/Cd+FP+g/Z/9/KX/hO/Cn/Qfs/+/lAHSUVzX/Cd+FP+g/Z/9/KP+E78Kf8AQfsv+/lAGjrukxazaLbyXd3aFG3pNZzmKRDgjqOvBPBqloPhey0Sea5SW6vb+dfLkvL6UzSsg5C5PQdOBwcDPQVH/wAJ54U/6D1n/wB90f8ACd+E8f8AIdsv++6AF8OeE7Dw8tzFZ3N7JZzkhbO4n8yKEEkkIuOBzySSTjmo7DwjDpjQJa6vq6WMDh0shcAxrg52527yue2726Gn/wDCeeFM/wDIes/++6P+E88J99esz/wOgBbjwpA+qXF/p+p6hpst3g3As5lCSsBgMQysM4HUYrJ8b+HrnUYPDNpaR3Fzb2uoRNcSGc7xEowzl8g5x3BznnrWr/wnfhTtrtl/38o/4Tvwpz/xPbL/AL+UAO8OeFLPQ7u4vlur6/vrhQjXV/N5suwdEBwMDI/l7Yt65odprR083ck0f2C7S8jEbAZdckA5B45PTH1ql/wnfhT/AKD1kf8Atp0o/wCE78J4wddsv++6ALc+g2sniiDXg80d3DA1u2xsJLGcnDKQc4JyMEe+cCqH/CH28Us50/VtUsLe6lMstrbXIWMseTtypZc5P3SP0qT/AITvwnn/AJDtlnP9+j/hO/Cf/Qdsuf8AboAn1Pw7Bfazb6pFc3VlfRRGEzWrKDJETnY24HjPOeCDVO38D6PFoN7pTC5ltry7a8YyTbnjkOOVfGf4Rycnk5JqX/hO/Cf/AEHbL/vuj/hPPCf/AEHrL/vugBlv4Pto9G1HTrnVNVvhfxiOWe7ujJIq46LkYHU9s8/SrN14XsLmw0S0aSdIdGmhltwjLljEMIGJHIx1xiof+E68J9tdsvxko/4Tvwpn/kPWXt+8oA09Z09dW0a90+R9qXUDxFvTIxn9c9+lZOhW93H8PLaw1XTHM8NgbeW0DqxkCqV2ghsfMB69+cU//hO/CfP/ABPrLnnl6D478JnIOu2RB4/1lAGB4Z8K3elfCO+0ryMapfWs7yRbs/vHUqq88A4CA9s55710segWjR39lPaD7BcvHIYt3EjDBYsAe5A3f3uc5yah/wCE78KEf8h6y59ZKP8AhO/Cn/Qdsv8Av5QBuwQw21skFvCkcMY2rHEoUKOmAB0Fcn4O8Oy6ZrXibUpbb7I+oXreQhkV/wB2MkOMZxuZmO09MDir58d+FMf8h6ywOmJKP+E78Kd9esv+/lAGReaLq03w7OjQW5hvrgRW11OZFcsMqJZiCeQVBP8AfORwCK7iFVSMIuAqfKAOwFc7/wAJ14Tx/wAh2xx/10pf+E78Kf8AQfsh/wBtKAOlorm/+E78Kf8AQfs/+/lJ/wAJ34U/6D9n/wB/KAOlormv+E78Kf8AQfs/+/lL/wAJ34U/6D9n/wB/KAOkormv+E78Kf8AQfs/+/lH/Cd+FP8AoP2f/fygDpaK5v8A4Tvwp/0H7P8A7+U638aeGbq4igt9ctJJZGCook5Yk8AfWgDoqKQfj+NFAC1wvxl/5Jtff9dIv/QxXdVwvxl/5Jvff9dYv/QxQBsweEPDBgQnQNNJKgn/AEVD2+lP/wCEO8Mf9C/pv/gIn+FbNv8A8e0X+4P5VLQBg/8ACH+GP+hf03/wET/Cj/hD/DH/AEL+m/8AgIn+Fb1Nb3OBQBh/8Id4Y/6F/Tf/AAET/Cj/AIQ/wx/0L+m/+Aif4VtBs85yM9vWnr065oAwv+EP8Mf9C/pv/gIn+FH/AAh3hj/oX9N/8BE/wreooAwf+EP8Mf8AQv6b/wCAif4Uf8If4Y/6F/Tf/ARP8K23YKeTj0/z/npSr065xQBh/wDCHeGP+hf03/wET/Cj/hD/AAx/0L+m/wDgIn+Fb1FAGD/wh/hj/oX9N/8AARP8KP8AhDvDH/Qv6b/4CJ/hW9RQBg/8If4Y/wChf03/AMBE/wAKP+EP8Mf9C/pv/gIn+Fb1FAGD/wAId4Y/6F/Tf/ARP8KP+EP8Mf8AQv6b/wCAif4VvUUAYP8Awh/hj/oX9N/8BE/wo/4Q7wx/0L+m/wDgIn+Fb1FAGD/wh/hj/oX9N/8AARP8KP8AhD/DH/Qv6b/4CJ/hW9RQBg/8Id4Y/wChf03/AMBE/wAKP+EP8Mf9C/pv/gIn+Fb1FAGD/wAIf4Y/6F/Tf/ARP8KP+EO8Mf8AQv6b/wCAif4VvUUAYP8Awh/hj/oX9N/8BE/wo/4Q/wAMf9C/pv8A4CJ/hW9RQBg/8Id4Y/6F/Tf/AAET/Cj/AIQ/wx/0L+m/+Aif4VvUUAYP/CH+GP8AoX9N/wDARP8ACj/hDvDH/Qv6b/4CJ/hW9RQBg/8ACH+GP+hf03/wET/Cj/hD/DH/AEL+m/8AgIn+Fb1FAGD/AMId4Y/6F/Tf/ARP8KP+EP8ADH/Qv6b/AOAif4VvUUAYP/CH+GP+hf03/wABE/wrk/GnhvQrXWPC6W2j2UST6mscypbqokXaeDgcivSq4vx7/wAhzwef+osv/oJoA1v+EO8MDj/hH9N/8BU/wo/4Q/wx/wBC/pv/AICJ/hW7S0AYP/CHeGP+hf03/wABE/wo/wCEP8Mf9C/pv/gIn+Fb1FAGD/wh/hj/AKF/Tf8AwET/AAo/4Q7wx/0L+m/+Aif4VvUUAYP/AAh/hj/oX9N/8BE/wo/4Q/wx/wBC/pv/AICJ/hW9RQBg/wDCHeGP+hf03/wET/Cj/hD/AAx/0L+m/wDgIn+Fb1FAGD/wh/hj/oX9N/8AARP8KP8AhDvDH/Qv6b/4CJ/hW9RQBg/8If4Y/wChf03/AMBE/wAKP+EP8Mf9C/pv/gIn+Fb1FAGD/wAId4Y/6F/Tf/ARP8KP+EP8Mf8AQv6b/wCAif4VvUUAYP8Awh/hj/oX9N/8BE/wo/4Q7wx/0L+m/wDgIn+Fb1FAGD/wh/hj/oX9N/8AARP8KP8AhD/DH/Qv6b/4CJ/hW9RQBg/8Id4Y/wChf03/AMBE/wAKP+EP8Mf9C/pv/gIn+Fb1FAGD/wAIf4Y/6F/Tf/ARP8KP+EO8Mf8AQv6b/wCAif4VvUUAYP8Awh/hj/oX9N/8BE/wo/4Q/wAMf9C/pv8A4CJ/hW9RQBg/8Id4Y/6F/Tf/AAET/Cj/AIQ/wx/0L+m/+Aif4VvUUAYP/CH+GP8AoX9N/wDARP8ACj/hDvDH/Qv6b/4CJ/hW9RQBg/8ACH+GP+hf03/wET/Cj/hD/DH/AEL+m/8AgIn+Fb1FAGD/AMId4Y/6F/Tf/ARP8KP+EP8ADH/Qv6b/AOAif4VvUUAYP/CH+GP+hf03/wABE/wo/wCEO8Mf9C/pv/gIn+Fb1FAGD/wh/hj/AKF/Tf8AwET/AAri/iNoWk6TN4am0vTLS0lfV4VZoIVQkdcZAr1KvPviv/zK/wD2GYf60AegDA6Y/CigUUALXC/GX/km99/11i/9DFd1XC/GX/km99/11i/9DFAHa2//AB7Rf7g/lUtRW/8Ax7Rf7g/lUtABTW6gYG739MimTSeXzhyMjhFLHk46Ae/+cVXF/bhVLShMgDEilDzjH3v94fnQByFhpulah42n1KysraKPS5HQSRRqr3Vywy5yOcJkjnOWY/3RU+kazqU76Bdve+cNXYiez8tMWoETsdpHzcMoU7ie/A6Vv22jaEt2L+10vTvtRYuLiK3jD7j1O7GcnPXPerkFlZ293NcW9pBFcXGDNIkaq8mOm4jk496AON0HWNZa18K3N9frdDV42SaIRKgDCNnDA9c/LhhyDngLjBm8KaxrmqXFpd3EU/2O7iLTLJ9nCQtjgR7HL9QQQ4z/ALuCD1qWFnGlukdpAi2v+oVYwBFwV+X+7wSOOxNJDp9jBey3kNlbx3U2BJMkSh3x0ywGTQBzetWca+OPDd95kzytczR4aUlEX7PJjCA4GeuevbpgDrV6VQu9D0i9u1urzSrK4uVxiaW3R3GOnzEZrQoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACuI+ILbda8Hn11hB+YxXb1w3xE/5DPg7/sMx0AdwO/OeaWkpaACiiigCC6nS2t5J5N+yJdzbEZzj2VRkn6VQ0vXtP1a7uLezlnE9uqtJHNbSRMobO04dRwcVb1K5aysLi6S3kuHhiLrDCpZ5COdoA5JP9a4mwS7ufC12YYb8azdTQ3WotJaS2/mDcu+OMuBkBFKAA9vegDvc/MME5PY0Lu45/DP8686fRzPrmnS6bp1zaaGb2BltxHJBsZY7jzHMZAKKdyKeAG96fcaVqMWm31laW7R6bBrBb7O9s8ytbGAEqsYZS6eY33VPUEDOMEA9BJxwWI7ZBz/AJ/+vVHT9Z0/UtQvLKzulmuLJgLhEJIjJJwCcYz8pyM8Yqr4TtXs9ERGlZ0aRnjU2rW4iQ8hFjdmZVHYZ46cAVnaJNGPGurGGzu4LaS1to4Wexlij/dmUMAWUAYDLj1zxmgDrEPFOpqHIP1p1ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXn3xY/wCZX/7DMP8AWvQa8++LH/Mr/wDYZh/rQB6AKKBRQAtcL8Zf+Sb33/XWL/0MV3VcL8Zf+Sb33/XWL/0MUAdrb/8AHtF/uD+VS1Fb/wDHtF/uD+VS0AJS0UUAQS2ltKczW8T57sgJpn2ODoodPaORlA/I1apKAKptnziK7nQe21vUdWB/n2pGW8BPlzxkc4Dxcjr3B9cdqt0YGMY4oApvLeqGIgikTBIIlKsfvY424/u9+59ORrqZGbfZXG0Z+ZShzjd0G7P8I7fxL74u0hAPUUAUm1CBHYSedGFySzQuF43d8YxhG7/3f7wy5L21eQxpdxM6k8BwTkFgRjPqjj/gJ9DVumyRRyqVljV1IwQwyCMY/kT+dACbsEgk59/8/WnL0qq+n2YDBLdI92dxjGzruJOR7s3PqxNL9jALGOedCSTkSlu5/vZ9f0HpQBboqoIJlPyXjseeJFDDqfTFA+2DgGCXHUcp/wDFUAW6KqefcrwbR2P+xIp/mRQbwKB5kM6E8f6st3/2c+tAFuiqgvrXC5m27um/5CenrjuwH1IqRJkkAaKRHBG4FWyCMA5z6cigCeimr06n8adQAVDczRW8LzTyLFFGpZ3dtqgAEk5+gqasLxng+F7uFgcXJjtjjriSRY//AGagDXSVJER45AUlGY2DZByM8evf8qlHTHpXnwvk0jV/sEysyaDbXl4irwXgCp5ePosjRj/rma2m1XUtOnRdUktZklsZrv8AcIyeWY9mRnc25T5nXAxjvkYAOoornU1rUUisEutLH2y+3MkEFxu8tQgb52YDHPBxnGRjNO0zxJHqE1qrWN3brdF0ilm2bDImdycMTkbW5IAOOCc0AdBRWP8A27aMbhf9JikhhafZNbyRllHUjcozzjoe49aSTV2tPDdvqd5A7PJHDmGEgtvkKqFBYgfebqSKANmiszT9VivZ5bZoZ7a6jRWkguAFYK2cEFSQRkEZUnmtFOh5zzQA6imt9SM96buBbbnn0JoAkopqcrnOc06gArhviLn+2PBx/wCozEOtdzXE/EP/AJCXhDp/yG4e3saAO1paSloAKp3v9oeYpsTbMuPnSbcCfowzj8quUUAZ0E2oi1lkvbKEXCfcjtbgybxj1dUAOfw460y11KeaZYrjSb61Y8BpfLdfzRmx+OK06KAMy41zTLWR1vbxbbyzgtMpjX6hmGCPfOKuQ3ME8STQTRSRyrujdGBVh6gjrViqt7p1jqEax39nb3UanIWeJXA+gNAFg9xz68YpcetUINIsLW3lhs7ZbaKddji3JjwD6bcbTz1GP0qGPSnimRrfVL+NFYMY2lWQMOPlJcM3PTgg89elAGrS1l3UOrNOXstRtY4iQfKuLRpCOOgZZF+vQ9fSpJW1SOziMMFrcXO7EgadolxzyDsb24x680AaFFZ9rdXcryJc6dPAFXIcyIyt7DDZz+H41EmtWxnEMkN/E7HHzWUu3/voLt/WgDVoqhNq2mwXf2WbULWO4I3CF51DkZ64Jzjg1bR1dNyMHB6FT1oAkopB3paACiiigAooooAKKKKACio5G25JbAAz1wBWZY65Y38sSWrXBEwJile3kSOVR3VyADxyMHkcjIoA16KrPcRJJFFJMqyS8IpYAsRzgf5NShhhct97gc/jQBJRTVzjk9adQAUUUUAFFFFABRRRQAV598WP+ZX/AOwzD/WvQa8++LH/ADK//YZh/rQB6AKKBRQAtcL8Zf8Akm99/wBdYv8A0MV3VcL8Zf8Akm99/wBdYv8A0MUAdrb/APHtF/uD+VS1Fb/8e0X+4P5VLQAU1s5470N6c8+lNboR+OM0Ac0dQ1xPGEGmiewuLQq89xstnR4IukeXLlSzNwOOise1XLLxJa3l1axpFcrFeHFpcvH+7uPlLnbgkj5QT8wXOOM1W0rQdSsNWvrhtUtp4b25aadGsf3hBG1V378fKuB93t7mlsPDbWclhHJeiaz0vmxhEW1o/kKZdsnfwxwQBj0PGAB2k+K7LUzpxSG8gi1GMvbyzw7FcqCWTOfvYGfQgHBODU+n+Iba+uIooorhEuEL2lxIoEdyAOSnJPGejAEjkZAJFay8M/ZLLw7A135g0Xd8xhx5oMbR9M8fez36Uzw/4TtdBug1vHYeXEmyGRLBVuFGP45Qfm/IUATa/qmpaVc2DwpbS29xdx2xhO7zWDdWUjjK8krg8AnIxXQKTzn1rlrvw/qkviibWINXtl/diK3huLHzfsy4w20iReWPJOM4AHIFdUO9AC0UUUAJgelGB6ClooASloooAKKKKAEqu9pbM4Y28RYHIbyxnOR3/wCAr+VWaSgCklhDGylDMoGAoWZwBjb2zg/cXt03DoxyiWsyFdt9cgDHytsYH7vquf4T0P8AG3+zi9gegooApIl+Np+0ROuMMGiIYn5OchsdnPQ/eH905Fe84863gYDB+WU57diox/F37D14u4HpS0AZv7uS5M82lsJnj8pnaONmKcHaSGPGWPHsfbOemlaILG6tBavCl1bm3k3LICIiMFFLfdGG4A4zXQ0UAZhjsbnVLa9S5RpbaGSJEWRSuGKEkjrkBF57Amq0ehrDFpqRXTD+z43VWKZbcy7Q/XAIBPbHPatqSOOTiRFcejLmq5srVVCpCIhjAEWY8fiuKAOUfwxqMljerJPC1xNpUlhHI00rlnc4LsXzjOBx7dTW34it55rGzjtbWS4WK8gkkjjKqdsbhsjcQOqjvV9rTCny7m4iYjqHDY4P94Hp/T0pWhuQD5dyM9vMjDYPPpt74/AH1yADldbj1i7S+1OG1nsysEdrHH9+YxtKpmkCxtnhBwA27IPtVe6mlsNKnnj1g29tc3trGkke4C3wVMjDzM8FR06DnPU12Lm/XOxIJW5xlynZsdm77R+Z9jVvo2mktpJ7CWU2szTR+U6YzskUZBIzkHGP7zr2BIAObuZrm6Se0tdXuDAms28EE6lSzABHkjLY+YA7vfOQSQCKkuLrUbHVtb1O3e3dLRba3mWRTvmKpvIUggL/AK4dj1rfuzp09oba7sC9qDkRtaM6DbuO7hSP+WZIPuvdly24j0iSOaCcxRieZZZgWKF2Toc8dBD+SHtmgDYXvzmlqJXV8bXUnOOD3HGPzB/KpB3+tAC1xPxD/wCQl4R/7DcP8jXbVw/xIJW+8IEH/mO24/U0AdxRSCloAKKKKAGO23knHGef1pMnnuRjgnHNQak1oun3P9oiM2YiJmEuCuwD5sj0xXC6PFHo2hXviHT7G3sp9UltxHBHGALWBnVFLKp5bDF29zg8CgD0Ne/OeadXA3era1Z+ILXR4dVFxG11bq13LAhYh47hnRtu1ePLQjABGRnPdZte1i2tJrHzJbqeLVjYG5iSJZTGYfMVsMRHvyQuTxnoMkCgDuzjnPA700EcgsMD17VleHZtRm0tv7VR0nSRkRpDHvZBjazCNmUNj044zgZxWJ4dW01DxdPq+juqacIWtzIshIvpdwzIAT8wXbt39Tk8kAEgHZigKB0AoU5z9aWgBMD0FLRRQAySOOVSsqK6nswyKqvplibX7KtrGkGc7IxsAPrxirtFAGba6VbWM7S2815kjG2W9llUZ/2XYgfgKh/s/UY2fytcnfLZAuIInC57fKFP51r4HHHSloAoXZ1NWH2IWsg2/MkzMmTzzkBsD8KbFcagtg8t5YobhTxDaXG/ePUM4QevBx0681oUYGc45oAzbbUZJZUjn0++tWfnEiKwGATyUZgOnc+3pUc3iDSrVnW81CG1KHaxuW8pcj3bg/hmtbA9KKAIo5o5ER0kDq43IVYHcPXPepAR93dnHvzVW/0vTtRRV1GxtrpU5UTwq+36ZHFMh0y0toJILaMwRyDBETlSP93HT8KAIfEllNqXhvUrG1YLNcWkkSFiQNzKQM/nWXqeqy33hnULWwtNQtL02jIgltpIvLkYFVCvjDEE5yhPTrWpDpcsNyjw6rfmKM4MDtG6uPQllLfkwpbmHWPtZa0v7FYs58qazZmx6bhIPzwaAMa+WTTL1oba8vBBHp13cyu8zSN5mY9py+Rxh8ADAz0qja3CeH9J0aOaU3sVlpc94GkSPcgijjXajADHDkZ5JHUmutle/jgjMdvbzzHiUeaUA+nynP44qnZwwNHJHLoP2SKOBo1+WJldGOWRQjE84yRgZ469gCIXeqWenGfU7nTfMlKiMIHiVWOcr95y59MYz6CqkGtT6k+jmHERk1OaGby5NyOkaS5IPcFlWmwxaI4htVh1O1linV4XlhuR5b4ZVCvICu3a7Ltzt5IxzVi0ttFsL+C3j1BFuLQzSCCa4DSFpm3EsCdx6nGexoAsahc6m+vQWGmTW0KrbNPMZ4WlJ+ZVVRh1x/Fzz06UWOvQS6ak96yWs/nSW7xbi37yNir7eMsOCRxnHUDs2706/bW5dS069t4xPbJblZ7dpNu13YMpVwOd/QjsORWfL4cktrjTp7RpLk28UyTf6S0Du8rrIz5Xg5ZTlTxyMdAKAOh+32ZhimF3D5MiCRH80bWUkYYHPI5HI45FPN1F9qS1Mu2d42kWMnkquAT+BYCuPNutt4iFrFoRv4rHSkRIgyOY2laTIzIRwRHgn3GfZ+k6UmlaxYfbrQSXVto0UK3aQlw8i7t43gdgq9T3GO9AHXWF1Fe2q3FuzNG5IBYYPBwf1FWa4jwxaT6ZL4dtjPdmW50ySW7jkmdk3L5XRCcIQZCOAPfJrtl6fSgBa8++LH/Mr/8AYZh/rXoNeffFj/mV/wDsMw/1oA9AFFAooAWuF+Mv/JN77/rrF/6GK7quF+Mv/JN77/rrF/6GKAO1t/8Aj2i/3B/Kpait/wDj2i/3B/KpaAILq3huoWiuYlkjPZulVbbSrW0uPtEDXQbGNjXUrp/3wWI/StGkwPSgDKbTr5Znki1u72sciKaKJkHsMID+Zqe6GpDyzZyWrBV+dZkZdx9QwJx+Rq/RQBn28+pLaSveWMPnp9yK1uN+8fVlXB68Hj39GWupTTSpHPpF7aE9DL5bKOO5R2A/GtKloAyptc021eSO6uhb+WeWnRo047hmGCPcHFXIrqGeKKSCeN45huidXBDD1BHXrVmqt7YWN9GI7+zt7mMdFmiVx+RFAFjIz19+valHes+DSNPtLaaGztltY5U2MLYmPAwR8u3BU+4x+lRrpTwyo8Gp36IjZaMyrIrjIOCXDHH4g8n2oA1aKy7uDVmn32Oo20aEjMc9o0mMDsVkX+tPmfU47OIww2tzcdJd0zQqOOo+Vvbg+/0oA0aKo29zcyPIs9jNAEGQ+9HDewwc5/Cqya7bm4EMkF/E7HAD2M238WCbf1oA16KoT6tptvdi0uNQtobkoG8mSZVcg9CAT7GraOkiBkcOrdCp4P0NAElFIPxpaACiiigAoorF1O+vn1ePTNLaCOXyDPNNOjSLGucKAispYkg9xgKevSgDaorHj1RbSa2sNVuIzqUvIS3ich1L7Q2MHaORnJIXPXvUcXiGw+1WtrcXdslzdlzCkc4cMqsVHJwcnjjHXI5xQBuUVWtZ/PiZikihZGT5ivODjPyk8cfX1GanGR16+goAWlqvDcRTmUQyBzC2xwpztbAOD+dSBgckEkDnOaAH4HoKMDGMDFHrS0AJQVBBBAIPUetLRQBD9mt/NEggj8wchtgyDz3/AOBN+Z9al9aKWgArhfiX/wAf3g//ALDtv/Ou6rhviUD9t8IHHA163H6mgDuaKQdKWgAqpdXsdtcRxSJcHzAcNHA7qMepUED8at0UAZM2paTdRLbXk9v5d2CiwXQC+aMcjY3X6YpdN07Q7ZZH0qw0+JJ1w7W0KKJAOxKjnrWoQD1FU5NK06WaKWSwtmliBEbmFdyA8HBxxkGgAttM0+2t4IbewtoYoH8yFEhVRGxB+YADAPzMMj1PrT30+xkguIXs7dorli06GJSspwASwxycADn0FVxpVsjxNC1xF5SsFVLmRV+YHJK7sE+5Bx2pEsLmNo2j1W82orKY5FjYMTnBJ27sjI7445BoAvW1tBaW6QWsEcEMYwkcaBVUewHAqjZ+HtDsbpLmy0bT7a4TO2WG1RGXIwcEDI4JFCx6sjoPtlrIqqwZWt2VnbnBDByAOVz8p6E9wACfVl2iWyt3GxixhuTnd82FAZRwQF5z1J4GMkA0qWsxdRnwDPpt7CNjOxwj7cZ+XCMTnAB4z94d+hHq1q2C5mh3RmX9/BJHhQTnO4DHQ9T0wehFAGnRVG21OwuwjWt9bzh03qYplbcvqMHpwR+dWwD0z7d6AH0Ug+uaWgAooooAKKKKACiiigBKWimOQMlm2gDJJ7fjQA+kAAGAMCmg9OSQenPWnD86ACggHqKWigBKjmt4LhNk8Mcqf3XQMP1qWigCjJpdibJbRbdIbZGLqkBMQUkkkjaRjJJ/M0yz0yGwkZ4Zrsgg58+7lmAzyT87HFaFGB6UAY8em6jDxHrMkpOA32q1ickenyBPerV4+pqwawitJxtHyTTNFz/vBW4/Cr2BxwOOlFAFA3N9HYNLPp5kuQQDBaTBt30Z9g/PH9KfY3jXQYyWk9swxlZgo/VSQfzq5S0AIOlef/Fj/mV/+wzD/WvQK8/+LH/Mr/8AYZh/rQB6AKKBRQAtcL8Zf+Sb33/XWL/0MV3VcL8Zf+Sb33/XWL/0MUAdrb/8e0X+4P5VLUVv/wAe0X+4P5VLQAUUU0/eHOKAHUVxlvaNc+N5HsL3UPsmmljehr2Z0mmZciJULFcKrbiAOCVA74m07xBqVw2i3U0dt9i1psQRJu82D920gLNnD8Lg4C4z/FjkA62iuL0TxNqtzD4eutShtEg1eJhth3bo3EbOGyeCrKv3cZBI5bs/w14mvtXu7V2s5fsV5CZEP2SdPI4BG6VgEkByeVxjj72cgA7GiuP8W3c2n3Ntfedf2lvFPEZrwyr9mjQuAyNHncc4wGK8F87gOnXL35zz60AOpKWigApKWigApKWigBkkccqlZEV1PUMMiq0mm2T2n2QW0aQA5CRjYB7jbjFXKKAM6z0m3sZ3kt5LwkrjZJeSyqPorsQKhGnahGxaHXLiRS2Qs8MTqvPQbVU/mTWtQQD1FAFG6Opqc2P2WQBR8kxZOfqAcDp2PekSfUUsZJbqwR7lDxBaT794x2Zwgz14OOnXmr9GB6daAM611KSaVY59NvbRmzgzKpA78sjMO1Y+q3tnDq4v4NYt9Nukj+zzi+hPlSIGyOrJyCThgSOTwe3U4HpS0AYunWkn9sNqU1zBOZ7KGJfKGASrOzMBk8HeuOTwOprN0vTL+xuvDpntvOEGnSW1w8boRFK5iZmOSCQTG33cmt/UNL07UQg1GwtrsIcp58KybfpkcUkOl2dvbyQW0bQRS8ERMyY+hB4/CgDkY7X7MNM/tmxupbU20kghit3nCXEkm9i4jBwcHg9Ad3NOvb2T/hI7eG2E1vKl9FBta/mLtGACxMOCm0rkZz15znp0sOlvBOjx6nf+VGeYXZJFf6llLfkwp1xFq7XBa1v7RIs58qa1Zm+m5ZBj64NAFDw9N5ehahfygYa7u5TkdVWR1X/x1BWLpNkmj6P4Te1Bhv7jyY5kRiBcbo8yll/iIGWz1yPTg9TdreiySFLG1uvMUrPE0uxSp6gAqQc88HHXrVTR7O2tZpZ10E2EqJtWQeW+9eu1CrEgcdMAHigCppXig6jc2ZFuEtbwMYmDvvUAFlZgVAClVJznrgc9al03xP8AbILOVtNu4RfWpubbcYz5oADFRhjgkHIzjI64PFUhLBa2N3aad/accjQPFa2k9rKsKOw+VVcoABuwB8+APSpLOx0+1kisLjX0lurO0NtDA0satArKOSBgk4CgE9vck0AFv4qaaw8P3bwm3TU3zKjozMF8lpPkA5PO3nnjPHp0tjdQ3lnHcW0iywyDKup61k6fpVzBNpLzTwtHYWskGIVK7yfLCsBz0VGyM/xe1XNAs5LDR4befb5wLPIEyVDMxZsZ7ZY0AaVFFFABXEfEn/j58I/9h+2/ma7euI+JP/Hx4S/7D9t/M0AdsO/1paQdPxpaACiiigApKhupWhieRInmZELCKMjc/sMkDPQc469aydI8QJqV3fWslld2UliFM32kx4G4EgbkduwyR2yD3oA3aTaPQVnw6tp1xBFPb6jbSwyyGNJEmUq7AE7Qc8nAPHXg8VIuoWTWP20XsDWQTf8AaBKvlhR33ZxigC7SVBBcRXVslxbTJJDIu5HjYOrj2I6/hVC31mKXV/7NkgubecxNLGZkAWVFIDMpB4wWAwwB9qANekKg9QKRM7eetOoAguLa2uQVuYIpQVKkSIGyD1HPY1TOjabHGEgtVtlEZhUWrGHapPQbCMdTyOnNadFAGX/ZuyPZb6hfQ7Y/LUifzCPfMgbLe5zTmttRSMrDqIdvKKhp7cMS3ZjtKfiBj8K0cD0HpRtHoKAM1m1ZAQEtLgiPg+Y8O5+/ZsD8yP1pXvL6PIl0yViI9xaCZGXPHyjcVPHrgcVokA9RRgelAGb/AGrCpImhvI2WISODbSEAHHGVBBbJHAJPX3oGsaf5hjbULdJVQSNG8oDKpwAxUnIGWXqOrAd60qR1V1KuoZT1BGaAGJJG6h0kDKeQVbPHXtT0zt5zn3qjNo+lyySSPp9t5skYjaVYgHKAggbgM4G1SPoPSmHSoA7tFLdxM6rGdl1IFUDGNqk7R06gZ7d6ANOsHxmA3hq4hYZFzJDbYx/z0lVP/Zqsiyu18xo9WuDvCoglWNlQjHIwoJJwc5J5PGKSe31FhIJHsbpRsaGOS3ZdrqQck7mycjIIAxx1xQBylvqa6VqC2FyzlPD9reSuinJeJBGYjz1Plv1P8Sn3rdudcvNMcjVYIVb7BNejypGITytu9CSOfvjDex4GOZ7i1kae8nutGtbh5LcQM0c255YyfmQhlUAck4LGqFxpVitlfwXGn6oFmtfsjTNK1w/ltwVTLOR78enXHABd/t+eNbVZ9Iuxc3e9oLaJ43cqoU5Y7gq/eA649+RT9M8RWOpPbrALlGuVYxGaJkUlfvKCRgke2eh9DTbm501dUj1G7u2thZQyQsLhTEmJSjZy2P8Ann/Oq1lpm2DTILTVIJZ9MtnjZ1QFmlZFCuVB+UdTj3FAGidcsjb3csUpZrWFpmRwUJQZ5G4DIOD83Sn3GqR2ujRahdrIiuIgUj+c7nZVCjA5+ZgP8K5iXw/q9xY6ms/lmefS2tEP2x5t0j53t8wG0cDAAx9Og3fE6MbSyVbeWWJL2GSQQxl2VUO8HA5+8o6UAXNP1W1v3ljgkkE0J/eQyxNHIuehKMAcHselaC98ZxXF6zPqJe+1exgktIhFb2yyTqYyV87MkhGCVVUY4JHGWPaoo7+8g0seRq9qsdzqUEFvLHem88sEgupd1GSy9Aem7g9BQB3P86bkZ4bp174riru71eRJdPttU/fQ6xDbx3MsWWlUIkzKwQoDj5gcYyOOOamfUr+y1fV70wwz29s9tays0hQklVY7EwQP9dnrz07ZoA7FelLTU+7znPfNOoAK8++LH/Mr/wDYZh/rXoNeffFj/mV/+wzD/WgD0AUUCigBa4X4y/8AJN77/rrF/wChiu6rhfjL/wAk3vv+usX/AKGKAO0gJ+yxH/YH8qrT3FwFdYxtkIO1tu4KfdeM/nVq3/49ov8AcH8qeVUnnGfpQBzy3GvQghp7C6IHTyZIPzIZ/wCQp6atqqjNxpMcjD+G0vFcn6b1T9SK3DDGwwVBpjWsTE5WgDkbKHSLG7a9/sfWrSV5mmZFlllQu2SSY4pHU5Psas2l14VsZ2vRKlizfd+2GSJI89diS4CZzyFAzXQtZIemRTfsbDO2QgketAGfptroT2+mx6c0EsenH/Q/KnL+XlGXsxz8pYc+/tVux0ixsLiSe0jeIycFRM5jX/djyVXr2AqreaBZXY/0uxtLgf8ATaBXx+Y9hVdvD1soHlpNbgdPs11LCP8Axxh/KgDSudHsLu6iuLmDe8ZDBGZvLDDBDbc7SwwMHGRWiOnNc4dNvVcC31bUYgOqBopQfrvjY/rS7tcj2+VqVs6jqs1kSfzV1/lQB0dFc8NR1qNgDZ2Eqd2W7dG/75MZ/nUn9u3KybZdFvQv9+N4XH6Pu/8AHaAN2isVfEun7isq3sBxnM1lMqj/AIFt2/rUtv4g0a4k8uDV7GSTPKLOuR+GaANWio1dXwUIYY7HP9adn3zQA6ik9aWgAooooAKKKKACiiigBKKWigBKMDGMcelLRQAmB6CilooASo57eC5TZcQxzJ02yIGH61LRQBQk0qwazSzW1SO3RiyRQfugpJJJG3GDkn8SabZ6XDYyMbeW8wwxia6lmA+gdjjp9K0aSgDMs7K9tpVMmsXF3EOqTxRZ/NFWtNe/OaMDIOORS0AFcN8TM+d4Tx/0Hrb+tdzXDfE3/W+E/wDsPW/9aAO5pCcdSAKWo5VLKQpINAClh/e56f5/KlBIyOM5Pesu901byMRXUccyA7grgcH1HvVH+wljffDLfxEf3L6baP8AgJYr+lAGxqUtzFYXEmnwC5uliYxQlgu9gOBuPA5/rXI2Ok6lceFZNPm06eC+aaK6uZ7mWLF7IJFaQfu2bAIXaMgAAgdBWstpqUTZTWb5weiSxwuo/JAf1pyz69Fndc6dOB0VrZ4vwzvb+VAGLc+H7zUvEVlq82lrBAbu3aS1kaIsqxJOPMOCVPzSpgAk8fgC68O6kWvGt1khSPWjfQxwNFvljMAVtgcFAd5Y/MBk5OQSDW4mrauu7z9Kt3x0+zXu5j+Dov8AOpE8QbQTcaTqMAHHEaTf+imY/pQA7w1Ytp+lFWFysk0rTOtw0W8M3JGIhs/L3Pes6y0y+j8WDUIoJLW1EciXH2q5a4MxOGTyssTGoJbI4B4G3oRojxNpHl7prk2qAcm6heAD8XAq3aatpt8A1lf2t1nkeTOrfyNAF1e/1p1MDAkDPv1pfT3560AOopBS0AFFFFABRRRQAUUUUAJgelGB6ClooASjA9KWigBMD0FGB6ClooASqt3p9jeRvHeWVvPG+N6yxK4bGeoI+v51booAzbjSLGWOVfLkiEpBc287wnI/2kIIpJtPkZZfJ1K8tWdwxKMj7fYb1YAc4/CtOigDMmh1Mbza30AJkBUT2pfavOR8rqeeOT054ORijqun3l+9sXtLK4ht7kyxwvMUWRDHIh3jYwOA446E85GMHoKKAOfuLW3+wrY/8I/KtrDMBEloY4wvX51w6lffHPzemTRONLeO6ilgvIxNexSyuIJQHlQqVIbBG390oz0/OugwPSgADoBQBnrqunbpEGoW+6NzGw81QVYfw4z146VdVgeQ2R65yP8AP+FK8aOMOisPQjNRW9jZ2rzPa2kELztulaOMKXPq2Op+tAE69K8/+LH/ADK//YZh/rXoNeffFj/mV/8AsMw/1oA9AFFAooAWuF+Mv/JN77/rrF/6GK7quF+Mv/JN77/rrF/6GKAO1t/+PaL/AHB/Kpait/8Aj2i/3B/KpaACkpaKACiiigBMD0paKKAEIz1APsaaUUnkZ/Cn0UAQtCjZ+U0xrSM9qs0lAFQ2a5ypZfxqKfThKuJQsi+jruH5GtGigDm/+EZ05CTFp1tA7HloEER6Y6rg96QaO8IJt7zUoS3cXskmPwkLD9K6WkNAHOCHV4QfL1iaQjobq3jcD/vgJn86VbvXovvHTrpu3yvbg/jmSuhIU/e/WmmNG6qDQBhrrOpRoDcaPvb0tbpGz/388upB4iiVA11p+pQHqVW1acj6+VvrVNtGeduD9ajayjPA4Ge9AFD/AISbRUAa41KG23H5RckwH8nxWjb3lrdKGtrmKdT3jkDZ+mOtRfYyOkhBPvWfdeHbC6YPc6fZzv8A3pbdGI/HGaANwEd2/WlHSucOgQhlMP2qAryFgvJo1/FVbH6UfYL+NwYdZ1FFU/dbypAf++kz+tAHSUVzm/XYW+W/tZEH8Etkwb8WEmP/AB2nLqmsqwEmn2bp6x3jBvyaPH/j1AHQ0VhJr0/mYn0a/iUD7ymKQH8Fcn9KcniXTSSJDdQbepuLSaMD/gTKBQBt0VmWeu6ReuUs9UtLh84xFOrHI7YFaG4HlW4IyKAH0U3OM8j86UUALRRRQAUUUUAFcP8AEzG/woxxxr9t/wCzV3FcR8S/+ZV/7GC1/wDZqAO2paQY7UtABSGlpKAEKg/eGfrSGNDxgfhTsD0ooAiNvE38PT2qNrSMn/61WqKAKZtCOVcg47E8VTvdFtrvi8tba5U9RNCrj9RWxSUAc4fDlmiBLe3aBAOFtJpIAP8Av2VoOmXUaYttU1GEDv5qy5/GRXzXSUhGaAOdI1yMDyNUifB5NzY7yf8Avh1x+VL9v1yPA+y2E4H3j9okiP5bG/nXQFVPUD6U0xIeCox/KgDG/tu8SRRLol4wPV4JYnUfgXDY/ClTxHZLhZ4r6E92ksZdo/4EAV/WtM2kRH3Tn04prWa5+ViD9aAKkPiLRZJBEurWfmkcRtOqsf8AgJOa0Y5EkTdG4dSOqnP8qqSaeJFKvh1PVWGQfzrNfwzpvnGRdMtFmPJkjgVG/wC+lwaAOgzjPP50ornF0TyWJt7nUYW9FvpWA/BywoW21aHJj1q7c9vtEETge3yqv+NAHSUVzqz69HnM2n3J548mWDH1O5/6U5NX1VE3XGkRv7Wt4Hz/AN9hMfjQB0FFYY8QBULXOmanBgdBb+fj/v0WNOHibRlQNNfC1UjrdK0H/oYFAG1RVO01CzvAHtLuC4Vhx5UgYH8qtZ5PqOuKAHUU3HXr+dL60ALRRRQAUUUUAFFFFABRRRQAV598WP8AmV/+wzD/AFr0GvPvix/zK/8A2GYf60AegCigUUALXC/GX/km99/11i/9DFd1XC/GX/km99/11i/9DFAHa2//AB7Rf7g/lUtRW/8Ax7Rf7g/lUtABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABSUtFABRRRQAlLRRQAUlLRQAhAIwRkUEZ4wOaWigBhRcfdH4CmNDG2SVzU1FAFZrOI9jj60w2Sj7hKntirdLQBl3WlR3K7bhI5lI+7Iob+dZ48NafEMW9lBbk8j7P+5yT7pg10dFAHNro00MeLS/1SEdm+1NMR/393g/lS+VrUCEQ6w0jDvd2iyD8dmw10RxnOBmjAz0+lAHPC912JASun3Teu6S3B/STFTLq2ohgJdFmkYnBW1uI2x6n52T/AD+uyYo25Kj+VIIY1PCigB6ElcnrTqQdKWgAriPiX/zKv/YwWv8A7NXb1w3xQ4i8MHoRr1tjn/eoA7ilpKWgAooooAKKKKACiiigAooooAKKKKACiiigBMD0opaKAEopaKAEP/6uKQqp6gZPrS0UAMMaN/CPbjpTGt4yc7eampaAKpsoz7Ypv2Mg/K5BPXmrlFAGJeaBZXePtljaXHP/AC2gV/buKrHw7bKFWJJoAOgtbqSAe33GHFdHRQBzh029jwLfVtSh2n7oaOXPt86MfxzSk69GcRajbSAdVnsyW/NXX+VdEQPQYPWmlV7r+GKAMEajrcbAGysJkHVlu5EJ/wCAmM/zqT+3blHAn0S9CjrJHLC6/kJNx/Ktgwxt1WmG1i/un9KAM1fEmn7tkyX0Jx1lsplX/vrbt/WpbfxDo1zIY4NXsXkzgoJ1z+WasmzXI2nB9zUU+nrMpEwSRcdHG4frQBdVlcAqwYYzwf8A69Oz755rnv8AhGNNQs0Wn20Dt1eCMRMe3VcGkXRmh/49r3UYie4vZJAPwkLAflQB0Y9xS1kaZa3tvKDPqlzdR45SaOL8MFFWtVenXJoAdXn3xY/5lf8A7DMP9a9Brz74sf8AMr/9hmH+tAHoAooFFAC1wvxl/wCSb33/AF1i/wDQxXdVwvxl/wCSb33/AF1i/wDQxQB2tv8A8e0X+4P5VLUVv/x7Rf7g/lUtABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFACUtFFABRRRQAVw3xQ/1Phn0/t62/wDZq7muG+KH+o8Mn/qPW3P4PQB3FLRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAJS0UUAFFFFABSHNLSUAH64paKKACvPvix/wAyv/2GYf616DXn3xY/5lf/ALDMP9aAPQBRQKKAFrhfjL/yTe+/66xf+hiu6rhfjL/yTe+/66xf+higDtbf/j2i/wBwfyqWorf/AI9ov9wfyqWgCKaVYlaSRgiINzMxwABnJJ+lQQXtrcWYu7e5iltiu4SpIGQgdTuzjsao+MhnwXrvA506f/0W3auaAnXVY/D/AJEj2WriK8ZycokaoPPTB7MUQEd/OY9qAOvOqWI00ah9vtvsZUt9oMyiLGcfezj/APVVqSWOKJ5ZJFSNBuZnbAUAZyST04NeY6smmD4SXR1Jrbz1kvhaCYjJk8+T7gPVgOhAyOeldn4nniuvAetXFpLHPBLptwyyRMGVh5bYwQcGgDSsdUsNSRjp19b3ipwWgmWQD8VPuPzFXl7/AFrzSz07UIfAi63O0NnNZ+GngtRas3mEGJW3u5A2sCowo6HJ3HtpTI+nLYLq2uX7aXdxyT3V5Lc+WRLiIIgeML5a43EAEZOc5zyAddf39vYtCLiUq08gjiRUZ2duTgBQT0BJ44AJOMVXttasLp7JLe43m+jaW2wrYkRSMnp23L9c1x3kXN5e+EZdTuLxpRqN0I3MjRs8QWVo2IXHJVV7cgkHqRT/AA9cz3M/gqe4meed9Jui7SOWZz+56k8k0Aegjvz3pa4Dwdd6rdanC15ewi5EJ/tC1+3vK4fHy/uTGFiIIPQ4Iz944Nd6hJHPUGgB1FFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFcP8UMfZ/DJP/Qftf5PXcVw/xQ/49vDX/Yftf5PQB24paQUtABRRRQA1iPXke/5UwkjqxA4rnfF+n3F3cWVzCbW4jtFkaXT7uQpHODjDZGQrLtOCVP3j061l619n1bQ/Desx/alVr2waGGSVgEDSoSWGfmOCBls+oxnJAO4HB+bp9TSqc+5+tcZ8WCy/DPVtjbWxECQ2ODKnH4iqdxFqehaXqN/ptumixSyWcNtZNtkWM+cFd2RSVXcHxhTkgZyD0APQB71XubmCCaCKaZI3nbZErPgucE4UdzxXLm41aK+fTb3XRFJaWy3bXa20aC43SSfIVYkBVVUHy8nPUZ5paXJfal4x8PajdXEkUs2hvNLbLGqqGLRbl5BYAlgev8I98gHZ299aXEnl293DMxQSAJKGJUk4bAPQkEZ9qsrnBz615j4e1Se2tJtUWFJLiLwvBMsccYjQlXnIAVRgDI7D8q6jwxd6xcXUn21Z3s3iEqSz/ZwQ5P3V8lzlMdN3PB5NAHUUU1M7eTmnUAFFFFABRRRQAUUUhz+FAC0U3J5x+ppefQfnQAtFJz6D86Q5z2FADqKQenp70tABRRRQAUUUUAFFFFABRRRQAUUUUAFeffFj/mV/+wzD/WvQa8++LH/Mr/8AYZh/rQB6AKKBRQAtcL8Zf+Sb33/XWL/0MV3VcL8Zf+Sb33/XWL/0MUAdrb/8e0X+4P5U9jg9cfU0y3/49ov9wfypJ4I5wBIufTkjHGDz+NAEi9KXAznHPrVU2aBiVkmViO07HGc9icdz27Uv2eZSSt5Nx2ZVI/ln9aALNLVXy7vJ/fxEe8RB/Pd/SobqXUo7aVre3gnlVCVQSlNzY4HT+ooAv4GQcciivPv+Ek+IAGf+EKj/APA1P8ahPirx6uA3gnOSBxcg+g9ff/OCaAPR6MDGMcV5svjDxuWUP4Rt0LYGJL5YzkkDufUgfUgdanXxJ4/niBt/CNm24AhhqUTA8A9m9x+YoA9DpK87Gt/E3r/wiNkf+3xP/jlH9t/E3t4Rsv8AwMT/AOOUAei0V54ms/Exmw3hXTox/ea7XH6SVJJqHxMKERaHpCt6tcFv03CgDv6K86/tD4qf9AbQ/wDvtv8A45SrffFRmAOk6EnuXb/45QB6JRXn+PijKuM+H4PfMh/xpjaX8UJmO/xDpFqucgww7z9PmjoA9Dpp645rgD4T8a3IP2nx46D/AKY2Sj+RWgfDi5mH/Ex8Za9c/wB4JcFM/gScUAd5LNHCu+WRY19WYD+dUI9e0ee9js7fVbOa6fO2GO4VnOBk4UHJ4B/KuTg+EnhhWLXIvrx+7XFycn8VAre0fwX4b0O7S50zSo4Z487Jdzuy5GDgsSemR+NAHQjpjOcUtVr27trKHzryeO3h3BfMd9oBbgfjk1KGXftDAtjON3P1xQBJRSCloAKKKKACiiigAooooAKKKKACiiigArhfipxY+HDn/mO238nruq4X4q/8ePh3/sO238noA7qiimn8R7igB1FZ93fT29z5a6ZeTRYB86Hyyo9QQWDfkMc/kv8AaUIsftUi3EMYOCHhbcPwx096AJryxs74Ri9tILkROJIxNGH2MOjDPQ+9Q3+jaVqbo+paZZ3jRjCG4t0kKj0GQcU211jTbq5+z299C9xjd5IceYR67Tz+lXIZ45VLRSLIB1KsDQAyaztbi0FrPbQy2w24heMMnykEcHjggY+lPnt4LmLyriGOWPIbZIoYZBBBwfQgH6ingnocfTNVNR1Ow0uIS6lfQWcbcK08ioCfbPWgCS70+yvjEb2zguDC++PzolfY394ZHB96kNvCblbgwxmdVKLJtG4KSCQD1wSAcewrjL74o+FLVtkN5NfTA4EVrAzFj7E4B/Oqw8beJtRJGheCb5kI+WW/kEAPvggA9ujUAdxb2FnalTbWkEJWIQgxxhcIMkLx/CMnA6cmm2mnWNi8zWVnb25mbfL5MSoXJ6lsDk+9cT9l+JmpANNqGk6PGeogj81x/wB9ZH6ikPw4ur/P/CReLdXv1Y5Mcb+VGf8AgOWH8qAOwv8AW9K07/j/ANUs7XP3RNOqZP0JFc3ffE/whZ7gNVNw6/wQQu+fxxj9alsPhn4QsyGGkJM47zyvJ+hOP0ro9P0nTdNXGn6da2nb9xCqZ/IUAcUfiU9ygOkeE9dvNw+UmDYp98jdSt4j+IF4o+weDYbUkdbu8UgfUZU16FRQB540PxSuxkXmg2XqFDMR+atTl8NeP7hcXfjeOI9CILJOPxwtegUtAHnn/CBeIZUIuPH+qsc7gYVMX8npV+HN3JtM/jXX5CO4uWHH4k16FSUAefn4YW7El/E/iBmz1N2Of0pP+FX2n/Qza/8A+BY/+Jr0GloA89/4Vfaf9DNr/wD4Fj/4mrOnfDq2sNRt7xdf1qY28gfy5boMjY5wRt5FdzSUAA7/AFpaSloAKKKKACiiigAooooAKKKKACiiigArz74sf8yv/wBhmH+teg1598WP+ZX/AOwzD/WgD0AUUCigBa4X4y/8k3vv+usX/oYruq4X4y/8k3vv+usX/oYoA7W3/wCPaL/cH8qkwPSo7f8A49ov9wfyqWgBMDGMcelFLRQAUlLRQAUUUUAJgelQva20jAvBExBzlkBI5B/mqn/gI9KnooApDT7SMKsUCQqpBCx/IBjbjpx0QD6DHQ0kdkIgixXFyAoXh5i5IG0clsk5Cc9/mbuc1dooApxwXEeN19M+CMmRU5xtHYDrtP8A32fbBGt8pXfcQSdM4iKf3c/xHvv/ADUdubmB6dKMD0FAFRJL0D97BFjv5cxPpnqo7lvyFKLmYEeZZzKOMkMpA6Z75457dj9DaAA6CloAqC9j43xzp0+9E2BnHU9KFv7Q4AuoxwOC4Bq3SEAjBGRQAxZY5AdkisP9k0/PPp7VC9rbPzJBE2O5QcVGbGA8KJI+2I5XUdPY/wCeKALQwecfpS1Ua3JDeXdTR9eQ4ODz/eB9f0HakaK62nyrsBu3mR7gOuOAVPUjv2x70AY/i+0h1JtI0u6Tfb3t4UlXH8Kwyt/MLj3rnrDWb1Lm+mkKNqFnDZ6Y7yKdgnaeSNpCPTBR8Z5BHIruGF6obYIJSAdu/cmT82Aevqoz9T7VBPCZYrhJ9Mt5opiQ4UhjKAGALBlAJwEHJPXrgZIBkXetajpkmoWziK8mg+yGBthj3NPKY9jYJ5BGcjs3TjJlvNd1CwkngksIp5bSz+13BS5CqqbnGBuGSSEJHAGQQSODVn7FYQ27Rf2RNFGk4uCEXcXkQkq52kk/6tSM+qAjsI9Qt9Pul1QTNdRNf2v2WaQROCEXzgNuVxkfvDnnPyn+JcgE9lrguppYpLG6tnFuLiNZNrF0JIGArEhuPunnn8mXuuLHp9w9sjrdQzQxGK4RgQZHVV+oO7gg+3Yiq+pWVreS3n2bVUt5pbZLdVVx8gR5Cc8g/NtYHBHCHnjiNPDkoknJltyJr+C5ZY4zGqpFtIA5PO5etAGrq+qf2e1nHHbSXU93MYo4omVWJEbuT8xAxhPXuKfpmpRajHOY1lhmt38uaCYDfE2A2GwSOhByCRz161R1xLxdW0q7tdPmvorXzS6QvGGVmUKpw7KCMFs85HFYWp2GqsrahPF5CX18r3MHlNc+VCsJVFdIyC43hS204HHVQTQB3S9D9e5pHOMep4xnrXCtMmnLpFpe6zLBaTSXM29Q9sqoMKsZ3HKoGfjJHO0A9KLF7rULvw6JNTu0Hn3k0Eny5mhRikbNuXnKOvPcHPXmgDuo3Vt21gxU4bBzg0+uL0q81CC4S4EkBtdQ1i4gMXlESYBkUNu3Y/5ZDjb0rsl6HnJzQA6iiigArh/iku7T9AP93XLY/wDoQ/rXcVxPxQ/5Buhdf+Q3bf8As1AHa+tLRRQAlLRRQAVm3GgaNczCa40mxlmDbhI9shYH1yRnNaVFAGffaXa3skZma6Qxj5fs93LBx7hGGaztV8Kabq1glrfGefy33xSysJXjJ64EgII4/iB/OuhpKAMPSdF/sgotnLBHbAHdGtnHGTkeqbQDnB5FWJjraSSNbrYzoSSiuzwkDtk4bnp27+3OpRgelAGfNdX0VvCy2BnkK/vVhmX5DgcKX27ueOQO3Si21CaS2nluNNu7PyhkxyhGZv8Ad8tmzWhRQBlw63ZzziIC6idm2AXFpLCCfZmUCpjq+mrdyWp1C0+0xn54fOUOvTqM8cVepk0MU6bZokkX0dQR+tAArhlBRw4PQjHNPHIzgj61Um02xmt0t5LSExRnKIFACfTHSo7XTLW0eR7drlTINpD3MjKPorNgH3AzQBoUVkDS7mOdJI9b1ERqeYW8p1YehJjLfkRUt5DqzXG6wv7OKIYBjntGkP8A30JF/lQBpUVnSPqcdiNsVrcXYPzBpmhQj1B2sfwx+NLaXF/JL5d3YGEbf9YkyuoPpzg/+O0AaFFZD60sWTcWGoxKDj5bVpT+Ue41PeatY2JUX13HbhlDZlOwY56k4x+PpQBoVR1XUItMsZLuYO6pgBIxlndiFVQPVmIA7c8kU601Czv7f7RY3kFzCDtMkModM+mR9RVTX7Oe/wBPi+xlDPb3EVxEJWwjlHBwSASMjIzg4ODQBNaXlzIzLeWUloFCkO0qMrZ/h4Ocg+2PepZLyCIO8kmyGKPzXmbPlgZOfm6cYPfisfVbe61uyt7W80sxW5u4mnjeRGyifOc4OMZVR1zz0rM17Towmst9jZbXFlbqkcRAEaylnZQOwErE49DQB163ETTiESDzWTdtz27H0qf1ritSvrizu777FdyQ2yQWMCSSsXEPmzOJJMPnLBSpy2egzxWhPeG3SK0tdXurueUvKjIkUjCNCobJ+VcAsOvzc8UAdG7YYY6n/GlXpjuPWuU0K7l1jVtHv7jb5o0TzpFThczsh4z2/dHipT9vv9Z1s2mqz2gsGjiiTajRFvLEh3AqSR86g4IOBwaAOoormbbxXbPo8F9LDPt+xRXt15S7hbxupIJ5yejcLk4ByKv3Gv6Zb3j2s10fMj2CTCMVQN90swGFBIxkkDrQBr0Vgz+J9Mhl1SFblHuNMhaeaLeA20KScDrgeuOMita2m86FX6NgEqT0J7GgCxRSL07/AI0tABXn3xY/5lf/ALDMP9a9Brz74sf8yv8A9hmH+tAHoAooFFAC1wvxl/5Jvff9dYv/AEMV3VcL8Zf+Sb33/XWL/wBDFAHa2/8Ax7Rf7g/lUN/ex2MYlmjuHQnGIIJJiP8AgKAmprf/AI9ov9wfyqSgChZ6pa3at5RmQou5lnheEgepDgGktNY02+C/Y9StLjPQxTq4P5GtGoJrW2nIae3ikIIILoGwaAJBzxnPsKcDkdaoXmk2N5N51xbqZiAPNBKNj03DB70DTY0sPssNxdxJktv+0Ozj/gTE/lQBoUVm2lhcWlwZJNWvbqMjHlzrFtX3BVAfzNRGHXllZl1Cwkjzwj2Tq3/fQkx0/wBmgDXorPu5NUSRBZ2drPEUG9pLp423c8BQhGOnJIpVvLkWcks9hMkyNxDG6Ozj1XnH546dKAL9FZkGqpNcpA9nfQu+fv277RgZ5YZUd+pGeg54plx4h0a1d0u9TtrZlO0ieQRDPTgtigDWoqBJ4pVjeKWN0cZjYPkMPUetS5AzyePfpQA6ikH40tABRRRQAUlLRQAUUU0/jj2oAXA9BRgelZV3rUFvevaxwXV1PCgeVLeIv5anO0nOOTg/KMsfSr4mT7N5xJCFN2SCCB7jqKAJsDGMDHpS1Ck0cqCRHyjLkHOOKfE6yRK6MGRgGVgc5B70AK6JIpV0VgQQQwzkHqKrtp9mzlvskGWzuYIATndnn/gb/wDfR9ask/5xR169R7UAVHsYmGC0y5BHyTuBzkHjOP4j+npSvbOWLJdTr1xgK3XPqD6/y7Zq1RQBmS2Mj6lHeedEZoo3iQvGSAjEMwwGA5KJzj+H3p9xayXDRNcWlldNDJ5kZlXGxx0ZSQcEev61oEA9RS0AZTW6L9mDaaMW0hkiETKBG5BBbqvZ2/M1dhmZztaGWMj+8B/Q1YpKAAemelLSUtABXEfFHH9maGT0GtWx/wDQq7euG+K3/IH0X/sM2/8A7NQB3FLRSGgBaKpTQ3jTO8F7sBTaqPDuUN2bjBP0yKiC6tGufNtJyI8Y8t4tz/XLYX8z70AaVFZom1NcmSyhOEB/dXRJLZ6YZAMe9IL+4Vis2mXiBYvM3gxsCeMoArFs8+mPegDTorLGsWwdkkW6jKxCQl7WRVCnH8RXaW5HAOfal/tnTTKYv7RtlkCCQxtKAwQ4AbBwcZYD6nFAGnRUCSo6gpIGU4wwORz0qRSMYOQfQ9aAH0UgpaACiiigAooooATA54HPWloooAKSlooATA9OlLRRQBDPbW9xE0NxBFLG/LJIgYNj1Bqna6JpVhMstjp1tauOhgiWPOQf7uM9T+npWlSYGc45oAym0aHznmju9QjkkZnJW7kYZJzgKxKgewAFTz2t04iW31CWIxLg7kRhJ/vcZ/Iir2BjGOPSigDPhhvxBOk91bXJZcR4gKAf73zNn8AO9Zx025uJoIL/AELR5bSLKh1lO6NSOdqGLGDxkbu1dCQD1FGB6CgDB/5B2oF7Xw9eSYhjtxNBJCF8tNxUbWkBABdsYGfwxVG/0+0RZ7i5udaht9Tk3XNnBB5isdiodxjjZ0G1QOGA4rraTA9BQBx0ul6Xqmoyz2n9myL5KJLBfWHmGMKCoK7ipUYJBB9O3OaywXesvr9tZyWB0/U7kRNI0zB0jEUcbFAAQ+dpwcrg+vSu6qnNpWmzyK8+n2sjqwZWeBSQQcg5I65xQBgX+nX08Hia1+yu66m6+VKjLgo0UcRUgnII2sTxjkc9hc0nTUsfEuoNaWkdvZNa26oIUCI0gaUscDjOCnPsPSr95pNleSmSZZlkYAF4biSJvzRgaX+zwlgLS3vLuEKflmEplkH1aTdn8aAL69PbrS1WsLeW1t/LnvJrtsk+ZMqBvp8iqP0qzQAV598WP+ZX/wCwzD/WvQa8++LH/Mr/APYZh/rQB6AKKBRQAtcL8Zf+Sb33/XWL/wBDFd1XC/GX/km99/11i/8AQxQB2tv/AMe0X+4P5VLUVv8A8e0X+4P5VLQAUUUUAJgelFLWZqmmPfSrJHqd/Ysi4zauoB6nkMrA/lQBp0Vgf2RrUX/Hv4nuHPpdWkMn/oAQ0CDxVEf+P/SbkDs1pJCT+Ikb+VAG9RWALvxREQJdH06Ze5g1FwfyaMfzobXNTjP7/wAL6lj+9DNbyD8vMB/SgDforAPii1iz9q0/V4MDJLabM4H4oGH60v8Awl/h7dtl1aC3LcAXRMP/AKGBQBqX2nWGoIE1CytrpFHAniVwPXqKih0qxtraW3tLdbWKYFWFuTF7ZBUjafcc0Wus6ZegfY9Ss5s9PLnR8/kavA5GAQffNAGbBpMdvIjQXl+qoQSkl08ob2YuWP6ilntdQaZ5LbVHQNyI5YFdF9uNrH860PT+n8qoLq1t/bJ0uR2hutu6NJRt85cZJjJ+9jvjke1AD5BqS2qCCS1luR/rGkRkRvoATj8zSWcmqMZRf2drGqj92be6aQt9dyLj8zV5OnXNLQBkJql4ZvLn0S/iGceaGhZPr8shbH1FTXer2tncmG4W7BADb1tJXjx/vqpX8M1o0tAFH+1LD7GLp7yGOFjgSSuEGfTnH5VPHPFMN0EqSqRkFGB4/DqKlZVcYZQw9CM1Wj06whujcQ2VvHcMNplSEBiDjI3AZ7D8hQBiRPc6PrGrmSwurqK+uFuIZIArA4hRCjZI2kGPjPHzDnrVHULS5Sw8Uamn2tL53kSyIkddn7lI1ZVBx94Zzj0+tbz6Bp7MpQXMGCDi3vJoh+SsAfpU17p890ymHUryzKrj9x5ZB69Q6tQBy99Imnar4r1GO6kN1a6ehWF5NwYJHIwO09st9M5rU0+fUrjUrm0tp7e3t9NeK3eMwZaRjGjsRggKNrhRxgEE88CtCXT7j7BNF9piuLpxtE93aq42/wB1lTbuHB9OtVIdLuDqqXl/Fp1xKuN88UTRMdoODgls4J7njJxQBWtvERk1pbYPHPaTQzTRyRRyrhUx0YjEgOeq/wD60gvb60+HFrdtMZNQaxiO+Ulv3zhQM+vzNUP9htayS+VpErxrBLaw+TqLOUicjhUkwqcKpwucYxzgCruuQmTQbezWG7hwYnXy4BMYjG6OFYK3P3cHB6ZoAfHqN1p+tLYarcwTQT28k8NwqmIoIyu8OMkdHBDDA4PA6m1a61YXcM0iXBRYQrSecjREKcgNhgOCQcEcHHBrBmsY9a07Vbi9vLjz/sclsrzWMlskKMMsQjjLZ2qWOTwoAx3ydQudPk0y8S3m0651K8ktrMQpq8l1vVplBQhwdi4JPAPf8QDtn1rTP7OuL5L6KW2tS3nSQP5oQqPmGFyc47dan+2Rf2j9iO7zvKMpx025A/n/ACrkdW027v4NWv59IaKOdbSEWjiORyscrM8mFZhna7ADOfl7dKTV9OiUa5e29vcWkFno8a2cdtvgCsPNkOFXHIOztwaAO6Ge/WlqOAMsCBzlwo3fXFSUAFFFFABXDfFb/kD6Lz/zGbf/ANmrua4n4pgHRNLPddWtiPzNAHbUlHrS0AJgenSilooAQgHqKKztT1i00yaJLv7QBIDho7aSRRz3ZFIXr3qlH4v8OPgNrllG/XbNMIj+TEUAb9IyqylWAIPUEVVtr60u/wDj1vIJg33fLlDZ/KrPPqDjqMUAUZ9I0yZ3eXTrV3ZPLZvIXcV4wucdPlXj2HpTX0i1Jcg3ERZAn7q5kQADGMAHAPyjnqeR0Jzo9/f+VGB6UAZradJyINTvodyKqhXWTbjHILqxyQMEnPUnrzRJb6msbi31KMtsVV8+28zBGMk7WXOefTr6DFaWB6CigDNY6sqSMgs7hgo2KWeEFuN2SA+B1xxntzjNKbq/jWQvp/mFVBAgmDFzxkDftHHPfHH4Vo4HpRQBmtqEkXmNNY3iLGoOQgkyT2AQknH0/OlfVbSPzhJJJEIcbmmhkReemGZefwJxWjgYxjijA9KAKMeqWE0skcWoWzvDjzFWZdyk9MjPGferYJ7E8985olhimQrNGkins6giqb6NpjPO4063WSfBldIwjSY6bmHJxQBeXkHp17HNOrNbSrYtI6TXcbTMM7LuQDj0UtgfgOaJLG4zI0WqXi+YQQpWNhHjOcZXODn1PQYxQBpUVmSRaoDJ5N9BywKCW1Zto5znDrnqPTpRNLq0fmeTb2c/zjYGuHjJXnJ+43PTAHXPUYoAzfGTai0Wm2uj3TW95cXRCsOh2QyyAN/slkUH61Ba+Jlmubi93StYGzszDCqAs00rSDaP9r/VggkAc5xzWletP9qS5k0e4uJLZysHkzRkkOCC2GZRwAMg5+9xntjSaVZWMOoyQxanbvLqAuhILdrjZJkn5FQElM5JH+2RkdgDVHiSyjtZ5r9Z7Frd40lhnwzLvICEeWWBBJ4wT0I7HE0niHSoyi3F8ltI8ayCK5zC4ViVBKtggZBHI9Kx3itVaS41TVohcfbYWuJZYGt48RElEQOTxlWbO487jnHR2p2f9oxeJBaXVtLNf2i2CKsoJjIEmQ3ocyNx7UAdJbXltcNKLa5imMLbJAkgby29DjofrSXt5DY2wnuHZY/MSPI5O52CKP8AvphXOalY3FvdanPZaZDLbPY2trFEYw6Mokk3/uwQWCo4O3jIBANULCymHmW4tDDbza3A0Sx2jW6BI4klLiNidoLIQff3oA7K7vbSy8s3l3DbCRtiGaQKHbBOBnqcCrEbiRAykFT0IOa57W5YP+Et0SC6aFYxDczDzSACw8tAOeDxI3FY+m6jJayTxaKqmwvNRf7K0ab0WJYkMhjUEBgZA2MepIB6EA7ykrmLfWNYc2Fm9nF9vuPtJYyboVCROqiQL8xG4MpwT3xmm2viK9vL7SYobFNt0Lj7SBNlozC4jbaCBld568HHYUAdTgYxjiiuZ0XX2uJ/Ju0uM3F/cQW8xQCNtjvtQHr9yMtkjHBGe1dKnK59e/rQAtLRRQAV598WP+ZX/wCwzD/WvQa8++LH/Mr/APYZh/rQB6AKKBRQAtcL8Zf+Sb3v/XWL/wBDFd1XC/GX/km99/10i/8AQxQB0UtxdtZBbNo4p9q7WljMijp1UMpPH+1/9esb3XYhwmnXJPTdJJAD+OHrbgVWtosgcoP5U8xoTnAoAwxq+pRpmfRy7Y6W10rZ+m/ZT4/EHy/6RpeowkdvJE3/AKKZ61TbR9l/+vTTZxntx780AZyeJNKIBkmntx63NtLD/wChqKntte0a8Yra6rYztnBEdyjH6cH3qc2YydrEZqGfTEuBidElHTEihv50AXlYOOGUhvTmnKeM+vSudHhjS0YtFplpE7HO6GFYyffK4NC6Ckbl4ZtQibHa/nKj6KWK/pQB0YIPQ0tc39h1JH3R61qCrjhHWFx+se79aUtr6P8AJqNoy9xLYtuP4rIMflQB0VBAIIIyD2rnzqGuxkYstPnHc/apIyPw8tv505tcvo8eZolxKc9beeEj/wAfdT+lAF+70TSLz/j80uynH/TW3Rv5iqH/AAh/h4BvJ02O2BP/AC6u0HP/AAAinnxFBH81xY6lD6j7E8mPr5YannxNoypuuL9LZfW6VoP/AEMDFAEA8MW0XNrqWrwnjGNQkkHHoHLCuW13TdT1SKfSdK1DVdQaM48+9ghjhgkHRhJ5auWHYx5x+Nd1a6tp17/x56haXGe8Uyv/ACNXB04wQew/WgCh4ftdRstHht9Wv0v7qPhp1i2bvqMnJ9+M+laVNyBxwMe9KKAFooooAKKKKACkAA6ClooASloooATAxjAxRS0UAJSPGj4LorY6ZGcU6igDNn0LSJ7t7qTS7Rrp8Fp/KUOx92Az2p0umwPbRQRyXEKQ8p5M7ofxweR9av4GQcciigCjaWMtt5n+n3c4cYUTFTs9x8oP5k0ltDqEM5NzfRzw7eF8gqwPruDYx1/hq/RtHoKABRjjn8aWkpaACuL+KP8AyA9M/wCwtbf+hGu0rifimwTQdNY9tVtj/wCPGgDtC2ADnt+dMaWMOE8xQzdAW6+tEsZfgNg1mXmj29/GEvLaC6QdFniWQDP1oA1up+9nPvRnHf8APtXPf8I3YxJthtFt0HGLdmgwPYoRSLo8sI2wXmpwnsRdPMR/38LCgDo+vXFI6JIpWRFZT2YZFc6tvqsPCa1cynsLiCJsf98Kv86clxr8ZPmXWnzDsDaSRfr5jfyoAuXXhvQbpi1zounTOe72qE/niqx8I6EABDZyWoXp9luJYMf98MKRdU1pWPm6dZMvrDetu/JogP1p669cB9suhago/vo8Lr+Qkz+lADP+EaRARa61rNvjv9tMuP8Av4GpRpGsxk+R4muXA4AubSF//QVSpP8AhJLINslh1CInjL6fMQP+BBcfrS/8JNoe8I+sWkLseEmmWNj7YbmgCIW/iqI/LqGlXIA4D2ckRP4iRv5UguvFER/eaTps4z/yx1BwcfRov61sQ3Nvc8280cv+6wOKmz2/Hj/CgDBOt6rGT5/hfUCM/egnt5B+RkB/ShvE8CY+0abrEB99PlcfiUVhW/3+vvSZ6HjtQBw2q+MoNMujfx6lHPZFQJbC5Q28yYByYi4Xcf8AZbr2Iziur0bV7DW9PS90u5S4t5P4lPKnuCOxHHHuKoXehS6nczDVdTnmsjwljBmGPbjo5U7n+mcdOPXXsbS2sbVbeztoraFOkcSBVH4CgCeilooAKTAxjHFLRQAmBknHJopaKAEAA6DFLRRQAmB6dKgns7W5BW4toZVJBIeMMCe3UVYpKAM9tG07Mmy0jiMshkcwjyyznOSSuCTyevrSDS41DmK6vU3yeYc3TvzzwNxOF9hgVokA9RRgelAGU+lSyBhJfyzgy7wtxDEwUf3RhB698mo7vTbq8iEdxJZTRrLviHkPG0a4xwwfIbkjcMcHGPXZwPSjA9KAOUutF1C41ezuGVIYbWN4YmgvpFkVWZSWJKfNwuCDnPXPAqWKx+yXmmTW+n30K2QktVVJInVo3KMWbc248oDkfMecjmumwPSjA9BQBysEFvbrosTrej7DdyOP9CkbzHZHGSVBCj96TknH4itg6xpq7RJfwxM8vkoJX8stJ/dAbGTyOO9adFAENtPFcRb4JUlQHG5H3DPpmpqZHHHECI0VAxyQoxk+tPoAK8++LH/Mr/8AYZh/rXoNeffFj/mV/wDsMw/1oA9AFFAooAWuF+Mv/JN77/rrF/6GK7quF+Mv/JN77/rrF/6GKAO1t/8Aj2i/3B/Kpait/wDj2i/3B/KpaAEpaKKACiiigBKKWigBCO9IUU9QDTqKAIzDGeqj64pn2WI9VA+lTUEA9RQBWNlGemR+tMNmASVkIP1q7RQBj3Wi212u24tra4BHImhVvX1FVB4Z0+Hi3sYrdc8CDMGPxQiuiwOeOtLQBzaaLJAMW15qUYHQm8kk/wDRhahLXVofua3dy+gnhhYf+Oqv866PA5460EA9qAOcWXxBGcteWEyjops3jP5+Y38qeup60jfvNNspFHeO+YH8jGB+tbxRD1UflTTDG3VRQBjDXrhW2TaJfY6l0kgZR/5EDfpTj4ktFIEtvqERboTYTMufqqkD861GtYyDx+Aphso88ZGfSgCj/wAJNoatiXVrWHPQTyiM/wDj2K0Le7trlM21zHKp7o4YfmKiayP981n3PhvTrk7rjTrOdvWW3R/5igDcyM4DdOTmjPp+prnT4ctQoWGOWBe32W5lh/8AQGFA0m6RdtvqepQH1E4mP/kRXoA6MUtc4IdZhXbFq8kjAdbm2R/zCbKEudeiX95Jp1y2OAsUsGf1egDo6K59NW1ZP+PnSYDg4/0e93Z/B0X+dPTxBLz5+i6jCB3/AHMmf++JCf0oA3aKxE8S6eWKyfbIcdTPYTIP++ioFSReJNDlcRJrFj5p6Rm4UN+ROaANeioo5opF3RyK4z1Vs09c4Oc/jQA6iiigArh/ivj/AIRzT/8AsKW+PzNdxXEfFf8A5Fuw/wCwpb/zNAHb0UlLQAlB79OfWlpKAE2g9R+FIY1PYflTqKAIzbxnqKjNpGe1WKWgCobNP4cg9qY1kdpXflfQ85q9SUAYNz4b026YG40yynKngyW6MR+YqJvDttgCNJ4RnOLa7lhH/kNhXR0tAHN/2XdRrtt9U1KAeqzJIf8AyIHz/OlEesxriHVjIw6G5s1fn1+QpXRH8aQqpxkD2oA58XWvRjDyadcMR/ckgH83P+e9OTVtWQf6RpMJbuLe83f+hov9K3TGjZ4Bz1pht4zn5RQBkJr7k/6Ro2ow+/7qT/0B2P6U5fE2mkkSfa4SO89lPGv5sgFaRtIielMNmP4Tj8aAKsPiTQ5n8uPWbFpAfufaU3fkTmtKKRJV3ROHXP3lbIqpJYb1IkIdT1DDNZkvhfTHmEp0qxMo/j+zoG/MDNAHQA8j164zSiubbw/ErK0b3sTD7ojv50X/AL5DY9OxobTr+PHk6xqUIHRf3T5+u9GP40AdLRXOOuux4EOqQHHU3FlvOPqrr/Kl+3a9GOIdOuD/ALUskOf/AB16AOiorA/tjUY13TaO7nH3bW5jfn6uUFPXxAqpuuNM1KHHUeT53/oovQBuUVir4l0vG6WeW2X1ureSAfm6ip7XXdIu222urWcxztxHcI3P4GgDTopisGwVOR1pRjHJPTvxQA6ik9aWgAooooAKKKKACvPvix/zK/8A2GYf616DXn3xY/5lf/sMw/1oA9AFFAooAWuF+Mv/ACTe+/66xf8AoYruq4X4y/8AJN77/rrF/wChigDtbf8A49ov9wfyqWorf/j2i/3B/KpaACiiigAooooAKKKKACiiigAooooAKKKKACiiigApMD060tFABSEA9RS0UAJS0UUAFJgelLRQAlB54PIPtS0lACFVIGRwOxppjQgjA9DwKfS0AQm3jP8ADTDaRn+HFWaKAKhslPQkexNRyWAcbWIYHs43D9av0UAY1v4e02G8S6/s2zFwn3Zlt0Dj/gWM1sCiloAKKKKACuK+KmP+EYtT6ajb4OP9uu1ri/ip/wAiva84/wCJjb/+h0AdmO9LSetLQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAlGB6dKWigAooooAKKKKAEoxzwMfSlooAbsXjjH4dKa0SEH5R9KkpMD0oAhNvGT05phs4zjt9eatUUAUjZgHKsQfaoJ9LiuAVmSOVTxh0DD9a1KKAObHhfS4yTDptpExOd0UQiJ98rihdB8pi0E+oxseoW/mYD6BmI/SukpNq8cDjpxQBzYsdSjO5Nc1DAH3ZFgcf8AoAP60pbX43GNQsmQdRJZMG/MSY/SujxTfLU9h+VAGANR11WUfYtPnXPJF3JGf++fLb+daNheXNwWFzZPb4GQ4lV1b+v/AI6KuvCjn5lBpUQL0H15oAcOOKWkFLQAV598WP8AmV/+wzD/AFr0GvPvix/zK/8A2GYf60AegCigUUALXC/GX/km99/11i/9DFd1XC/GX/km99/11i/9DFAHa2//AB7Rf7g/lUtRW/8Ax7Rf7g/lUtABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFcV8VnEfhS3cjhb+3P/j9drXD/ABb/AORQiI/5/oP/AEKgDtxS0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAlLRRQAmB6daKWigAooooAK8++LH/Mr/8AYZh/rXoNeffFj/mV/wDsMw/1oA9AFFAooAWuF+Mv/JN77/rrF/6GK7quF+Mv/JN77/rrF/6GKAO1t/8Aj2i/3B/Kpait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the critical depth of a channel","description":"Problem statement\r\nWrite a function to compute the critical depth of a channel with discharge . The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . The geometry of the channel’s cross section will be specified by a structure channelStruct as in Cody Problem 58314.\r\nBackground\r\nSpecific energy for a flow is , where  is the water depth and  is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity  and differentiating with respect to depth gives\r\n\r\nThen using the definition of the top width  gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number :\r\n\r\nFlows with depths smaller than critical are supercritical—fast and shallow (), and flows with depths greater than critical are subcritical—deep and slow (). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the field, in the laboratory, and even in a kitchen sink. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.642px 8px; transform-origin: 226.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139.633px 8px; transform-origin: 139.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAAnCAYAAAC8L0AUAAAD60lEQVRoQ+2ZyY9NQRTGu/8AxLAjIoY1EVOEhQ3CEkHYEVOsjDFsJIhpSxALC4JYE0PCgogxYSEWhoWFlSH8A3y/Tp1OvXr16tat1++9ju6bfLnd9546db46p845dV9/3wi8+kcg575R0iPF6/+bp2fLcYuEccJX4WbMkcOF9EQZd17Y0Ea0XXDjX+q+wul5rftW4Z2vd7iQ3i6j9gszC0kf0Li53qKxiPeEecJ9YWUpaUJnjPBN+FJoXKthr/TiinCpUC/j1wd2Ye9bp2+S7j9Md5WnWbE9wgzhs7BTGC9Ew6bQ4OlON3OULuYqjb0bmf9vCWlChJBb6FYK5Xecoh1teMa374T+WS7ML1y01DBI46AG3SlPk1RuCLcEP8Gwf6YJ5zzPtFrpHB6fJHRUiGbaHAUtZJbo+ROhyTkp0hjBPglJh3MQng9cRNS10fZdw56rq6SFPNkcDzdFUIo0yYHsV0UaOfbjhAJjMYxx7ZSq2LQs5mNhmdBQrhBOkbYkkCKN0SS3X4Wkf2rcZiGWhArWcGAIyfe6cFx4GlMSkmYfLHaCp92dRHDbG/xMf38QaCYIfy5In/JkzmRYTB64lrFYfpeFWpufriuW7dmWeLll+cshTam67JGg2FOvWZxtAqHNddDdf6cm9PRgHJ7elVgg67KIhj/CFGGvwLaLVQ/kCeeQMAv8Qhio1e2GNyWNlq9ueBOC34U5zsgYb6seq/XSD3/GfhQOBeRa5Qeid7cwmDd6RRoD2HOpttOqx1LJhXuTsulHFG3sxUTEbNS7wZLYK9JkfPJEau9bFLGdNlloOmLs88kuAvD8lgRhXjXM0wvSuW2n7z2It8zGFYSbXveCNKG5TshpO61XMMMpn4eF0h59QE8vSNdpO+2cbaXRyLfV93ebdGnbSQa+Klh5hPxJ4Ujd0O6Fp+u0nWT48BDCM3RwvOWKZfbKdei2p60ZyTlRkb1pXML9638cKArzoSQ9SwYOfp2ILHdu22lDIf1IiJU1K2dh41Lp5VR4W8eETNM3Jk8zmdh6dGsAKDVcYStIWHKl2k7faPuAsUYP/ZOSdWREjX3cyCJrQjFPU0f3CZye7ILQQyH0JLIcSGyPIR9LMLaIdfageZPe/6zwXhgrHHPz8bWlqHSlDhyx1cPr4fkU4msF2sLnkffoyWk7w/nYu8yF/gXCVCfAKSt6ZIwZHHtW9WEwV0+VHF57IxSVmCrldd93g3Ru21nX9mL5bpAmsfErQ07bWUykzsBukKbtJBGVfsivwydLttOkS9vOLONLhTpNOvyNqdTOIR3XadIkMUpZqlMbUkI5yjpNOseGrsuMku76kvdown/8EOgoTEGFhgAAAABJRU5ErkJggg==\" alt=\"ft/s2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 8px; transform-origin: 17.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSpecific energy for a flow is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"E = y + V^2/2g\" style=\"width: 95px; height: 19.5px;\" width=\"95\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.7333px 8px; transform-origin: 72.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.908px 8px; transform-origin: 122.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"V = Q/A\" style=\"width: 61.5px; height: 18.5px;\" width=\"61.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and differentiating with respect to depth gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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\" alt=\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\" style=\"width: 257.5px; height: 36.5px;\" width=\"257.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.583px 8px; transform-origin: 127.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using the definition of the top width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = dA/dy\" style=\"width: 70px; height: 18.5px;\" width=\"70\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.6px 8px; transform-origin: 211.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr^2 = Q^2T/gA^3 = 1\" style=\"width: 95.5px; height: 36.5px;\" width=\"95.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.283px 8px; transform-origin: 230.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003e 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003c 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.533px 8px; transform-origin: 240.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=qsC9FUYpHqU\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efield\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/5etwhZ0d2GU?t=373\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003elaboratory\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8417px 8px; transform-origin: 47.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and even in a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/OoA1ASjMfag?t=24\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ekitchen sink\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yc = criticalDepth(Q,units,channelStruct)\r\n  g = 9.81*(units=='SI') + 32.2*(units=='USCS');\r\n  yc = solve(Q^2*T/(g*A^3)==1,y)\r\nend","test_suite":"%%\r\nQ = 12;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyc_correct = 0.33;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 10;                   %  Width (m)\r\nyc_correct = 0.74;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyc_correct = 1.26;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 2.34;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyc_correct = 2.84;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 14;                                     %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1;                    %  Side slope\r\nyc_correct = 1.65;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyc_correct = 3.72;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 8;                                      %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyc_correct = 1.1;                           %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T13:28:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-18T13:25:33.000Z","updated_at":"2023-05-18T13:28:20.000Z","published_at":"2023-05-18T13:28:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSpecific energy for a flow is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"E = y + V^2/2g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE = y + V^2/2g\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and differentiating with respect to depth gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dE}{dy} = 0 = 1 + (-2)\\\\frac{Q^2}{2gA^3}\\\\frac{dA}{dy} = 1-\\\\frac{Q^2}{gA^3}\\\\frac{dA}{dy}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using the definition of the top width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = dA/dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr^2 = Q^2T/gA^3 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr^2 = \\\\frac{Q^2T}{gA^3} = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026gt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=qsC9FUYpHqU\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efield\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/5etwhZ0d2GU?t=373\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elaboratory\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and even in a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/OoA1ASjMfag?t=24\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ekitchen sink\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57879,"title":"Route a hydrograph through a river section with the Muskingum method","description":"Problem statement \r\nWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph , the times  at which the hydrograph is reported, the routing parameters  and , and the desired time step . If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph , and a Boolean flag that says whether the time step is within the guidelines .\r\nBonus points to anyone who can solve this problem using the FILTER command. \r\nBackground\r\nHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow  and outflow  are connected to the storage  in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\r\n\r\nThis equation is written in discretized form as \r\n\r\nwhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow  and the current storage . \r\nIn the Muskingum method, the storage, inflow, and outflow are further related by \r\n\r\nwhere  is a time scale related to travel time in the river section and  is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\r\n\r\nwhere\r\n\r\n\r\n\r\nNotice that . With the assumption that the first value of the outflow equals the first value of the inflow, this equation for  can be used to compute the outflow hydrograph. The guideline for  above ensures that the coefficients , , and  are positive.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 882.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 441.35px; transform-origin: 407px 441.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.783px 8px; transform-origin: 383.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I(t)\" style=\"width: 26.5px; height: 18.5px;\" width=\"26.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2167px 8px; transform-origin: 34.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.875px 8px; transform-origin: 187.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at which the hydrograph is reported, the routing parameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the desired time step \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 284.583px 8px; transform-origin: 284.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O(t)\" style=\"width: 30px; height: 18.5px;\" width=\"30\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 234.942px 8px; transform-origin: 234.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2KX \u003c= dt \u003c 2K(1-X)\" style=\"width: 149px; height: 18.5px;\" width=\"149\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.925px 8px; transform-origin: 251.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.742px 8px; transform-origin: 368.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eO\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are connected to the storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.25px 8px; transform-origin: 97.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dS/dt = I - O\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.583px 8px; transform-origin: 141.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis equation is written in discretized form as \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\" style=\"width: 156.5px; height: 38px;\" width=\"156.5\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2333px 8px; transform-origin: 76.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the current storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S2\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.317px 8px; transform-origin: 249.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S = K[XI + (1-X)O]\" style=\"width: 143px; height: 18.5px;\" width=\"143\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.917px 8px; transform-origin: 185.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a time scale related to travel time in the river section and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.75px 8px; transform-origin: 156.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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alt=\"O2 = C0 I2 + C1 I1 + C2 O1\" style=\"width: 152px; height: 20px;\" width=\"152\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.0667px 8px; transform-origin: 19.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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V0zomSCVtlRSbyAfhtJDCEP7PXSWtcYrBU73mDJbLIEPjIW4gS8VVhCaB/xuSuEKMHiATcs2rGfQjiaOlsmsVD69dNIaB7ACFucsUZhZEIen2defBoSAQV/zYF1/TY5XwjkxZCAf1G7kEuhoaAVxHA364R/2BB0a/tEdZQitDb452rC9o+qNrUoQx1g8j50b1Et4T9Zijx67nGv7fuDW2CJBHI2AbSA5NI+sNXwD5V+6iIFXB+JBHB2gbeAVGOMeEmmJfLWBas1SRGhnMDbG04BAEEcDWJE0EAgE/odAEEf0hEAgEGhGIIijGbJ4IRAIBII4og8EAoFAMwJBHM2QxQuBQCDwBBqkyHR7zIhNAAAAAElFTkSuQmCC\" alt=\"C0 = (dt - 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1 = (dt + 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.8px; text-align: left; transform-origin: 384px 17.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35.5px;\" width=\"135\" height=\"35.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 66px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNotice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0+C1+C2 = 1\" style=\"width: 108px; height: 20px;\" width=\"108\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.742px 8px; transform-origin: 289.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAACeklEQVRYR+1XPSiFURi+d1f+JhYDg0EW+VmslMiGTEr5mUwUgwyiGCSDn2RUlMHIakKKUgwMFiai7DxPnaP3nnu+73vPjXvFvfX0Hd93znmf87x/Rzr1S3/pX8orVSQW6pmiYv9esQ4oMAw0AvVCjVuMV4GNUIXc+aEx1owN1oBW4BRYAfbMpiRLUiT6BLQD97kSDCG2BCOTxtAMnoseoxV4dw1UGXINeL7kQk5LjKr0JZCy9qcxWDB/LOM59VPEJKktGBlNMESXHpk5dGn1TxAbw6brwojGNZIYl1bm4s44VzJeHoASQ2wATxvocSK4xLTrMvaMIyZdyAzsUp5cqkxj30qsFhveiSNEZaFPuU28HBEfWjA+D42zKMXczeuwsbYm3WCuLbrvGNcolVa5Um5ON7YpT8y4fBZzQ9aqiH2IWZoSYafLGsZ3ISGQSIxt50zMCgneR6xj1eePNcwtL+wePcLV+xiP+1zti7Fc091dR4OymTPLy4AdoByYMAS9cegj5saJVjEZl64StvnLkiP7apbLo7JSusQ9uS8PZIPn1acbkFnM7xeAW6Bt9mfFcRQxaYin7/exMe9kQfWRilmasnbUikmZuXFUvyPhbYBti6emIW294762u2QV4biWxLg4BOzdagjjY3N8fpsHGPDuhTFOIfcbQ+bE55Gk+xiV4zWnF+Ct1f5I5go4EGRDCHEuQ2AW8N50k4iFGtPOt6EivZCxtlDEWFrmgMhrVCGIkcwl4Puf4Uu1fBMjqVcTt9J1TKImSTafxFhMB4Fd4E2wKsWY/TMjCfJFzL3VuknCMtQpX+aLmDZbCxZjaoJFxdRSmYlFxf6MYp8ieIIpmC0ETQAAAABJRU5ErkJggg==\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.717px 8px; transform-origin: 207.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.892px 8px; transform-origin: 111.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above ensures that the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACVklEQVRYR+1XyysFURx290pYWVEsKErJo5SyYS3lUdYeC1kR/wBF1h4r2YiFskTZkUcKJTYWSnaU2PN9Nb86c8yZc87MvbcrM/V1Z+6cx3e+33NyZSV25UqMT1lGyGaRTKF/oVAVTjkEDAAtQI1y6i/cnwG3QAXQA3QD7zZl5L2PD5HIPDAFlAMXwBZwDDwFC07idyV4z7+OgH5XMhznSqgdY7eBRoAqLAJLho049iQgtYnfiXwTUjcgmcHg5HH7bODlODAC7OaTUD0Wu1FM4LpBH+YcAg2KOZ142Uz2EJiJi/nKT0KjgLND23xoGQNmg2PRVK2+p3WSRBsUp9CnYqo93A8n2cB3jokQw3dNWYyhyxAu+GUixMhg8uNFc9X6+kJS5iZCr1hQMvAj7puSbuA7z0ToW1mIGbnLd+Gk410I+YZ7FBeWHdUn6QLTwJU+2IVQWoVI5hlg0ZW8tIB7lp8OnZSJ0DkGdgbs0/qQBIgeqUwrL7p/mgjJCURR1xJANXYUJfj8FixSrUWqHDpE1ERIZGabwYstxZzFUTnnFGBXIJ2A1LQolaUShHw0LlOzyl8qJNgHrRtISR+ktyWyaRyhkI/aiitJHQBqTqIC10Al0AaMAR/ADKBncxdCIbI2QiIIFegFGK6qs9/heR9g1xhV1QtGyOI+xtcSHHEmS6RQUkJ5deqkJPR5UoZ095CwD3Whrj6UhlxcYmRybFb9rxiEJKfdY2Mp0uJbv3r0YhCiuvxYYI5ilPIjsg5YjUgTzt9laUzmNbdYCjmTygjZpMoU+nMK/QB7534p343IYgAAAABJRU5ErkJggg==\" alt=\"C0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACaElEQVRYR+2XyytFURTG750rMTMyYEAhJVGiTCgzKY8ykIHHQDIg/AEUIyOPkUw8BsoQZUYeKUwYMDBhRmLO99XZt9U5Z9+997n3nm45u37d0zn78e219lp73XSqyFq6yPSkEkEmjyQW+hcWKscu+0EvqAcVYtc/eL4A96AUdIA28GGyjPrucoYoZB5MghJwBbbBKXjxJpzA76r3na9OQLetGPazFdSMvjugBtAKS2BZsxD7nnmitvA7nm9BcgGK6fN2nm2dTXwcA4NgP5+CqjDZnXCB7QJdGHMMqoU7rXSZXPbouYmTuZqfgoaA9YE2naEVdJj1tkVXNbru1sokvk7ZLPQtXHWA54EoC7iO0Qli+K6LyRi6DOGCN50gRgaTHxvdVel6FqIq1wl6w4QqAz/huTbqAq7jdIJ+xUTMyK2uE0ftbyPINdzDtDAgZkCL95GbnAI3/s42gnK1EANkGqyBTzAKmDjZAsGiE3QpdpPrGeJ5bAfqAqYQJk2KCly+OkEL6MwLVDXbK4AVwS5QGZqL8u7zX7B04R4IbFYniBO/ApYZbCwp5oTAsEeOOQesCnSVgBqn7jprC3Egb/lrsTLroA2NKFUHZStL5FCVeBf94k2XK0UdAZmTaIFbUAaawDD4Ajy4ttmcibcBBKpJkyC1K+6oEzBjq9Cl/x/AIWDVaHurs6R5BqHXka0gjacivWYE0+qh5yxuQawk2bRlbZyClNsZHFr3xiWIYkZAj08MUwXLnEytFYcglQRZ5DG3ycYI5R2X+SNQaEHyH0tYBLzjZZ20WqEFOYdhIshkssRCiYVMFjB9/wNeiG0p2l1pygAAAABJRU5ErkJggg==\" alt=\"C2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t2,O,dtOK] = Muskingum(t,I,K,X,dt)\r\n  y = x;\r\nend","test_suite":"%%  Chin example 5.38\r\nK = 40;         %  Time parameter (min)\r\nX = 0.2;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:600;   %  Time (min)\r\nI = [10 10 25 45 31.3 27.5 25 23.8 21.3 19.4 17.5 16.3 13.5 12.1 10 10 10 10 10 10 10];   %  Inflow (m3/s)\r\nt_correct = 0:dt:600;   %  Correct time (min)\r\nO_correct = [10 10.000 12.234 23.361 35.133 32.120 28.799 26.195 24.294 22.100 20.094 18.259 16.592 14.410 12.623 10.949 10.343 10.124 10.045 10.016 10.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Chin example 5.39\r\nK = 0.604;      %  Time parameter (h)\r\nX = 0.102;      %  Weighting parameter \r\ndt = 0.5;       %  Time step (h)\r\nt = 0:0.5:8;    %  Time (h)\r\nI = [42.4 46.3 51.8 56.2 57.6 65.1 80.3 90.6 103.2 81.5 78.3 65.8 59.6 56.3 50.8 53.1 50.7];   %  Inflow (m3/s)\r\nt_correct = 0:dt:8;   %  Correct time (min)\r\nO_correct = [42.400 43.327 46.510 50.893 54.574 58.266 66.191 77.540 88.774 92.714 84.880 77.757 68.741 62.190 57.167 53.698 52.750];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c5e-3))\r\n\r\n%%  Gupta example 12.7\r\nK = 3.07;       %  Time parameter (h)\r\nX = 0.39;       %  Weighting parameter \r\ndt = 12;        %  Time step (h)\r\nt = 12:12:120;  %  Time (h)\r\nI = [100 300 680 500 400 310 230 180 100 50];   %  Inflow (cfs)\r\nt_correct = 12:dt:120;   %  Correct time (h)\r\nO_correct = [100 222 573 626 373 359 235 197 123 58];  %  Outflow (cfs)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c0.6))\r\n\r\n%%  Homework problem 44a\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 6.424 15.930 23.650 20.977 19.035 17.713 16.841 15.948 14.981 13.746 13.187 12.289 9.465 6.074 5.258 5.062 5.015 5.004];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b1\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 35;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 7.350 18.103 22.845 19.774 17.965 16.839 15.781 14.614 13.436 12.489 9.898 6.283 5.214 5.036 5.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b2\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 10;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 4.223 5.122 7.129 10.048\t13.062 16.139 20.271 22.245 22.793 22.094 21.428 20.785 20.119 19.543 19.027 18.519 18.104 17.751 17.450 17.150 16.850 16.550 16.250 15.950 15.687 15.344 14.948 14.442 14.073 13.796 13.597 13.398 13.199 13.167 12.773 12.140 11.404 10.444 9.334 7.865 6.894 6.252 5.827 5.547 5.362 5.239 5.158 5.104 5.069 5.046 5.030 5.020 5.013 5.009];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44c\r\nK = 35;         %  Time parameter (min)\r\nX = 0.6;        %  Weighting parameter \r\ndt = 45;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 5.711 26.085 18.977 17.719 16.407 15.024 12.997 12.606 8.234 4.247 5.175 4.959];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-02T23:02:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T16:23:33.000Z","updated_at":"2024-11-11T12:36:59.000Z","published_at":"2023-04-02T16:31:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at which the hydrograph is reported, the routing parameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the desired time step \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2KX \u0026lt;= dt \u0026lt; 2K(1-X)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2KX \\\\le \\\\Delta t \\\\le 2K(1-X)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are connected to the storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dS/dt = I - O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dS}{dt} = I-O\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis equation is written in discretized form as \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{S_2 – S_1}{\\\\Delta t} = \\\\frac{I_1+I_2}{2} - \\\\frac{O_1+O_2}{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the current storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = K[XI + (1-X)O]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = K[XI+(1-X)O]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a time scale related to travel time in the river section and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2 = C0 I2 + C1 I1 + C2 O1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2 = C_0 I_2 + C_1 I_1 + C_2 O_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0 = (dt - 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0 = \\\\frac{\\\\Delta t – 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1 = (dt + 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1 = \\\\frac{\\\\Delta t + 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2 = \\\\frac{2K(1-X)-\\\\Delta t}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNotice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0+C1+C2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0+C_1+C_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above ensures that the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56205,"title":"Measure the hydraulic conductivity with a falling-head permeameter","description":"A falling-head permeameter is another device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . Unlike the constant-head permeameter, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area ) that falls. In other words, the head difference , or the difference between the water levels in the tube and the outlet, decreases in time. \r\nThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\r\n\r\nDarcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nDerive and solve an ordinary differential equation for the head difference . Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the previous problem. Use  and .\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 902px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 451px; transform-origin: 407px 451px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82px 8px; transform-origin: 82px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_c\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37px 8px; transform-origin: 37px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Unlike the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003econstant-head permeameter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_t\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147px 8px; transform-origin: 147px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) that falls. In other words, the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145px 8px; transform-origin: 145px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116px 8px; transform-origin: 116px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDerive and solve an ordinary differential equation for the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eprevious problem\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 981 cm/s^2\" style=\"width: 90.5px; height: 19.5px;\" width=\"90.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-2} cm^2/s\" style=\"width: 94px; height: 19.5px;\" width=\"94\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 359px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.5px; text-align: left; transform-origin: 384px 179.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 401px;height: 359px\" 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alt=\"falling-head permeameter\" data-image-state=\"image-loaded\" width=\"401\" height=\"359\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n)\r\n  K = f(delta,t,L,Dc,Dt);\r\n  isDLvalid = (Re \u003c 1);\r\nend","test_suite":"%%\r\nDc = 11.28;                                 %  Diameter of cylinder holding sample (cm)\r\nDt = 2.26;                                  %  Diameter of tube (cm)\r\nL  = 10;                                    %  Sample length (cm)\r\nn  = 0.15;                                  %  Porosity\r\nt  = [0 1 2 5 10 15 20 25]*86400;           %  Time (sec)\r\ndelta = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];    %  Head difference (cm)\r\nK_correct = 3.08e-7;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                %  Diameter of cylinder holding sample (cm)\r\nDt = 2;                                                %  Diameter of tube (cm)\r\nL  = 15;                                               %  Sample length (cm)\r\nn  = 0.25;                                             %  Porosity\r\nt  = 0:60:420;                                         %  Time (sec)\r\ndelta = [25 20.63 17.03 14.05 11.60 9.57 7.9 6.52];    %  Head difference (cm)\r\nK_correct = 3e-3;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 7.5;                                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.75;                                             %  Diameter of tube (cm)\r\nL  = 7.6;                                              %  Sample length (cm)\r\nn  = 0.2;                                              %  Porosity\r\nt  = [0 1.25 2.36 3.74 5.40 7.20 9.28 12.08];          %  Time (sec)\r\ndelta = 88.9:-10:18.9;                                 %  Head difference (cm)\r\nK_correct = 5.25e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                                                               %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                                                               %  Diameter of tube (cm)\r\nL  = 7.5;                                                               %  Sample length (cm)\r\nn  = 0.2;                                                               %  Porosity\r\nt  = [0 1.06 2.11 3.62 4.88 6.53 8.39 10.67 13.52 17.37];               %  Time (sec)\r\ndelta = [56.02 50.36 44.7 39.05 33.39 27.73 22.07 16.41 10.75 5.09];    %  Head difference (cm)\r\nK_correct = 3.89e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                              %  Diameter of tube (cm)\r\nL  = 7.5;                              %  Sample length (cm)\r\nn  = 0.2;                              %  Porosity\r\nt  = [0 2.28 5.13 8.98];               %  Time (sec)\r\ndelta = [22.07 16.41 10.75 5.09];      %  Head difference (cm)\r\nK_correct = 4.79e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                      %  Diameter of cylinder holding sample (cm)\r\nDt = 2.5;                                                    %  Diameter of tube (cm)\r\nL  = 15;                                                     %  Sample length (cm)\r\nn  = 0.18;                                                   %  Porosity\r\nt  = 0:7200:50400;                                           %  Time (sec)\r\ndelta = [50 43.15 37.23 32.13 27.72 23.92 20.64 17.81];      %  Head difference (cm)\r\nK_correct = 2.99e-5;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-01T17:35:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-01T17:35:38.000Z","updated_at":"2026-02-10T14:28:46.000Z","published_at":"2022-10-01T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Unlike the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econstant-head permeameter\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) that falls. In other words, the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDerive and solve an ordinary differential equation for the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 981 cm/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 981\\\\rm\\\\,cm/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-2} cm^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 10^{-2}\\\\rm\\\\,cm^2/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"401\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"falling-head permeameter\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57605,"title":"Determine flows of given probability using empirical frequency analysis","description":"Write a function that takes as input  observations of peak streamflow  and exceedance probabilities  expressed as percentages and returns the flows  corresponding to the probabilities. \r\nUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank  (e.g., the highest flow has ). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with . Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return NaN for any probabilities that fall outside the range. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 158px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 79px; transform-origin: 407px 79px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.158px 8px; transform-origin: 109.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e observations of peak streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Qo\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5417px 8px; transform-origin: 94.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and exceedance probabilities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p1\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5083px 8px; transform-origin: 45.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e expressed as percentages and returns the flows \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q1\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.925px 8px; transform-origin: 108.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the probabilities. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 345.033px 8px; transform-origin: 345.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.4917px 8px; transform-origin: 31.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (e.g., the highest flow has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m = 1\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.142px 8px; transform-origin: 311.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 100m/(n+1)\" style=\"width: 115px; height: 18.5px;\" width=\"115\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.2833px 8px; transform-origin: 87.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for any probabilities that fall outside the range. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q1 = floodFreq1(Qo,p1)\r\n%  Qo = observed flows\r\n%  p1 = exceedance probabilities at which the flows are to be reported\r\n%  Q1 = flows corresponding to the probabilities p1\r\n\r\n  Q1 = Qo*log(normcdf(p1));\r\nend","test_suite":"%%  Small sample from lognormal distribution\r\nQo = [27 360 71 8798 58 122 468 638 19 114 3542 781 356 635 6093 748 8305 8 6253 875];\r\np1 = [5 10 20 50];\r\nQ1_correct = [8773 8100 5583 552];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Larger sample from lognormal distribution\r\nrng(1)\r\nQo = 10.^(randn(1,500)+1.7);\r\np1 = [0.2 1 2 4 5 10 20 50];\r\nQ1_correct = [106602 21248 6176 2975 2432 1062 326 58];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Yellowstone River at Livingston, MT\r\n%  Flows from here down are in cubic feet per second\r\nQo = [18300 15400 13100 10600 18500 30600 13500 20400 15800 20600 26800 17500 21400 20000 22800 21200 20400 14900 25800 21900 17100 24200 15700 15600 20400 20200 20200 27900 16000 24900 24600 21200 24400 29200 26700 21100 36300 25700 21400 14200 26000 20100 15000 23800 27900 18600 17900 15200 24000 7450 16200 16200 17200 23000 13800 24000 16900 23700 37100 38000 18800 23400 19300 14800 25900 27200 13300 17900 22600 15200 26300 23500 28100 40600 23500 17900 32700 15600 12800 26300 33600 22800 30600 18500];\r\np1 = [9.58 13.53 50];\r\nQ1_correct = [30000 27900 20850];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Mullica River near Batsto, NJ\r\nQo = [1190 407 815 360 382 350 384 245 287 1170 645 990 1050 435 430 630 489 1380 499 240 857 1840 380 204 420 705 946 143 419 666 269 579 490 565 401 488 578 149 401 473 747 364 335 343 201 509 452 420 449 1320 258 312 867 1860 303 332 537 387 222 342 517 676 249 285];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 1854 1564 1365 1110 747 433];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Charles River near Waltham, MA\r\nQo = [690 1520 1020 1370 2540 1020 2180 1020 1600 555 1470 1180 1000 1240 1360 692 1730 575 869 933 1250 1360 1550 2490 1990 957 1940 1460 1510 1850 1540 1340 890 904 637 1250 2670 1800 1790 1110 1670 1630 1090 895 4150 1610 1740 3480 1140 1220 2960 1970 2410 811 1110 2710 837 779 1240 1030 637 2180 1430 757 1430 2990 2180 1080 1090 2190 721 1170 1510 1510 1590 1250 1390 1390 4270 1770 1080 1570 1460 1640 634 1150 1250 1180 806 1520];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 4172 3166 2974 2482 1840 1367];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Merced River at Happy Isles Bridge near Yosemite, CA\r\nQo = [2500 3320 3180 3800 2720 2720 3240 2620 1240 2620 2240 2820 2050 2520 1870 1350 2570 2520 935 2820 2380 3020 8400 1210 2620 3220 2800 3480 1980 3040 3690 2450 3080 2480 2520 9260 3580 2180 2500 2800 9860 2910 3640 1520 1710 1080 2230 5200 1720 9240 1640 4640 1480 4980 2330 2170 2690 4240 3260 4650 1440 1800 4190 3500 4040 2100 4880 5450 2860 1600 4040 1750 1640 1910 1090 2310 1490 3140 1870 5220 5900 10100 4150 2810 2920 2330 2290 4550 1830 5680 4350 1180 2760 2750 4470 4610 2250 1750 1190 882 2490 5210 8060 4240 2160 1410];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [10083 9776 9005 8281 5213 4247 2700];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct));\r\n\r\n%%  Quashnet River near Waquoit, MA\r\nQo = [41 36 33 41 40 35 28 34 39 42 32 27 39 26 33 40 36 61 83 32 39.2 52 44 42 58 30 32 30.1 50.1 48.4 53.2 40.8];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 76.0 68.7 56.6 49.1 39.1];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end),1),Q1_correct(3:end)));\r\n\r\n%%  Illinois River at Henry, IL\r\nQo = [104000 108000 53700 106000 95200 46300 45100 45000 40200 53700 30900 67000 47000 58900 78000 117000 88900 55000 40400 71800 88500 38400 52100 84600 32400 90300 128000 92400 58300 64000 49000 161000 65400 98500 107000 93100 111000 108000 120000 64200 51600];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 138560 127200 115800 106600 67000];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end)),Q1_correct(3:end)));\r\n\r\n%%  South Skunk River near Ames, IA\r\nQo = [1990 600 3490 2580 3000 2890 3230 2320 3050 2530 4500 8060 4010 2270 6550 2620 3000 3820 5320 1630 980 8630 1340 376 3540 3150 1720 6210 1990 4300 1820 2170 5260 2900 2790 4890 4380 1330 3660 3030 3340 5780 5230 3580 5300 2240 4980 2720 1880 3490 5150 5020 1980 4040 3040 565 370 6600 4700 2350 11200 2340 1640 14000 2080 4760 3630 906 1990 1070 2030 2520 2310 3330 6510 11000 4560 14800 1620 730 6740 9250 11200 6420 1890 4380 6740 3260 455 4210];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 14144 11181 11060 7092 5292 3190];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%\r\nfiletext = fileread('floodFreq1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-21T19:33:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-01-21T19:33:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-21T19:29:29.000Z","updated_at":"2023-01-21T19:33:03.000Z","published_at":"2023-01-21T19:29:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e observations of peak streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Qo\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and exceedance probabilities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e expressed as percentages and returns the flows \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the probabilities. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (e.g., the highest flow has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 100m/(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 100 m /(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for any probabilities that fall outside the range. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49743,"title":"Determine aquifer properties: unsteady pump test in a confined aquifer","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 714.15px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 357.075px; transform-origin: 407px 357.075px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 7.79167px; transform-origin: 382.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.633px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.3167px; text-align: left; transform-origin: 384px 53.3167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.567px 7.79167px; transform-origin: 297.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose a confined aquifer initially has no flow. In that case, the piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the level to which water would rise in an observation well, would be a uniform value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.467px 7.79167px; transform-origin: 124.467px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. A well turned on and pumped at a rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q0\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.9083px 7.79167px; transform-origin: 38.9083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will create a cone of depression; that is, it will draw down the piezometric head to a level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h(r)\" style=\"width: 29px; height: 18.5px;\" width=\"29\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 7.79167px; transform-origin: 24.8917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.2917px 7.79167px; transform-origin: 95.2917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radial distance from the well. Applying conservation of mass and Darcy’s law to this situation leads to a diffusion equation whose solution for the drawdown \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s = h0 - h\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 7.79167px; transform-origin: 79.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as a function of distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 7.79167px; transform-origin: 7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s = (Q0/(4 pi T)) integral(exp(-x)/x, u, infinity)\" style=\"width: 117px; height: 44px;\" width=\"117\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.9833px 7.79167px; transform-origin: 65.9833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transmissivity, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.15px 7.79167px; transform-origin: 67.15px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the storativity, and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.025px; text-align: left; transform-origin: 384px 18.025px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u = Sr^2/(4Tt)\" style=\"width: 49.5px; height: 36px;\" width=\"49.5\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 349.917px 7.79167px; transform-origin: 349.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that achieves the objective of a pumping test: to determine the transmissivity and storativity from measurements of drawdown in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 347.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.733px; text-align: left; transform-origin: 384px 173.733px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 497px;height: 342px\" 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data-image-state=\"image-loaded\" width=\"497\" height=\"342\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [T,S] = confinedPumpTest(t,s,Q0,r)\r\n  % t = time, s = drawdown, Q0 = pumping rate, r = distance from well\r\n  T = f1(t,s,Q0,r);\r\n  S = f2(t,s,Q0,r);\r\nend","test_suite":"%%\r\nQ0 = 0.15;                                %  Pumping rate (m3/s)\r\nr  = 100;                                 %  Distance from well (m)\r\nt  = [100 1000 10000 1e5 2e5];            %  Time (s)\r\ns  = [0.0402 1.236 3.664 6.276 7.05];     %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 1.042e-2;                     %  Transmissivity (m2/s)\r\nS_correct = 9.864e-4;                     %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.30;                                %  Pumping rate (m3/s)\r\nr  = 100;                                 %  Distance from well (m)\r\nt  = [100 1000 10000 1e5 2e5];            %  Time (s)\r\ns  = [0.0804 2.472 7.328 12.552 14.1];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 1.042e-2;                     %  Transmissivity (m2/s)\r\nS_correct = 9.864e-4;                     %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.1;                                      %  Pumping rate (m3/s)\r\nr  = 40;                                       %  Distance from well (m)\r\nt  = [300 2000 8000 12000 24000 40000];        %  Time (s)\r\ns  = [0.494 1.749 2.830 3.153 3.709 4.120];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 9.838e-3;                          %  Transmissivity (m2/s)\r\nS_correct = 3.4e-3;                            %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.1;                                      %  Pumping rate (m3/s)\r\nr  = 65;                                       %  Distance from well (m)\r\nt  = [300 2000 8000 12000 24000 40000];        %  Time (s)\r\ns  = [0.125 1.050 2.067 2.383 2.931 3.339];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 9.838e-3;                          %  Transmissivity (m2/s)\r\nS_correct = 3.4e-3;                            %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 2e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.05;                                     %  Pumping rate (m3/s)\r\nr  = 5+10*rand;                                %  Distance from well (m)\r\nt  = [4e5 9e5 14e5 19e5 24e5];                 %  Time (s)\r\ns  = [0.859 0.918 0.951 0.973 0.991];          %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nlogfit = polyfit(log(t),s,1);                  \r\nTapprox = Q0/(4*pi*logfit(1));                       \r\nSapprox = 2.25*Tapprox*exp(-logfit(2)/logfit(1))/r^2;      \r\nassert(abs(T-Tapprox)/Tapprox \u003c 1e-3 \u0026\u0026 abs(S-Sapprox)/Sapprox \u003c 2e-3)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-04T00:26:53.000Z","updated_at":"2026-01-09T18:01:40.000Z","published_at":"2021-01-04T05:23:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose a confined aquifer initially has no flow. In that case, the piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the level to which water would rise in an observation well, would be a uniform value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. A well turned on and pumped at a rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will create a cone of depression; that is, it will draw down the piezometric head to a level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radial distance from the well. Applying conservation of mass and Darcy’s law to this situation leads to a diffusion equation whose solution for the drawdown \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s = h0 - h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = h_0-h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s = (Q0/(4 pi T)) integral(exp(-x)/x, u, infinity)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = {Q_0 \\\\over 4 \\\\pi T} \\\\int_u^\\\\infty {e^{-x} \\\\over x} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transmissivity, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the storativity, and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = Sr^2/(4Tt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = {S r^2 \\\\over 4 T t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that achieves the objective of a pumping test: to determine the transmissivity and storativity from measurements of drawdown in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"342\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"497\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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an ODE: equation B","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.625px; transform-origin: 407px 106.625px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.358px 7.91667px; transform-origin: 211.358px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWsAAABOCAYAAADmUDdJAAAPIElEQVR4nO2dPZLruhGFT+pYmUOlDhQ41QqmyvnsQDuY2Mndgqq8gymvQHsYL0Fr0BbGAXUejyCABAmABMj+qljv1WiuRsLPQXej0QAMwzAMwzAMwzAMwzAMwzAMwzAMwzAq4AjgE8AXgAuAw7ofx9gJHwC+1/4QG+GMbv5+Pf/f5YpujhsN8wngF8ANwOP5/w90E8kwSvGJbpyd1v4gjXMA8APg/vzv7/P5xqvRdULX3ibYjXJG18naqVf0gm0WtlECGghmEKRzQ+cNE4ryLzorWzk/f26C3SBX+CcMO9smk5GbD5hg5OKIzpp2uaBrY99rXCit/RuBK3FIjG8wsS7Jce0PsBK0+q5rf5CNcIQ/jEQL2ifWQO89WwiqQv6gE+A7+njWEBTrvYRBDnh1JXNzRDeBLuj64k/Bv1UrB/Rx1b2Mq7WgWA+Nsx9YqLNa6H7+YlyYYgR9CxzQxfUez6cEx+ff0M2fPXosZs0txxfG2/qEPrHAqAyutmOdyF36rbvqF/SxeW6oloQTaE8eC6Gh4G54GWW4I85745gs6VUaM2DHDLmhdFW3vvlwQbd48fsuIda0LPdmybCNzeVehgu69o7B+qZS6IYPbe5csb9VlvH50mLNRWFv1iWNhK0bADVwwvQ9AWaH2KZvJRzQu+ChSXPBPuLULkuINeODv/CfLtsqR3TfOdbSM+bDwzFzxhcNia2HPpuAq2eoQz7hF+oTtr8htIRYM+91b+4mQz9mVU/DTck7oBPhkBAf0I1j3+sxbW/W9Uqc0Qnvz/O5op80oSR59xQj0A2Ym/Pzr+d782i67/24mdTKJmUJsdY6DZxIboYN0/lYk8XHRd6jNWhVr7FAUdhaaTdfxhCPi1/lZz7vmBa1L3zJ8RMDN9tbmLPNo6KgxZi+0Xeyu0Os7rnv8a207gBy09A0RbCFfOKcYs2F7wddO1zwOgEv8ntf6N1PXztq9k6L4SnGqpccA3/wOn4faKswmc6dK/rN/gM6EdXsJVreOr99T6z4su3Mui7MCf3Ed90eTRlz3SSuvKEn1NEH9APHJyQtHSnOIda6gLmDne/vS5nUdvRlibScQbK0pfYH3Vg8oj/kNLZPUxsarrzjfb7qYnRBN56G5u+U701PaI+ppYuh6Wc+K4ZindsdVevaRysuVQ6xpvXsW7j4/qFNNp2Avva6ob0MEi7WoePOueGi58K2bWWxG/JYgVfDq4THwnG8t4ywxaAYhFJ2fPHSHKjL5loAH2hngqSK9ViVQi6kIfdSQ1E+S+iO9jZ56ZovNelP8IvbWI2M2qA3EprLKtYl2naoAJSRiApm6Ahzyc4NxbZvA5+nNlLEWuPKvu97HHmdhGq2nNHexNE00bUXGfZPC3FYXbRDnpTGp0ukgOp4bcErXgKG1JhY8Y2ZYTW6Lb5sDuA1BlZi4qhVT854zyKpmRSxpsiGQhza/kPtEbLOW1r0CA2IGnKraSm20IYaYw/NVVreofmeA45pC4X0pTfU0znLz6I1VVfikOUwFiJJxVfvojWBmSvWalWHLCEupmMhId+i2qJVDYQ3WtfghvbCcaG5qmOkpJAyzt9iBlJONAU59NodkR6Idp7PLHfTgErghgE+kdeqZv5pyQ22uWI9lGUDxIk5UfeTE5Hpf60RykpaGrZ/TiNlLEsqhbGNw9KGF1Hd2CuapTVmiEVpq4qFO6n1j+nEuSD/QFNByn2nHidcydOFc8VaU/LcyaMZOirmQ22vGT0XtGMRKrrorBmvZvvn/gylvtvY3oeegC3drtqHeyqNoKi2htpbs+xG+0Qta1V/XvWjmxG8vdy9RDMHKlq504laFWseaNA4NIvshGD44I42M0CA1zG5JjeUsexLibWmb7pjieHOB5YTTxp6e41bx1TinOI5v1nPvIGEp7Z0deDx8xLuGwdaiU2PJcSa7szUv6EbQnSFeESfO8dslxPGBVjfr7W8alJDXnOocmQOgS0l1nrKVefQB7pxeSvwN4cole7bAroXODSOD5G/9xfchFJRPstrD3QiUbK+BBeFEvHVkmLNePgvXkUytp3cUIfrXahnE2Mpn+V3W4WTPKeH5aZOMWb8hffiRayD43IK/HwqJcRaJ/0d3fdkDZ7Qhdal0dr3MbDQFGP6Ic+Ge1o1l6HQmP3YYsXfK11eORtXlGv8UmKtA8v3xE6QA/o6H+5+AAUl9r24uLYcJ8ztGfA2n2/0Asl0KtcSpcDcPE8ugS0h1ho6qmVDWb28GCjW2je+OTsnT5wCn/rE9pkbkRhCjbTqw5a5sz9clgiD1MI32o4RqoWYY8FhDN83YVz384ThiZorG6rExNQj5rWcTYi9AtDHUJaaFpubI54pz5y/N2aEqmddtVhzw6zkSae9iDXd3pbRCZ4q1mMFrNaK7ZeYmJzwNeXUp16WMVTk7Yxp+1ssJZz6xDLlSP9QkbZVuaAvN8kNsxwW1JBFpJt/Q79XcwxsjE/kiVOPWZcxT0o7aqwvxULUlCifIaBCUiIrY6h91KIfemLR71LbGI4VLB96ItflgjoOTIVQsR77nL6StaujVhM3LXPFVnO4OC1ZpZpMz8tNc7i/2kdrtKMO8rlojm9IvBhPLZF9pII895niBWrK3tqHiFxSvJehIm+1p6VqGGdKzLqWENZLrOmKvKGPIddFNzqGfq+lojO6GueM9+vVT3OflHbMIdZqkYU+S6joVQ5OGG4ftTZDvxMjREf4rfhSpyPnwHaeI9a6f6GLLs961Iz28+ayQUqyxZg1s0RazvrwQStxbuxVJ3hokqjVs8ZmbHUub0FonM3NmffVxZljVS+dDQL0/Tw0ltULHF2A/tvA85+xLzFCTrH+x8wn9/vl/hy1kDq51XX2CbGb176GBZpLrJeeh3NI7U8u3jzBO3cTfelsEKBPMRy6sEXH62gIK8cXKP2kimwusf4n5n+H/2V+v7lPLe5xiNTJPVTrBuhCJG5JYN5NuBQ5xPpvWG7M8Pn7jM+Zc/FlBsicvlo6GwQYr9UCDG+i7pKclvW/Zz7/yvx+c5/aSZ3cQ3cmXvF6hJ81bn48v1uSHGLdCqn9qWGtB9oroUDr2ucNaKmP2jaGV2OLMeutkjq5NQZ4R2fR8Ho4Thi+zrTOpePWJtbTqDGHPBYaAw/4jYdf1JduGYVmIuTExLodckxuta4p2irInPwP2AajwlBBzs+Voz/5Hq1uph/QCfPj+V/WPXHHZRNoSp9rFeXAxLodckxuoF/4fcLD19aiNrHm4TSdf1MzH0Lk6M8ftBf+CNFimvAL7Axu9GjQvZYBXSOtWhpD5BJrI44junlGw4jlHxh2SM3fT+1PptwZFfABf/CdA2YrK2oqWpmPdcW32DYm1svCG4WUnMW0UvpzibpBu+GI9Ib8DLwHU7CaDL4XgK77nPKQLWFivSyhBZ/9kBqKnNKfGh7IWTdol5zQdS6PuJaoq0Ao1pbS8ooWKKqmjkBG9PsZ60GRTTXGYi+EdW9MMqFO5ITXJPWS1g8tyC0KUgpDeZtbIEdtECOdB/KkyrEvx0J2rq7YXlUmYjtgLkwW32JMNpWtX0I69XYRIz/Mnsph2U7RiiNMpLNSsg4w+UKbCfCl0eOrWx3Ue/iOtZOrtrtuVNZy1diuKFkHGOg3Fiz88U7JG+BrQcXaYpbLw0uFc2B9uTJaVyE3DH+0lKpzwuut2SqirBJ2w/Swhd68zRheaLPmgM5y4cav+7eYRZKz7nVJQrU9jLKwUFIuNA5tLIy6NbljpjxD73N9a3WHeYu5XlbK2By/D38ee8CAR1OZtqjXn/lEjIeIvvB6jJp/S2s3tyKAKQXrjXnQGHDHaEpFQsvsWZBPdELAGJaulEMdONXaHKp8dgn8vDbcYjPf6MX2griYnVrP7nfW4/ihtldh/kAv8ry5hKdEa8dyrdNgX9/w7oVxcb+hD02cEPZovwM/j2HswmIjAx/oJvkPepFhIRLGTEPMsTZv8F9my2pVLaBH5OcUSNdyiT6LkgIWe+vEn+fvthgrpEWW0yXfC1ooyI0XU5Q1n5nj7o73+XdHWrjTTiEXhhPFdYl0syD2VuEYa3Psup1WUtTUqp1TIF3rMfgYEnJFwyWtTpJcN5zvGXfh5g05H+j3Q04Yv4k9ZbG3TJCCqEXjik3MrQcuqdZmS8TcqB1Cc4tDMfvYXXX1aFoVupy1KfYMF27W8l7S8FG9aHUcVotaMz4xpqBMOeacam22BidHrOdBaDWHYntTjphrm7fc3uZCp6ML99JxY+qFnZfIjF4iGrJ+ecx5SqenWJutoYvdlDi7imvI8hnrG0X3BFoJIflgTrltTs3H3XBeEurF1uf94qgb7nM7xza/hphrbbYEawKrJRObbkhRCv0b7Zsx8dUCW6Vy4ZdCQz/mRs9DjaWlM6qoF7Wm3TYLJ3foZJyu0FMaf6612Rq8x08nhwrrUNxVd+3dtuci4La9z0r6QF/713djco5ytkvDcdlC6maNqCGw5MLNeW/ZPJnRzZzQDbxjYu4jxdpsCd6YTVyrlrnqIbQ+tYop0xwZ1mDbf+K9n9zav+7iyvTI1tqfYrNlr6wUTL+lMbCksdT0RbA1o7u2vsb1rc4x1bFSrM2aUauBueC6gKlVe8X4TRcqrMyL/kR/matOtou8H0X8G+83J2ubr3WDdw74PbZau7sUR/SLt88rPqDswk1vsDVPrno0NuhaMJ9437CilTYktqnWZs1oDNknxOeR132odc2FQA8jaf9QtDQ84hPi28jrrcDvYaGQOOiRsc99xtIV5dqTxoxtDBdCD1Jc0Bf+4RFwtbx9Vlpua7N2eHw7xHHk9aF/47N4zvDXbBi7JbnpW5SfcPxZClgYer8Mm7mGkIYxv1E2fk3DwxbXQpzxaqmpFacrs1p8Sglr0zAIxabV0Flp1DPzCfHXyOu5oFbYxuICnOG34mJi1CWsTcMAeuu61dDZEoS8MnIaeT0H9KDNqjaMHUPr2ryyOjGr2jAMAH0ozTau6oRWtXnPhmH8FZs1QagLZpS1fGLWMIyMaO1lox5Yd95y4Q3D+AumidrpuDpgponVrDYM4w3mFVs4ZF0Y/rCF0zCMILwKzrJD1oE1g2zD1zCMQbTQlcVKl8Xa3jCMSahoGMvBkhEm1IZhREPBttONy2BCbRhGErbZuAyt1URvmv8D8OwNApJjdPgAAAAASUVORK5CYII=\" alt=\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\" style=\"width: 181.5px; height: 39px;\" width=\"181.5\" height=\"39\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.0083px 7.91667px; transform-origin: 35.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y'(x0) = y'0\" style=\"width: 74px; height: 20px;\" width=\"74\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1167px 7.91667px; transform-origin: 38.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.275px 7.91667px; transform-origin: 25.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eyp0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.708px 7.91667px; transform-origin: 109.708px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assigned numerical values, and the other will be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.742px 7.91667px; transform-origin: 128.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.9px 7.91667px; transform-origin: 80.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.483px 7.91667px; transform-origin: 194.483px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the applications for this equation is in groundwater. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAkCAYAAAAjMNwcAAAB2UlEQVRoge2ZUZGDMBRFjwccYKAGUFAFOKiDOKiFalgJeMDCasAC+xFeeTCEkpRCdvrOTGY/CAl7uXk3pGAYhmEYhrFEAVwBN7TruY+TNw7ogAdQ4cVqh2bCzXgA/fBXU+BF7DHRnlzxgvR4gebUw7XfwPWv4xcvSBO4XjAKej/qoXJFu8ut9GsZXfbVSO16VaN0v0vMBAVjgrhhICmUJd6yzdAc+a/5hm1CONXvFjOBCPbDdF07vF3vTN9GS5xobodWR8zXEy/YPEk3UakBGryAGv3mYuK436HNn2XrfOVKv1vi+E+04ksD6OsxybKHw1JeUPeinzZIkmCSGh3LbyZVsKPRgq05rOYNwfS+JHTzXfXJeYcsu/iP1jC9dwkV2JZtteFsPp6SMKZgx3IClqTb9+iU1Cuh2qHfIvIpsWU5Rm3y1H1HpaReLWvOESeGTBJEu2dpgpKxLqx9aoQ4OiXhw9+SOi2W3CO1Kyl6T0JcFkrKmkR3wXSHP785dKb0H1g7DxMHJqW9jmEZQJ9MRhfEjJDaOz9x7UgU68J0LdeMqZTz1iGGkvH/crxpAL0XiU2/r0RHq/GCLZ9DhmLrBu/rkR82JVrFYRX5n6aegpywLjUTzDCM3PgDF8YKvLGFg5UAAAAASUVORK5CYII=\" alt=\"p = 0\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.567px 7.91667px; transform-origin: 136.567px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.975px 7.91667px; transform-origin: 141.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the normalized distance from the well, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEB(x,coeff,Xbc,bc)\r\n%  y = values of the solution\r\n%  x = values of the independent variable where the solution is requested\r\n%  coeff = [a p], the two parameters in the ODE\r\n%  Xbc = values of x where the boundary conditions are specifified\r\n%  bc = [y0 yp0 y1] = boundary values (see description)\r\n\r\n  y = f(x,coeff,Xbc,bc);\r\nend","test_suite":"%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [1 NaN 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [1 0.505461057363874 0.265959532078956 0.140787844664873 0.071276733472728 0.029333752731051 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [0 NaN 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000035290165611 0.000065476121971 0.000315436935125 0.000552779648598 0.000757412623201 0.003086031722519 0.012031119481478 0.040129255417251 0.089700339919646];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [4 NaN -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [2.974028994378906 1.041176175714286 0.308462205553512 -0.076175488441917 -0.426089583908447 -0.952692417292867];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [2 4];\r\nXbc = [1 Inf];\r\nbc = [3 NaN 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [3 0.005688558853080 0.000051725255081 0.000000653418086 0.000000009396692];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n%-------------------------------\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [NaN 1 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-0.696760997897786 -0.352185550727323 -0.185310228971762 -0.098095479140575 -0.049662847941353 -0.020438614824974 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n \r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [NaN 0 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000053997354167 0.000075728700374 0.000316920386259 0.000553525214653 0.000757922298088 0.003086129240342 0.012031140116004 0.040129260776539 0.089700342119009];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [NaN 4 -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.047695617799804 -0.816404083826666 -0.431398160565887 -0.374418157507686 -0.532801281305956 -0.958228725044217];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 Inf];\r\nbc = [NaN 3 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.098451806781317 -0.173147136186896 -0.018397012773047 -0.002117248575316 -0.000253600440751];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-16T01:10:22.000Z","updated_at":"2025-05-09T06:39:10.000Z","published_at":"2021-05-16T01:19:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2y}{dx^2} +\\\\frac{1}{x} \\\\frac{dy}{dx}-\\\\left(a^2+\\\\frac{p^2}{x^2}\\\\right)y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y'(x0) = y'0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\prime(x_0) = y\\\\prime_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, one of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyp0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be assigned numerical values, and the other will be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the applications for this equation is in groundwater. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the normalized distance from the well, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAnCAYAAAC7bZ4BAAADs0lEQVRoQ+2Zt6sVQRTGfX+AiKESsTB0goIJxEowlyoGxEowlIIBtTSgoK8ygXZiAEERFbWxUMRUKFgIhkJbA/oP6Pd7znnMm507d3b3ce8u3IGP+9yZ3TnnmxPHoQmDMcLA0ICH/wwMiHCWMCCiz0TM0v4rhUnCb+FSv120HxaxRUpfFx4Jc4TZwhths/ClAiG79M434UGFd0df6TURWMJjYZWn9A1Hwu6KlvFT7+0V+E7l0WsiOL0XwjtP4uX6+6lwQjhSUpN1Wn9VmFLyvcLyXhMRkxdl7gsLAoJydDvvFmERtUYTiHgoDW5XcIupeue7sF6oFR9gsJ9EEC840SXChQpuQdA9JhBwa49+ETFfkq8WVrhfFDkonC6hEcHxcwUCo1v0iwhfGEunKJV7ulgT66vElcYSgWC4yB5hmvAjwyrIPjuFxRlrs5akLMKqP6v6+Df+PNN9+ZZ+/QKI4LVUmOfmKZj8NJkS6IAmDwlzM4l4rXWXhVRFGsrzVetfCRNjcoVEoOxGYZOwSPglkKMR9FREE4vYnNBJYXKwJjeiH9d7C4U1GcdHfHkrUJF2qkRZ80Qgjlxz31yr38OeTmO2ihExXSuGPSLwRU6ADz4TbBOUZo5KEbIgAgugQLrrSAn9nrkZTkAThJP7KGwXctIgpEECsaXT+OQUDl3HLK9QgHVyDd8CtgaCsznCwC7jZkQoLOSim/cDGjUD2YLe4ozwR9gh3InskVLyaGK9WQyuGVoYpL8UCkE5h4hYZLayGGFjPYI/7xOJILgeXSfjuYCV5Q4rqVOxxN875pocciFN94KIqs1UjJzckppGzOIV+xPYk9moTUSUiSXWvxiZBP1kh9omIsqW1OZGfiYjblDBFtJ6m4ioUlJjRfsEC+xYCJlsQ0hGW4goU1KzlhLAD8I8476DWzBGIaO0hQjS8X4hpxcha2xzMSEMuHYbZoXi6HxbiMgpqU0pK+hiKdZSK3XMmGKrDUSYW6RKav/kU1d/VigWUnqMCLtgZWMGvnVWsDxMADrn+Vt4Ax36Y50bavYv04ew3i+ouPC5J1DBLhPol6L3HiERfIQXYuOKHlIRUhnGxns9/JCYL9ON+t+nb0iV1KEsHBRy0pD5+lj3GW3UmnAx04HXkcd2urn3FKlvJeeaTkRuSV2ZAHux6UTQM+S257XIaDIRlNRYRO3/vMlhqMlEVCmpc3SOrmkyEX8l8bjdUndjqMlEcNOUe/nbTc+u800moqvw47lgQIRjc0CEI+IfjbbsKMTiRisAAAAASUVORK5CYII=\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57635,"title":"Compute the average precipitation for a watershed using the Thiessen polygon method","description":"Several methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \r\nThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \r\nWrite a function that takes the precipitation amounts and the (, ) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.425px 8px; transform-origin: 366.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.458px 8px; transform-origin: 190.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the precipitation amounts and the (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.767px 8px; transform-origin: 156.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Pavg = spatial_average(xd,yd,P,xb,yb)\r\n%  (xd, yd) = coordinates of the precipitation gauges\r\n%  P = precipitation values\r\n%  (xb,yb) = coordinates of the boundary of the watershed\r\n\r\n   Pavg = integral(P*dx*dy)/integral(dx*dy);","test_suite":"%% Rectangular catchment with simple gauge placement and values\r\nxb = [0 5 5 0 0];    % km\r\nyb = [0 0 10 10 0];  % km\r\nxd = [-1 6 6 -1];\r\nyd = [-1 -1 11 11];\r\nP  = [20 20 40 40];  % cm\r\nPavg_correct = 30;   % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.05);\r\n\r\n%% Example 3 from dreamcivil.com\r\nxb = [0 10 10 0 0]; % km\r\nyb = [0 0 5 5 0];   % km\r\nxd = xb(1:end-1);\r\nyd = yb(1:end-1);\r\nP  = [11 15 12 10]; % cm\r\nPavg_correct = 12;  % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01);\r\n\r\n%% Rectangular catchment with more complicated gauge locations \r\nxb = [0 10 10 0 0];\r\nyb = [0 0 30 30 0];\r\nxd = [-3 8  4 13  1 9];\r\nyd = [-2 2 12 21 25 33];\r\nP  = 132+3*(yd-33);\r\nPavg_correct = 77.65;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)/Pavg_correct\u003c0.01)\r\n\r\n%% More complicated boundary\r\nxb = 10*[0.5497 0.4705 0.3840 0.3214 0.2937 0.2882 0.3379 0.4632 0.6271 0.7284 0.7947 0.8241 0.8039 0.8039 0.7689 0.7302 0.6452 0.5497];   % km\r\nyb = 10*[0.1857 0.2512 0.3867 0.5152 0.6717 0.7909 0.9007 0.9591 0.9498 0.8797 0.7605 0.6320 0.4708 0.4708 0.3914 0.2745 0.2194 0.1857];   % km\r\nxd = 10*[0.4 0.63 0.5 0.7 0.8];\r\nyd = 10*[0.9 0.6 0.35 0.8 0.32];\r\nP  = [113 166 140 183 125]; % mm\r\nPavg_correct = 148.271; % mm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% Example 5.5 from Chin\r\nxb = [2.0084 2.4293 2.8156 3.0028 3.2368 3.4126 3.6713 3.8467 4.0235 4.2117 4.3540 4.5197 4.7338 4.9362 5.0688 5.2611 5.4307 5.5418 5.6399 5.7033 5.7094 5.6167 5.4566 5.3269 5.2170 5.1962 5.2033 5.2325 5.2838 5.3351 5.3630 5.3672 5.3594 5.2956 5.1854 5.0638 4.9172 4.7914 4.5239 4.2432 4.0206 3.9153 3.7154 3.4805 3.3047 3.1412 2.9657 2.6980 2.4305 2.1494 1.9034 1.6444 1.3955 1.1317 0.9849 0.8611 0.7998 0.7605 0.6858 0.5893 0.4919 0.3519 0.2515 0.1265 0.0875 0.0801 0.1796 0.3474 0.5154 0.6832 0.7618 0.8867 1.0592 1.2773 1.4249 1.5055 1.5835 1.5910 1.5914 1.6825 1.8099 1.9151 2.0084];\r\nyb = [6.4122 6.4364 6.4348 6.4401 6.4466 6.4391 6.3966 6.4015 6.3566 6.3246 6.2539 6.1839 6.0530 5.9218 5.7761 5.5824 5.3632 5.1423 4.9708 4.7859 4.5496 4.0617 3.4599 3.0456 2.7688 2.6686 2.3950 2.1719 1.9991 1.8263 1.6529 1.4912 1.3416 1.0910 0.8266 0.5494 0.3337 0.2182 0.1485 0.1406 0.1468 0.1439 0.1756 0.2064 0.2139 0.1969 0.1920 0.1347 0.0650 0.0695 0.0751 0.1301 0.2475 0.4890 0.7338 0.9917 1.5500 1.7106 1.8828 1.9921 2.1387 2.5703 2.8288 3.1364 3.2847 3.5707 3.7975 4.1008 4.3918 4.6951 4.8218 4.9746 5.0914 5.2593 5.4377 5.4897 5.6412 5.8032 6.2388 6.3409 6.3942 6.3972 6.4122];\r\nxd = [1.3 1.0 4.2 3.5 2.1];\r\nyd = [7.0 3.7 4.9 1.4 -1.0];\r\nP  = [60 90 65 35 20];\r\nPavg_correct = 59.301;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% C E 372 problem 11\r\nxb = [33.6241 31.3609 26.3820 25.3635 24.0062 22.8754 21.4057 19.4844 18.2414 17.5648 15.1930 15.1935 15.5336 15.8735 15.8742 15.3089 13.6128 12.9347 12.0319 11.4673 10.2237 8.8694 8.0782 7.7400 7.4023 7.4049 7.7466 8.2004 9.6732 11.4838 14.6517 15.7834 16.4627 16.8027 16.8037 15.5614 14.0926 13.0759 12.3981 12.5118 14.5502 15.4557 16.7001 19.1891 22.2439 24.2812 26.3185 27.5654 27.9054 29.1500 30.9595 32.7690 34.5782 36.2742 38.0830 39.1005 40.6836 41.9275 46.9026 47.6937 49.5021 49.8399 49.8383 49.1574 48.2507 46.8905 45.1911 44.5108 44.0567 43.4877 43.0343 42.5763 42.4619 41.2167 39.1791 38.8389 38.8379 38.3850 37.2537 36.0095 35.5567 34.6511 35.2149 35.4394 35.5514 35.5496 35.3221 35.2082 33.7370]; % mi\r\nyb = [5.2159 3.9673 1.3564 0.6755 0.5609 0.7865 1.4650 2.9363 4.1815 6.2206 9.7311 10.2976 11.2045 11.7714 12.5646 12.7907 13.1290 13.6949 15.8471 16.7530 17.3184 20.3766 20.9425 22.0753 23.7747 26.6075 29.1008 30.5743 33.2952 34.3168 35.4529 36.1339 36.9277 37.6079 38.7411 40.6662 42.2512 43.4967 44.4026 44.9693 47.6908 48.4848 48.8259 49.6215 50.7575 52.3458 53.9342 56.8815 57.5617 58.1295 58.0179 57.9063 57.4547 56.8898 56.0983 55.6460 55.3075 55.0821 53.6137 53.0479 51.6898 50.1037 48.4040 46.0238 43.9832 40.8092 37.7481 35.9344 34.1209 30.4943 29.3608 23.4680 22.1081 20.9738 19.0455 18.1387 17.0055 16.5518 16.2108 16.0963 15.6427 14.8486 13.0361 11.2233 10.0903 8.1639 6.8039 5.8973 4.9894]; % mi\r\nxd = [15.9758 6.0340 4.0115 15.4546 38.1999 50.7358 40.6553 33.7370 31.4005 19.7352 28.4331]; % mi\r\nyd = [0.3267 12.1020 26.1511 47.3517 60.0644 40.6995 25.2792 4.9894 45.8937 28.9988 17.5623]; % mi\r\nP  = [29.79 34.97 25.60 24.27 24.60 42.61 42.35 15.51 39.99 43.04 28.41]; % in\r\nPavg_correct = 35.011;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-02-04T01:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-02-04T01:17:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-01T17:01:04.000Z","updated_at":"2023-02-04T01:17:57.000Z","published_at":"2023-02-01T17:03:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the precipitation amounts and the (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":53975,"title":"Compute the effective conductivity of more heterogeneous aquifers","description":"Cody Problem 52070 asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single value of conductivity set such that the aquifer produces the same flow under the same total change in head. In that problem, the aquifer had soil units either in series only or in parallel only. \r\nWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided.  \r\nFor example, if in the aquifer below  = 0.1 m/d,  = 0.2 m/d,  = 0.01 m/d, and  = 20 m/d, then the effective conductivity is 0.092 m/d.  \r\nHint: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \r\n   and   \r\nThen conservation of mass leads to \r\n\r\nSolve this equation for the head , compute the flow through the aquifer, and get the effective conductivity from the definition.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 725.117px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 362.558px; transform-origin: 407px 362.558px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.25px 7.79167px; transform-origin: 318.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.017px 7.79167px; transform-origin: 331.017px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.79167px; transform-origin: 25.2667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.933px 7.79167px; transform-origin: 359.933px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.858px 7.79167px; transform-origin: 110.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if in the aquifer below \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.1 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.2 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K3\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7px 7.79167px; transform-origin: 52.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.01 m/d, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K4\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.35px 7.79167px; transform-origin: 88.35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.79167px; transform-origin: 13.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.683px 7.79167px; transform-origin: 342.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"vx = -Kdh/dx\" style=\"width: 72px; height: 35px;\" width=\"72\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 7.79167px; transform-origin: 23.325px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   and   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v_y = -Kdh/dy\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.408px 7.79167px; transform-origin: 112.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen conservation of mass leads to \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\" style=\"width: 173.5px; height: 35px;\" width=\"173.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.358px 7.79167px; transform-origin: 100.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSolve this equation for the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.9px 7.79167px; transform-origin: 251.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 246.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 123.233px; text-align: left; transform-origin: 384px 123.233px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 513px;height: 241px\" 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\" data-image-state=\"image-loaded\" width=\"513\" height=\"241\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity2(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 0.1; K2 = 0.2; K3 = 0.01; K4 = 20;\r\no = ones(50,50);\r\nK = [K1*o K2*o; K3*o K4*o];\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.0916;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 5; K2 = 3; K3 = 8; K4 = 6;\r\nK = K3*ones(50,110);\r\nK(1:20,1:50) = K1;\r\nK(21:end,1:30) = K2;\r\nK(1:20,51:end) = K4;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 2.5471;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 0.1; K2 = 1;\r\nK = diag(K2*ones(50,1));\r\nfor j = 1:9\r\n    K = K+diag(K2*ones(1,50-j),j)+diag(K2*ones(1,50-j),-j);\r\nend\r\nK(K==0) = K1;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.2945;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 1; K2 = randi(9)/10;\r\nw1 = 10*randi(9); w2 = 100-w1;\r\nK = K2*ones(100); K(1:w1,:) = K1; \r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = (K1*w1+K2*w2)/(w1+w2);\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-02-02T15:06:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-28T03:19:00.000Z","updated_at":"2026-04-05T08:16:36.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55825,"title":"Measure the hydraulic conductivity with a constant-head permeameter","description":"A constant-head permeameter is a device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . By supplying a flow  to a standpipe, water is maintained at a constant level so that the head difference , or the difference in water levels between the standpipe and outlet, is constant. \r\nThe hydraulic conductivity can then be determined from Darcy’s law\r\n\r\nwhere the head gradient  is simply . Darcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\r\n\r\nwhere  is the acceleration of gravity and  is the porosity of the soil \r\nWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use  and .\r\n\r\n                              ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.2px; transform-origin: 407px 419.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.342px 8px; transform-origin: 256.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 8px; transform-origin: 65.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. By supplying a flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8417px 8px; transform-origin: 75.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah\" style=\"width: 21.5px; height: 18px;\" width=\"21.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.533px 8px; transform-origin: 188.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.533px 8px; transform-origin: 209.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4167px 8px; transform-origin: 77.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 18.5px;\" width=\"39.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 8px; transform-origin: 30.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is simply \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah/L\" style=\"width: 38.5px; height: 18.5px;\" width=\"38.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 214.6px 8px; transform-origin: 214.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.025px 8px; transform-origin: 91.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.417px 8px; transform-origin: 175.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.733px 8px; transform-origin: 114.733px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.492px 8px; transform-origin: 371.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.55px; text-align: left; transform-origin: 384px 18.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K = (gd^2/(180nu))(n^3/(1-n)^2)\" style=\"width: 114px; height: 37px;\" width=\"114\" height=\"37\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.95px 8px; transform-origin: 78.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the porosity of the soil \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.683px 8px; transform-origin: 363.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAnCAYAAAB5cRjAAAAIJ0lEQVR4Xu2c2+ttUxTHz/kDkMsbeXB5EKJcEy/K/UUhRPoV5ZoiDs4hyV2klFtRHlxDSrk/eCC5PRDyggfJk/s/wPhojl/jN/ecc4251l5773X2XDVav73WvIw55neOOS5z/bZva1eTwEQlsH2ifDe2mwS2NfA2EExWAg28k526xngDb8PAqklgX2HoBKEjAmOvyf2nFJMNvKs2ddPm5wlh/+Ec2BxDO0rKfCj0o9DeQgeHOrfI/aG4fgOvQ6KtiEsCAO+rALikpuxoBY37mdCG0Meh7EVyfyn8fYp5/v+jBl7XvLRCDgncG4AL4Ppc1DtSaFdU+WX5faHQffG7dQTvQSKE04T2CkJ6T+5f95F2VAfNcZjQSeb5J7G2cPRDO+cLPe0ou0pFfhBmbhcCbH2uk6XS90K/R5V3yO8H1x28gOJxoWOFrhf6JwDtVrljY93QA2gqZwRMO08KvRMeHi73+0PbV8i9a4HA3+WhHZrYpw8CllTnbOn3LaH9EuAbypKC9xxp6G3b2LpoXrWncABiAbPiPwpCmbGrHJLHSbla6GKhWOuoA/KHvDtdKGcLXhmAjpPC9efEwIsMuK5xyKu2yLtS4fiUPNYFvAjgDCE0Y0rACkA0MGGaeOvKCVydFMB2aKaetp30mKUOwP1OiC0Th4UFNjXwsjgvFdqiGWtRmiiPiceczGhdyq4DeBVgjDelHXmu2x5/XyXktTd1SyuBTcu8Iu12OTO6yKYEXsbEAh3DzGEnY2EkNfo6gFfBAzCPFkrZnpgVv4WV/6Xcj3NqDU/beOE7hWa85UQfUwQvAEM7xlECpwizxVgU55YW/DqAVwFRAi/v/g1iLJkAsaStVidqcYlQbHLghWMK5BaObXMoeOGHiIfa3vw+UYjIyt9CZKssf2zL2JMHhvcfyL0mRquLvmtsth/G+60QJtIBQillAt+vCxVNOC9445Tdz9IwA/XahvGkL/K3F7xfCFNEIri6JiMFOJ4BYLY4BUCXvRvLoQ94cTjPEiIWyiLBPLlWiMgKz+yFhjxP6BehG4XYEVLvuyIjWgd7/WahQ+KBmN+aaMAcw7bfU+iywFvKlAK4zwidKWTxpRjctKu7wEsFHSTb6Z2Bqcfkjo3zefj9htw9diIrkBjm0KsmfqpBbvrM2by884I85h0ZUVeBj+YGwBthUgGLFwx9wMtk7y/0vBDRCuYJEN8m9Gno22aqAAzvXxXScwOA8KkwsJxTm5ozFjxAy829Olwpk4mx/iVk/QDVuMhOs2z0i4zvFnrRPi+B104KGoWVoJe19fCivWCyYamUMLzPapwq78T0Ba8K1wKYZ2i5UngsNdY+4NV2LP+AM97+7c6Skp8ucq+zqMBM9aU8qexTkRawcJ0Brw1npmSDPLdo+BJ4LUBjBu27msD0vDRvTVZMhYxAmBg0ZMquw6vVOGuN2aCCph+0nrahACYh4g0hzQO8OfB1OZel+U6BCUf0mEipxeW0TTVX4h2I93rghoiPniRL9TejIEvgVUcj1ro0bLfiGvB6Neu8y9mJie1SQHeTEIkGBXguZpvjS7c7ZPacELauBXEyTplobFXA61m8nnSwdWgB8JD08Yy4SuBV7ztlr6iWSgF73sCbV3sWwLQJ71x42w8IkT/nqgmVUd4e41MnQ1PR1mHyAGIq4FXzz6O4NFSo84h8h6TiN/Hg0bwxeK3x79Uo8wLg0HbiqAlbEZktDuro0btcJizXt+5QKVlotEEXi/UbUu1NBby16eBYcTB2HMM7hHpHrDw2r9VE1q6rcZp0ouZl83odRC/YFYCU92gTbVczc6XYsAVkzt7W9qYC3j7pYOYe0JOm1ysXG3fNW1eojBXDaan3hbBZsAu5EzLzOiGWkWVEG7oEYaMRtQvSkx62O1WX6TAF8Nakg5nvX4Wsg8yzR4U0tFi7023OZ1eo7AUpSXhiI9SIGekCRvx+Xpq3JtpQ4lHtVZyrPva7Ar8UXrILthRWgs8pgLd43iASNoubhFZ82s6GxTxnPpJzWAKvCrLPpNaCehnl4zh2KrULXxogJynD+Vwb7rFhuNxxStW8Hkdw1cHrTQfrfALeU4VStr7uWp4zH9XgtXFPTAVWyDeJVbQM4A3t02rcLsfBmhUzgXJhRL3pnP2myQHPWWEt600UWDl0Ab8mzpszb1iI94Td2DMH2mfKmVV+u0ypbD8lzcukaL7cNsAE1gTePYNcVBk0JV8rkNP3jsMel8xtceob0OYjQpwdIId/lxAmyYaQTXfG41VzSsN1vMcWfFbI443HvkScBqd9/Bb9GjdesBqnzr1XfllcpJVnvuTNTGAqE0tRMmtkHwedAU6BV71CzTuzVRBKYgKspzilMJluX9jvTOKWHHlG8PYx4OAEVOkwUhyG4xQXB1FKoKUP2rbfvcXscAKr5ByjDTkVFl/0z5mDUvvsFnsU+reLx5MOjnmgDnxw2f/FoKfKPAszOz0xeDUUxoGblJ2CIN4U6uvgOHAyShH47gLRKB3vRo2iAC4Q8p51Hn3oMXg1qF7SqjUOyOgDaB0sTAKedPDCmKGjGLxqRJfAqzZg7/jcQkfYOpuHBPSMQk0CZx79FtuIwauedS48puElzIaaDxVHH0jrYFQJsCMTKrRnb0ft0NN4ymGzoR8OmeN0cPF/CDg1j8MzKCftYayVWSkJ9EkHjz6AXKgs999fUv/RZHQmWwdLlYA66WN8HTxoYF1nGwY13irvFhJAkfEBZ82HmQsZeAPvQsTcOhlDAg28Y0i1tbkQCTTwLkTMrZMxJPAfm3EkRnJ8+GwAAAAASUVORK5CYII=\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-6} m^2/s\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 338.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.35px; text-align: left; transform-origin: 384px 169.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 494px;height: 333px\" 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Xn311cf3+fHHH+8bgotUzRKkonc7l17+Y9Whb3z9lO187Wtfq974xjfWIaQ3xPR7bkW/ZdlWKnrZVm/wLevffffd1a233lrPK+Ev+3rZFX+9eurJk4/t6Wyv9xjPduz7Hd/8U5ATlrLNHMNUD0fdl9kkwL797W+v3vOe99S3B70Hii7PDZhHCZOMj2l6SY6F4nkfpsVCvs5dtv3tb3/76LEwUN93lOHYl3Zzz6NH169fX887FpyaOSfs27evXrZ27dpmzmBZ99zzzjtl3bL9Y4GkmXNC7pP9PhYkmjmDddlO5r/uwv77P+x591s223F62XknP07Zp9ynn67b63essizb6l027DHa5rovw2T97MfXnv1uM+dFx8Jg/Rh33HFHM+eELs8NmD/6TI6hVJYmfWhXnOZbms/6PeYkDZGKzbgo/SEj1Z1jfxv6DqlQ9Xrqz79Rj3fu3FlXlNpDKlLxuc99rj6Bpy3VrFSN2ut+/3vfq+e3HQsD9TiVpUFGOZu7nDAzbDvRu52c5f3sd37Q3Doh78NB+i0rjz/oOH3ney82xfYatL9dt3csdDVTJ+TzWl7b9vM/+JffqseXX355PR6kvEbD9iXVw9leo3jkkUeqn/qpn6pevey8Zs6L0n8yPvrRjw7czlyeGzCPjn1BMEbaFZ9JlrdWv8ri6Q5l25NuIV/nLsenVCYzDNu3fuuUitGwYVDFq9/QW8Eq2z8WjJo5JwyrSPXqsp3M71ctjWHVuH7L5nqcyj4NqujN9/Z6n39e48xLZba3Stiry3tgkGPBb+B7MPuTbfUe87k+N2B+qUyOmWF9vpge4/Y6t8/UHqbfOuW5pAp27G9K36FdIfvQhz5Un9CRatGxEHB8nS9/+ct1Zam3ejTqsZqPqlNvhTPXL3z5sWPTb9tzrUzO9TgVsz2v+dpeXtv288/+po9pzvD/8/2fq+cN0vW59cpJPOljOug1T6UzUtXvrXTHqM8NmF/CJHDSNSSHyTq9SnB66qmn6vFsvvjFL9bjcrmZ4oUXXryGYG+QmG37JdwOCiBFOYFj2H72Xq8y1y/ML+P02/aw60z2WzbX4xS55NGg5zXK8+n17WOvc7/tJWTlte19/qPu86tf/ep6PJd96ZV9yKWVfumXfqmZc6r169fX79GcdNXv7PC5PDdg/giTwJwqk73yBR+D+oAmNJazwKN8ofcGrlQr8/i91aNB2y9n8MYoVae1a9fW40HbKc+9dzvz1WdylOOUvqVt55577sDnNej5FL3bO+ecc+oqa7/nktckr20uOVRCfVxzzTX1uN9jtLf/vve9rx4P25f2e6Cfhx9+uK5K5r04SP75KNXJXMO0V79jVZ5bzPYeAboRJoH6S3a2yuSgdRLEcmHpVItyclEqZuXki9xOU2m7YlUuz5P11q1bVw8JX+Vknd7qUbZ/7bXXHt9+tpvrDub6jwkJWTZK1WmU7UTvdvLLKhe+7NQ/lXOtTI5ynHrDZAx6XtleAuqo20tIHPRcIq9tLvWT0Fkk3LWPWV6rftsf9NwSMsu6s1Ut77vvvuMBeZh3v/vd9Tjhsx18Y9CxynOL2d4jQEdHYQHkrdXvBJrTHcq2Gazr8cmJD7nv4SEn4AxbZ/fu3fVJDllehtze0+eEl5xAcSyUnrJetn8svDRrnexYWDlp28fCZz0/J13k/sP2u23YdnpP/viLv/iLej9vuOGGZs4JZTv9TsAZtmzU41ROKhl0PIpRt/f5A39Vb+9nfuZnmjkne81rXjPwON59990nvV45TuW4tc3lPdD2h3/4hyfdZ9QhxzlmO1bZ397XFpg/LlrOgkg14lj4a27Nn9VXLK237W07mOMDwJmkmRsAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmgYmxbt26ZopJ47WD6TVz9JhmGubNzMxMtfvJQ82t+bP6iqX1tr1tB5vm4+O1n1xeO5heKpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQAd7N+/v5qZmamuu+66Zg4sTsIkADSOHDlSLVu2rA6Jg4as07ZkyZJmarwl/G7YsOGU57Nq1apq7969zVowd8IkADQSDC+44IJ6evny5dXKlStPGq699trq8OHD9fKlS5fWQ2+4HEf33HNPdckll1T33ntvfbs8n0iQTKBct25dfRvmSpgEYOJ95evPN1OnJ8Hwueeeq0Pi448/Xu3Zs+ek4dFHH61WrFhRr5tQmWHcK5MJkhs3bqyn77///uro0aPHn0+md+/eXS976KGHqs2bN9fTMBfCJAAT7/3b/rTa8hufP+1QWSqTpfo4zKRUJrds2VKPEyRvuummerpt9erVdbCMu+66ayIqrYwXYRKAqfDZLxw+Hiq7BqJ2ZXI2s1UmH3vssbr5eLb+iVkvy/qdyJOq4mzLhlUTs072MU3a/YJkUZrw4+GHH67HMCphEoCpklC57p/9f9XHdzw950rlXCqTMSh0JsStWbOmDo5r166t1q9fX4e10j8xy4tUBtM/c9euXaeE4DS1R/Zn0LJsf5CyzihnnN9yyy31+L777qvHMKqZo+kwAfMs/y3vfvJQc2v+rL5iab1tb9vBpvn4eO3Pnrv//f7q3/3RV5tbk+Vv/w+vqza++8V+jqPI2dwJbwlpmW67+uqrq1tvvbWeztnROakl6z344IP1vEilMUEy9u3bd7yPZbSXtauaOcs6J8f0NkWXfYk0RZeTZiLL8vilibqfhMiE1EFN3G0JuOlb2ft8YDbCJAtCmDx7hEnG0UK/dtd9+I+bqRNecf451fve/erqp9+yvJkzmoS/AwcONLdOlupiTsKJVAoT5hLwyrxIs3P6Hg4KcP2WlyDX3n6pYqaqmaC5adOmauvWrScta6/fz1zC5KjbhF6auQGYKgmRW/7uj1af+pW3zjlItvtMpiKYANwe2iEry9vVxaJUCi+//PJ63Oviiy+ux0888UQ9jhL0ShUyPvvZz9bjhMnsT/uxyyV+StP0fCiPN6gPKAwiTAIwFdoh8pqrf7iZOzdz6TOZgNevz+TTTz9djy+99NJ6PEi7eTqPm+blVAczxM6dO+uqZ7ZT+l+WfpOHDr3Y8nPDDTfU40FSaYx2cB3k4MGD9fiyyy6rxzAqYRKAifcPb/qR0wqRRbsyOZtSmexVwtgzzzxTjwdJc3Jb6UuZ6z2mP2bCY5qpEzTLspxpnWVZJ+FztipiqYKWgDtMCbdXXXVVPYZRCZMATLy5NmcPMpfKZCR09p5lXaqBTz31VD3uVS4SXoJekabubG/Hjh11YMw+lGBXluVM60ceeaSed+ONN9bjYa6//vr6fgmfpeLZT/pspm9lzFbthF5OwGFBOAHn7HECzvx6z0f3Vl879N3m1nCvWfbS6rfvOHG2LSdM0vuynMGdM7GHVf4S+NIMnarhXM/mzv36nYWdSmRCX9ZJAEygLPtQluW+CX7tZcOUM8Wj34k427Ztq0/uiVFO1IFeKpMAQ7z/nW9opmY3l3UZX3OpTEZvZTLXjSzhLGd75zevE+hSsSwhc/v27fW4V6qNeex+zdi5f5YlSI7SxF3ksbJ+3HzzzXWwz7YScjNd9jV6nwuMQpgEGCJ98FJxnE3WOd3+epx9pc/kXPQLdbmET5qzczHyBMNUBlNVzJnZqVamuthPaZaO3hNhUpksRmnibkvlNPtT+mlmX3L5o+xfLlOUZXncXJ4oITNVVxiVZm4WRP7b1cx9ZuRLIZWFVCzyZZCqRb6oMp15t91229Q0W52t1/4PHv/L6s5Pfqm51V/OIhYmB/O5HX8J0qmilr6T7etawjAqkzDhEhxzpmZCZfkSKNOpgOj/dPoSEl9/0fnNrVOpSjINUmHNtSxLRXXUZnQQJmEKDPot3TvvvLOZ4nS95x2vb6ZOdeu75+dMYhgH6fOZZu7bb7+9mQPDCZMwBfLHP5WEtjRzl98Q5vQNqk6mKvm2N13Y3AJYfIRJmBK91UlVhfnXrzqpKgksdsIkTIl2dTJVSWFy/vVWJzOtKgksdsIkTJFSndRXcuG0q5O/8K5zmymAxUuYhCmS6mSuI6ev5MIp1ckMb3rTm5q5AIuX60yyIFxncu42b95cXzy4aF/jzbITy977D26v/t4tH66Onn9O9f3vfa867wc/VM/P7SNff75a+sr/pp6eef6F6nsv+a+ntbzMz3TGxZcO/lU9/tGL/1o9Lsvb4yjTp7sfk7484zVXLnOdSZhSwiQLQphkISzU+2q+JeSee955zS1CmITppZkbYJ4JksBiIkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnc0cPaaZhnkzMzNT7X7yUHNr/qy+Ymm9bW/bxclrP7m8djC9hEkWhDDJQshrz+TyuYXpJEyyIIRJFkJe+z3bmxtMlFUb5h4mjxw5Ui1ZsqS5BYwrfSYBGDsJkldffXVzCxhnwiQAY2f79u3VgQMHqm3btjVzgHElTAIwVlKVLCFSmITxJ0wCMFZ27NhRHT58uJ7OWKCE8SZMAjA2UpXcsmVLc+tFwiSMN2ESgLGRvpKlKlmoTsJ4EyYBGAvtvpK9hEkYX64zyYJwnUkWgutMTq5RrjO5f//+6nd+53eOX19y06ZN9ZDpzFu7dm21cuXKZm1gXAiTLAhhkoUgTE6uLhct91mHyaCZGwCAzoRJAAA6EyYBAOhMmAQAoDNhEgCAzoRJAAA6EyZhDDzwwAPVnXfe2dwCgMkhTMIYeOaZZ6o77rijuQUAk0OYhDGwZcsWF2cGYCIJkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAwIfbv31/NzMxU1113XTMHzj5hEoCptGzZsjp4JYBNk6VLlzZTp2dajw9nnjAJwNQ5cuRIPU7wmq/wdSZkv1N1TMjbu3dvM/dkhw8frpYsWdLc6mZSjw/jSZiERSRfIOVLpNBsxjRK2Lrgggvq4DVJ2iHxueeea6ZOKOGv93M8V5N6fBhPwiSMmQ0bNtThrgyrVq2qduzY0Szt7rHHHhv4RZR5p1vpgHGS93jCWN7bkyphr1fC33xVJif9+DA+hEkYI+nDdO+991bLly+v1q9fXw9p6rr55ptPO1CWL6Zsu98X0elWOmCctCtvo1Tf8s9W/nFr/yO3efPmUz4XpZKfZZlu//O3YsWKejuD9P6j2B7SMlCW79q1q16/vT/33HNPPS/aAXAuj9821+MDwwiTMCbyZZE/6mvXrq2/pLZv314PmXfttdc2a3W3cuXK6ujRowM726tMMm1K5W226ls+e2vWrKn/ccvnL//E5T533XVX/dnr94/W008/XX+m8s9f1s96Bw4cOL6dtty//KOY+2T9jIvcTjj9uZ/7ueOPHWVfMlx//fX1vMjfhD179hzfZpYPe/xBRj0+MBthEsbEzp076/GNN95Yj4uEvEcffbS66aabmjkLY9oqk199tplg0RqlT2D+udqyZUtdsc8/Ww8++GD9T9yhQ4eqTZs21cHs4YcfbtY+0WfxoYceOv4PWtbPZ/T++++v18n92tKqkP1IOE0IzPoZJyxGwuDq1avrIcsSCCPbye0MqTpGefwEx1Eff5BRjg+MQpiEMZEmrXjiiSfq8Sj6Nc3ldr/qY+Zl+bp165o5J5u2yuTv/V9V9dNbqurTx8YsPvnnqN8JLL0S8BKotm7d2sw5ISEvyj96kXUzJMglwLW99a1vrce9Ae3xxx+vx70tDCU0PvXUU/W4GPaPXZfH72fU4wOjECZhTJQqRb7cRukf2a9pLl9WuX3JJZec1MeqSEVj0BfVtFUmI9XJf/qbQuViVPoEzmbfvn31OIEx/Q/bQz6LkX/E2p+PfI5KpbAt81LhjPb6aY6ei9n+sZvt8Z999tlZP8+jHh8YhTAJYyKVhtI8lRNuUkVMqOz3pZCK5MaNG+vpfBmWprlUKnbv3l3Pz/J+9x30RTVtlck2oXLxyXt/Lmcrp9k6/Q97h6L9+RhW+SvVvvb6F198cT0uJ9YUpeJ5+eWX1+NitiA4TB7/wgsvnPXzPNfjA8MIkzBG0tSWMFiawxIq88e+t8pYmrfSR6q3QpF+VyWUtvt6FYO+qPrNz0kB7Sb0sz3Eqg2jDff+Xr36SdqhUp/K6ZYwNUqfwBK60ocx/Q/7DVlW5PM4LIDlMXsrgzl5JvfJ5zLdUFL1zDjhMq0K+UeybbYgGIM+x6XaOGh5MerxgVEIkzBmEgYTFlNxLF8yqTIm2BXly623olGUSki//peDvqj6zU+47ffleraG2LN9tGH9T9Wrn+Jv/c2quufDVfW6C5sZTK1R+gSWJujefouDJHwNCmAJcP0qg+mCkvtknM91Kp7pjpJm9LQq9JotCEa/z2t5/Bj0OW8b5fjAKIRJGFOpOCY0ljM088VTvmRyWZK49NJL6/EgZb22QV9Uo3yBTbKEyN+9s6r+8f8sSC4Wo/QJLCfZtP9Za0uXkt5L7aTK2O/zkgBXKpNt+RymL+O2bdvqs8TLP0e33357s8bJysl4wwLusMePUT7PoxwfGIUwCWMulwQqzWrPPPNMPb7sssvqcbk9SFmvbVDFYpRKxiQSIhenhKlSebv66qvrgNYeylUNSl/lXGonXSmyrJyAk9s5ya1fqBv0eSmVybb0x8z8fI7b3TbKfvRefaG0LKSbS/YjFzTvPSlv2OPHbJ/nUY8PjEKYhAnQW0HIH/sYVLkoJ+FcddVV9ThKIB1UsRilkjFJVv6YELmYJUyVz02CYqqL7aF9hnbpq5xgmWXl5JvcTutAv2u8Dvq89KsMJkymmTvVyVRCy1CW5eoL7V+uufXWW4/3e85+pG/lqCfp5PHnejZ3v+OT5z3bNqCYOVo6IsE8yn/du5881NyaP6uvePE/+2l72+aLLZWA22677ZQvrlQm2l9skS+eco269MFqn4RTlrXXjzxGvrTS4b/dTyvzs27u06//1jjJa5/+kEyenBQ118/tNHzWy+ex93NX5OS69IlON5ZBzd4w7lQmYUwkFJZLAiUcpvqY6QTJyKV/ivYZ2wmICaLlDNESMtvrF6U62Y8qBMy/Uv0bdK3JgwcP1uPStA2TSJiEMZDwmKalNH0l8JVmp8i8VGdSPWxrN82Va+SVbbTPBG8bdhmQ2fpYAXOXk+Tymc7nM/8clv6Y+QcwATMVyXxWF/rnUmEhaeZmQeSPpmZu5ltee83ck2mxNnNHqv45kzuX/Cr/JEZCZLq23HDDDf6ZY6IJkywIYZKFIExOrsUcJmHaaeYGAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQDGwt69e6tVq1ZV1113XT2O9u0dO3bU84DxMnP0mGYa5s3MzEy1+8lDza35s/qKpfW2vW0Xp7z2e7Y3N5goqzZUI31uV6xYUR04cKC5dcLSpUurQ4fm/28KcPpUJgEYG/fdd18zdbI777yzmQLGjTAJwNhYvXp1tXz58ubWi1KVvPXWW5tbwLgRJgEYK73Vydtvv72ZAsaRMAnAWGlXJ1OVFCZhvAmTAIydUp3UVxLGn7O5WRDO5mYh5LVncs31c5tLAj366KPNLWBcCZMsCGGShbBQ76vF6lvffK768r6nqjde9eI1HRfSmiuX+dzClBImWRDCJAtBmJx/7/7vVtShMn0UV7zxb1SvX3F59Zb/fk31mh95Q7XsVRc1a50+YRKmlzDJghAmWQjC5Pzb+Vt3V//71juaWyc797zzqgf/wxeqV7zygmZOd8IkTC8n4AAsYmvXfWBgWPz7v/DL8xIkgekmTAIsYkfPP6d674d+sbl1wtvWvKu68b0bm1sAgwmTAItcQmNvBfLwN/5zdegbX29uAQwmTAJwUnXyf9vxmep/fOfPVu9751urRz71b5u5AP0JkwAcr05+cPNH60sF5fbW33iw+o1//kvV//pPP1zNPP9CsybAyYRJAGoJj+1+kgmVO3d/sTr0l1+v/s7fWlVfkxKglzAJQK3fxctzgs7/8i9/u/rb791Q/cOb3qHZGziFMAnArFKxTF/K3/rEx6pf/tB7NHsDxwmTAIzkDZdcXv3bT++pL2au2RsohEkARpZm74/86r+q3vsPfrF637uc7Q0IkwB0cP3P/p3qX//+f6ybvX/lw3+//n1vYHESJgHoJM3e/+eu/6c697yXVht+9ierzz+xp1kCLCbCJACn5Rfv/Jd1s/cvb/y56tM7/nUzF1gshEkATluavf/FJx+ufu+Bf1Pd8b53avaGRUSYBGBepNl7+6f+sPrh5VfWP8Wo2RsWB2ESgHn1j/7xr1b/6J/8at3svfO37m7mAtNKmARg3r1tzbuqe3/3/64+86kd9UXOgeklTAKwIJa96qK62fs1P/KG+vaf/Mmf1GNgugiTACyoD27+aD3+iZ/4iWrbtm31NDA9hEkAzojDhw9XDz74YLVq1arqyJEjzVxg0gmTAJwRS5Ysqfbs2VNdd9111SWXXFI99thjzRJgkgmTAJxRW7durR599NFq7dq11ebNm5u5wKQSJgE441auXFnt27evDpWavWGyCZMAnBWl2XvdunV1s/eOHTuaJcAkESYBOKtuv/32ukL5wQ9+ULM3TCBhEoCzrjR7p1KZZu/9+/c3S4BxJ0wCMBbS7J0KZZq9Ey6d7Q2TQZgEYKyUZu+c7b1hwwYn58CYEyYBGDul2fvQoUPVtddeq9kbxpgwCcBYSrN3fjGnNHs72xvGkzAJwFgrzd4503vv3r3NXGBcCJMAjL1UJtPUnTFnV16HSenHmn2dmZmpf8KThSNMAjBxEhJyck6CQhlWrFhRN4mrXi6cnGGfC8wvXbp0ok6MSpeJxWTbtm3HPxf33HNPM3fhCJMATJR8OSbQ3HvvvfXtVCszHDhwoHrooYdcp/I0pYqXENLv0kwXXHBBPV6+fHk9HncJvZMWfOfDrl27mqmq2rlzZzO1cIRJACZGAs7GjRvr6fvvv786evRofaHzDJnOGeC5pFACBHPXDl0lOLYltOc4J6xPQrXv8OHD9bCYKpN5bVKdz1UQEvoTLBc6TAuTAEyMBMVIkLzpppvq6bY0decM8MXWrDlfctym7dgttsrkI488UgfoW2655fhn5OGHH67HC0WYBGAipCqZL8lUx/oFyX7KCRg5EzzTaQIv/SvbASOXHSrNu2XIuoP6X2b9sq0ypL9m7zZnW2eQUe/bb730lxv0GFk/z72sm+myfumDmq4C0d5u7hfleGZf+sl6ox7H3tem3Qc2+zXo2Peum2HQYxSzBeS5bLN3v8tx6veeah/DDINemy7PaZDSrH3DDTcc/+droX/zfuZo6tUwz/JB2P3koebW/Fl9xdJ62962i9NCva9YeGuuXHban9t8Id51113Vpk2bqq1btzZzh8uXdMLnmjVrjoek3M6XdGn+TB/M0nSeL99ly5bVzeWl39ndd99d3XrrrfV05L75oo/2+tle7pNtjrLOIIPu+/TTT9fPp+i336UfaZo3H3/88ZMepxy/6F0/ld6LLrqoeuCBB+rKbvazrBPr16+vj1s5nhlyuaa2uR7H9muze/fu+jHzOO37ZP7q1avr6cixSVjNumnGTd/ZYesP29+i6zbn+p4a9NrM9fGHyT9c2a88Zl7HSPDPfs5lO3MlTLIghEkWgjA5ueYjTOYLN1+wg5q4+8kXf76cI1/46VvZVr58I1/gqS4V7WUlJKSqlC/n7Efv+m1lX4et08+o2y/Pq99zKqGxfZzKc0mQyX3bsiyPUx6r7Hu2m+23tYNUCSsx1+MY7demHX6ihLGEq3YIzLYSSj/2sY+d9BiD1i+P0bv9tq7bjH7Hvyyfy2szl8cfJtXNhNb2a1e2k8fNNVsXgmZuAKZWOZs3EpB6lS/pfLm3v8gjVZxUQaP0OUsQKmEoP/U4m1HWaRt1+6XKddttt9XjtlT38pzvu+++Zs6J59mvopvn2X7u5fGH6W2qHfU4lubyKK9NAm5v0EvQyrKEz/ZjZVtZt/cxyvq9+14eo1/TctF1mxn6vafm+trM9fGH+cxnPlMfz/Y/AWU7CZXDjsPpECYBmFoJIxlSmer3pVwqR5dffnk97nXxxRfX4yeeeKIeR6o8kaboVIJSiepVmpOHrTPIKNsv+53+cVmnPeSxy/MuZnuebaMEjt5jOepxfO655+pxlH0sTfqD9Hvdso8JpuU5f+ADH6i31bvv5TFGCWRz3WaqrcPeU6O+NsWojz9IKpy5PFa7K0FkHxMus2yhTsQRJgGYCCV0tIPdKFKVGST9EOPSSy+tx4OUgBCpJKX/WZofU4VKk2aqSu3Qly/vfuukf9xsRtl+kb5wWad3iGefffZ4EBn1ecaowatt1O33VvIGvTbZh3Jpot7HStDK/W6++ebjz7f0Xey378Ne/6LLNgeFvLL+qK9NzPXx+ynV4VQ5SyBNl4mMi3ZFdD4JkwBMhFLdGrX/WNGvClRcdtll9fiZZ56px4Mk2LUl8GU/su004abqk9DXDov91kkgHjVQzrb9SMhNX9R+Q8JnCSKjPs8YFJLaegNO1+M47LUpVcz2YyUYJWglrKdvZnmumR4W8IY9p67bHBTyyvqjvjZdH78t2yvV8LxH2oE04xLiMx5le3MlTAIwEa6//vr6yzVflun/NYqsn2GQUu186qmn6nGvVAijBNleCQTph5gTKKLfdkZZZ5BB951tv3vNZf1BIamtN5B0OY7ltRkUblKZ7K3gJWDF9u3bT+ljGIP2fdhz6rrNQfs919em6+O35dqSkUDZDq3tIV09YiGauoVJACZCvmjL9Q3Tr7B9MkeRCk3ORi4VvFS+hlW/sm6kebG3GTl90FLZScUoJzEUuU/vugcPHmymXjTKOv0koIxy3xIMPv7xj9fjXtn39jZKiOu3ftZtVzzL5YCGhaHegNPlOJbXpl9YynFIZfLCCy8cKUyVvoj9DHv9hxm2zRi0X+VYjPraDFIef1BobSvXluyt/LaVM+oXoqlbmARgYqR6U84MTnDJ5aJSCcqQ6TQF9+uXN+gLOc3JZXu5b+ljlu2VL988ZluCV9bNOmXdfPEnLOVC0aOu008CyqD75izdEsaynex31i3HIOtm/3M7+16qVZGTMhI0yvrleZZ128Hxmmuuqcc5vlkn4ag3uPcezy7HMQZVjXMcSmWyLb/qEtluHiND+xqOvfs1W/Uz5rrNYrb31KivTe/jl9elPP5sYTrBNI/VexZ3r7wHsk4+H1l/PgmTAEyUNPuWE1QiX4zlyzSXXkmzYe+X6rAv5LK93L/0Mcv2Bm2rLMu4vW76yJXHyf1mW2eQQfftrWa197usm/3Pcck2es/qTR/MNJcnXJXnmfsmqLYrhpkuwTDrJHz0nqXd7zmU/cnxGuU4xrDKX6lMtmXfcvmh8hwyZLs5rnkuvfuV7WcYdsznus1i2Dbn8tr0Pn7WzXp5/MybTfn5xN7Xu593vOMd9TiPM59mjqYhHeZZ/qty0XLm20K9r1h483HRcmA8qUwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMMlEmpmZMSzCAYDxM3P0mGYa5k2++Hc/eai5BSx2a65cVvm6gemkMgkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0NnP0mGYa5s3MzEzlrcVCeOwLh5spJsmaK5f5mwBTSphkQSRMArT5uoHpJEwCANCZPpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHRUVf8/76ZBHolDVTQAAAAASUVORK5CYII=\" 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margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = CHP(Q,L,D,dh,n)\r\n   K = f(Q,L,D,dh);\r\n   isDLvalid = true;","test_suite":"%% Coarse sand #1\r\nQ  = 8.92e-6;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #1--larger cylinder area\r\nQ  = 3.57e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.1;                   %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #2\r\nQ  = 2.44e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 9.69e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1\r\nQ  = 1.52e-5;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.1;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1--reduced head difference\r\nQ  = 7.61e-6;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Medium sand #2\r\nQ  = 7.08e-7;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.3;                   %  Porosity\r\nK_correct = 1.2e-4;         %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Fine sand \r\nQ  = 3.57e-7;               %  Flow (m3/s) \r\nL  = 0.075;                 %  Sample length (m)\r\nD  = 0.075;                 %  Diameter of cylinder holding sample (m)\r\ndh = 0.4;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-5;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Silt \r\nQ  = 1.17e-7;               %  Flow (m3/s) \r\nL  = 0.05;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 3.88e-6;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nfiletext = fileread('CHP.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-08-18T23:24:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T14:41:04.000Z","updated_at":"2025-12-01T14:29:21.000Z","published_at":"2022-09-17T14:42:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. By supplying a flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is simply \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah/L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h/L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = (gd^2/(180nu))(n^3/(1-n)^2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = \\\\frac{g d^2}{180 \\\\nu}\\\\frac{n^3}{(1-n)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the porosity of the soil \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\rm\\\\,m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-6} m^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 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OpEm5dynLeGghLdUqtrrR9bP/WYz1+0kdGX/8pzyfCKhJtvIOMOP//iPV29+85vr55zQ+cADDxxflu1lyLI7fvmfVZ/8zX818DhdccUV1ZNPPlkvizx27rtmzZpq9+7dx49ltvvtb3+7DvfDjvso2+s9BrMd+97HSJ/Qm266qV42l32ZTfY1+/boo4/Wt3Ncs495v5R5bVn/TVdeUi2/YlX1F19+ZuTnBswPYXLMCJOLw7iFyUgF58CBA9Xy5cvrZuN+EmQiX9YlHOaL/O1vuaS68HV/vfqzP/uzel6RKlgqTO3QkW1k3sc+9rH6MYtcSieVvN7AkPVT7Yr24ybcXn311cf3+fHHH+8bgotUzRKkonc7l17+Y9Whb3z9lO187Wtfq974xjfWIaQ3xPR7bkW/ZdlWKnrZVm/wLevffffd1a233lrPK+Ev+3rZFX+9eurJk4/t6Wyv9xjPduz7Hd/8U5ATlrLNHMNUD0fdl9kkwL797W+v3vOe99S3B70Hii7PDZhHCZOMj2l6SY6F4nkfpsVCvs5dtv3tb3/76LEwUN93lOHYl3Zzz6NH169fX887FpyaOSfs27evXrZ27dpmzmBZ99zzzjtl3bL9Y4GkmXNC7pP9PhYkmjmDddlO5r/uwv77P+x591s223F62XknP07Zp9ynn67b63essizb6l027DHa5rovw2T97MfXnv1uM+dFx8Jg/Rh33HFHM+eELs8NmD/6TI6hVJYmfWhXnOZbms/6PeYkDZGKzbgo/SEj1Z1jfxv6DqlQ9Xrqz79Rj3fu3FlXlNpDKlLxuc99rj6Bpy3VrFSN2ut+/3vfq+e3HQsD9TiVpUFGOZu7nDAzbDvRu52c5f3sd37Q3Doh78NB+i0rjz/oOH3ney82xfYatL9dt3csdDVTJ+TzWl7b9vM/+JffqseXX355PR6kvEbD9iXVw9leo3jkkUeqn/qpn6pevey8Zs6L0n8yPvrRjw7czlyeGzCPjn1BMEbaFZ9JlrdWv8ri6Q5l25NuIV/nLsenVCYzDNu3fuuUitGwYVDFq9/QW8Eq2z8WjJo5JwyrSPXqsp3M71ctjWHVuH7L5nqcyj4NqujN9/Z6n39e48xLZba3Stiry3tgkGPBb+B7MPuTbfUe87k+N2B+qUyOmWF9vpge4/Y6t8/UHqbfOuW5pAp27G9K36FdIfvQhz5Un9CRatGxEHB8nS9/+ct1Zam3ejTqsZqPqlNvhTPXL3z5sWPTb9tzrUzO9TgVsz2v+dpeXtv288/+po9pzvD/8/2fq+cN0vW59cpJPOljOug1T6UzUtXvrXTHqM8NmF/CJHDSNSSHyTq9SnB66qmn6vFsvvjFL9bjcrmZ4oUXXryGYG+QmG37JdwOCiBFOYFj2H72Xq8y1y/ML+P02/aw60z2WzbX4xS55NGg5zXK8+n17WOvc7/tJWTlte19/qPu86tf/ep6PJd96ZV9yKWVfumXfqmZc6r169fX79GcdNXv7PC5PDdg/giTwJwqk73yBR+D+oAmNJazwKN8ofcGrlQr8/i91aNB2y9n8MYoVae1a9fW40HbKc+9dzvz1WdylOOUvqVt55577sDnNej5FL3bO+ecc+oqa7/nktckr20uOVRCfVxzzTX1uN9jtLf/vve9rx4P25f2e6Cfhx9+uK5K5r04SP75KNXJXMO0V79jVZ5bzPYeAboRJoH6S3a2yuSgdRLEcmHpVItyclEqZuXki9xOU2m7YlUuz5P11q1bVw8JX+Vknd7qUbZ/7bXXHt9+tpvrDub6jwkJWTZK1WmU7UTvdvLLKhe+7NQ/lXOtTI5ynHrDZAx6XtleAuqo20tIHPRcIq9tLvWT0Fkk3LWPWV6rftsf9NwSMsu6s1Ut77vvvuMBeZh3v/vd9Tjhsx18Y9CxynOL2d4jQEdHYQHkrdXvBJrTHcq2Gazr8cmJD7nv4SEn4AxbZ/fu3fVJDllehtze0+eEl5xAcSyUnrJetn8svDRrnexYWDlp28fCZz0/J13k/sP2u23YdnpP/viLv/iLej9vuOGGZs4JZTv9TsAZtmzU41ROKhl0PIpRt/f5A39Vb+9nfuZnmjkne81rXjPwON59990nvV45TuW4tc3lPdD2h3/4hyfdZ9QhxzlmO1bZ397XFpg/LlrOgkg14lj4a27Nn9VXLK237W07mOMDwJmkmRsAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmgYmxbt26ZopJ47WD6TVz9JhmGubNzMxMtfvJQ82t+bP6iqX1tr1tB5vm4+O1n1xeO5heKpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQAd7N+/v5qZmamuu+66Zg4sTsIkADSOHDlSLVu2rA6Jg4as07ZkyZJmarwl/G7YsOGU57Nq1apq7969zVowd8IkADQSDC+44IJ6evny5dXKlStPGq699trq8OHD9fKlS5fWQ2+4HEf33HNPdckll1T33ntvfbs8n0iQTKBct25dfRvmSpgEYOJ95evPN1OnJ8Hwueeeq0Pi448/Xu3Zs+ek4dFHH61WrFhRr5tQmWHcK5MJkhs3bqyn77///uro0aPHn0+md+/eXS976KGHqs2bN9fTMBfCJAAT7/3b/rTa8hufP+1QWSqTpfo4zKRUJrds2VKPEyRvuummerpt9erVdbCMu+66ayIqrYwXYRKAqfDZLxw+Hiq7BqJ2ZXI2s1UmH3vssbr5eLb+iVkvy/qdyJOq4mzLhlUTs072MU3a/YJkUZrw4+GHH67HMCphEoCpklC57p/9f9XHdzw950rlXCqTMSh0JsStWbOmDo5r166t1q9fX4e10j8xy4tUBtM/c9euXaeE4DS1R/Zn0LJsf5CyzihnnN9yyy31+L777qvHMKqZo+kwAfMs/y3vfvJQc2v+rL5iab1tb9vBpvn4eO3Pnrv//f7q3/3RV5tbk+Vv/w+vqza++8V+jqPI2dwJbwlpmW67+uqrq1tvvbWeztnROakl6z344IP1vEilMUEy9u3bd7yPZbSXtauaOcs6J8f0NkWXfYk0RZeTZiLL8vilibqfhMiE1EFN3G0JuOlb2ft8YDbCJAtCmDx7hEnG0UK/dtd9+I+bqRNecf451fve/erqp9+yvJkzmoS/AwcONLdOlupiTsKJVAoT5hLwyrxIs3P6Hg4KcP2WlyDX3n6pYqaqmaC5adOmauvWrScta6/fz1zC5KjbhF6auQGYKgmRW/7uj1af+pW3zjlItvtMpiKYANwe2iEry9vVxaJUCi+//PJ63Oviiy+ux0888UQ9jhL0ShUyPvvZz9bjhMnsT/uxyyV+StP0fCiPN6gPKAwiTAIwFdoh8pqrf7iZOzdz6TOZgNevz+TTTz9djy+99NJ6PEi7eTqPm+blVAczxM6dO+uqZ7ZT+l+WfpOHDr3Y8nPDDTfU40FSaYx2cB3k4MGD9fiyyy6rxzAqYRKAifcPb/qR0wqRRbsyOZtSmexVwtgzzzxTjwdJc3Jb6UuZ6z2mP2bCY5qpEzTLspxpnWVZJ+FztipiqYKWgDtMCbdXXXVVPYZRCZMATLy5NmcPMpfKZCR09p5lXaqBTz31VD3uVS4SXoJekabubG/Hjh11YMw+lGBXluVM60ceeaSed+ONN9bjYa6//vr6fgmfpeLZT/pspm9lzFbthF5OwGFBOAHn7HECzvx6z0f3Vl879N3m1nCvWfbS6rfvOHG2LSdM0vuynMGdM7GHVf4S+NIMnarhXM/mzv36nYWdSmRCX9ZJAEygLPtQluW+CX7tZcOUM8Wj34k427Ztq0/uiVFO1IFeKpMAQ7z/nW9opmY3l3UZX3OpTEZvZTLXjSzhLGd75zevE+hSsSwhc/v27fW4V6qNeex+zdi5f5YlSI7SxF3ksbJ+3HzzzXWwz7YScjNd9jV6nwuMQpgEGCJ98FJxnE3WOd3+epx9pc/kXPQLdbmET5qzczHyBMNUBlNVzJnZqVamuthPaZaO3hNhUpksRmnibkvlNPtT+mlmX3L5o+xfLlOUZXncXJ4oITNVVxiVZm4WRP7b1cx9ZuRLIZWFVCzyZZCqRb6oMp15t91229Q0W52t1/4PHv/L6s5Pfqm51V/OIhYmB/O5HX8J0qmilr6T7etawjAqkzDhEhxzpmZCZfkSKNOpgOj/dPoSEl9/0fnNrVOpSjINUmHNtSxLRXXUZnQQJmEKDPot3TvvvLOZ4nS95x2vb6ZOdeu75+dMYhgH6fOZZu7bb7+9mQPDCZMwBfLHP5WEtjRzl98Q5vQNqk6mKvm2N13Y3AJYfIRJmBK91UlVhfnXrzqpKgksdsIkTIl2dTJVSWFy/vVWJzOtKgksdsIkTJFSndRXcuG0q5O/8K5zmymAxUuYhCmS6mSuI6ev5MIp1ckMb3rTm5q5AIuX60yyIFxncu42b95cXzy4aF/jzbITy977D26v/t4tH66Onn9O9f3vfa867wc/VM/P7SNff75a+sr/pp6eef6F6nsv+a+ntbzMz3TGxZcO/lU9/tGL/1o9Lsvb4yjTp7sfk7484zVXLnOdSZhSwiQLQphkISzU+2q+JeSee955zS1CmITppZkbYJ4JksBiIkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnc0cPaaZhnkzMzNT7X7yUHNr/qy+Ymm9bW/bxclrP7m8djC9hEkWhDDJQshrz+TyuYXpJEyyIIRJFkJe+z3bmxtMlFUb5h4mjxw5Ui1ZsqS5BYwrfSYBGDsJkldffXVzCxhnwiQAY2f79u3VgQMHqm3btjVzgHElTAIwVlKVLCFSmITxJ0wCMFZ27NhRHT58uJ7OWKCE8SZMAjA2UpXcsmVLc+tFwiSMN2ESgLGRvpKlKlmoTsJ4EyYBGAvtvpK9hEkYX64zyYJwnUkWgutMTq5RrjO5f//+6nd+53eOX19y06ZN9ZDpzFu7dm21cuXKZm1gXAiTLAhhkoUgTE6uLhct91mHyaCZGwCAzoRJAAA6EyYBAOhMmAQAoDNhEgCAzoRJAAA6EyZhDDzwwAPVnXfe2dwCgMkhTMIYeOaZZ6o77rijuQUAk0OYhDGwZcsWF2cGYCIJkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAwIfbv31/NzMxU1113XTMHzj5hEoCptGzZsjp4JYBNk6VLlzZTp2dajw9nnjAJwNQ5cuRIPU7wmq/wdSZkv1N1TMjbu3dvM/dkhw8frpYsWdLc6mZSjw/jSZiERSRfIOVLpNBsxjRK2Lrgggvq4DVJ2iHxueeea6ZOKOGv93M8V5N6fBhPwiSMmQ0bNtThrgyrVq2qduzY0Szt7rHHHhv4RZR5p1vpgHGS93jCWN7bkyphr1fC33xVJif9+DA+hEkYI+nDdO+991bLly+v1q9fXw9p6rr55ptPO1CWL6Zsu98X0elWOmCctCtvo1Tf8s9W/nFr/yO3efPmUz4XpZKfZZlu//O3YsWKejuD9P6j2B7SMlCW79q1q16/vT/33HNPPS/aAXAuj9821+MDwwiTMCbyZZE/6mvXrq2/pLZv314PmXfttdc2a3W3cuXK6ujRowM726tMMm1K5W226ls+e2vWrKn/ccvnL//E5T533XVX/dnr94/W008/XX+m8s9f1s96Bw4cOL6dtty//KOY+2T9jIvcTjj9uZ/7ueOPHWVfMlx//fX1vMjfhD179hzfZpYPe/xBRj0+MBthEsbEzp076/GNN95Yj4uEvEcffbS66aabmjkLY9oqk199tplg0RqlT2D+udqyZUtdsc8/Ww8++GD9T9yhQ4eqTZs21cHs4YcfbtY+0WfxoYceOv4PWtbPZ/T++++v18n92tKqkP1IOE0IzPoZJyxGwuDq1avrIcsSCCPbye0MqTpGefwEx1Eff5BRjg+MQpiEMZEmrXjiiSfq8Sj6Nc3ldr/qY+Zl+bp165o5J5u2yuTv/V9V9dNbqurTx8YsPvnnqN8JLL0S8BKotm7d2sw5ISEvyj96kXUzJMglwLW99a1vrce9Ae3xxx+vx70tDCU0PvXUU/W4GPaPXZfH72fU4wOjECZhTJQqRb7cRukf2a9pLl9WuX3JJZec1MeqSEVj0BfVtFUmI9XJf/qbQuViVPoEzmbfvn31OIEx/Q/bQz6LkX/E2p+PfI5KpbAt81LhjPb6aY6ei9n+sZvt8Z999tlZP8+jHh8YhTAJYyKVhtI8lRNuUkVMqOz3pZCK5MaNG+vpfBmWprlUKnbv3l3Pz/J+9x30RTVtlck2oXLxyXt/Lmcrp9k6/Q97h6L9+RhW+SvVvvb6F198cT0uJ9YUpeJ5+eWX1+NitiA4TB7/wgsvnPXzPNfjA8MIkzBG0tSWMFiawxIq88e+t8pYmrfSR6q3QpF+VyWUtvt6FYO+qPrNz0kB7Sb0sz3Eqg2jDff+Xr36SdqhUp/K6ZYwNUqfwBK60ocx/Q/7DVlW5PM4LIDlMXsrgzl5JvfJ5zLdUFL1zDjhMq0K+UeybbYgGIM+x6XaOGh5MerxgVEIkzBmEgYTFlNxLF8yqTIm2BXly623olGUSki//peDvqj6zU+47ffleraG2LN9tGH9T9Wrn+Jv/c2quufDVfW6C5sZTK1R+gSWJujefouDJHwNCmAJcP0qg+mCkvtknM91Kp7pjpJm9LQq9JotCEa/z2t5/Bj0OW8b5fjAKIRJGFOpOCY0ljM088VTvmRyWZK49NJL6/EgZb22QV9Uo3yBTbKEyN+9s6r+8f8sSC4Wo/QJLCfZtP9Za0uXkt5L7aTK2O/zkgBXKpNt+RymL+O2bdvqs8TLP0e33357s8bJysl4wwLusMePUT7PoxwfGIUwCWMulwQqzWrPPPNMPb7sssvqcbk9SFmvbVDFYpRKxiQSIhenhKlSebv66qvrgNYeylUNSl/lXGonXSmyrJyAk9s5ya1fqBv0eSmVybb0x8z8fI7b3TbKfvRefaG0LKSbS/YjFzTvPSlv2OPHbJ/nUY8PjEKYhAnQW0HIH/sYVLkoJ+FcddVV9ThKIB1UsRilkjFJVv6YELmYJUyVz02CYqqL7aF9hnbpq5xgmWXl5JvcTutAv2u8Dvq89KsMJkymmTvVyVRCy1CW5eoL7V+uufXWW4/3e85+pG/lqCfp5PHnejZ3v+OT5z3bNqCYOVo6IsE8yn/du5881NyaP6uvePE/+2l72+aLLZWA22677ZQvrlQm2l9skS+eco269MFqn4RTlrXXjzxGvrTS4b/dTyvzs27u06//1jjJa5/+kEyenBQ118/tNHzWy+ex93NX5OS69IlON5ZBzd4w7lQmYUwkFJZLAiUcpvqY6QTJyKV/ivYZ2wmICaLlDNESMtvrF6U62Y8qBMy/Uv0bdK3JgwcP1uPStA2TSJiEMZDwmKalNH0l8JVmp8i8VGdSPWxrN82Va+SVbbTPBG8bdhmQ2fpYAXOXk+Tymc7nM/8clv6Y+QcwATMVyXxWF/rnUmEhaeZmQeSPpmZu5ltee83ck2mxNnNHqv45kzuX/Cr/JEZCZLq23HDDDf6ZY6IJkywIYZKFIExOrsUcJmHaaeYGAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQDGwt69e6tVq1ZV1113XT2O9u0dO3bU84DxMnP0mGYa5s3MzEy1+8lDza35s/qKpfW2vW0Xp7z2e7Y3N5goqzZUI31uV6xYUR04cKC5dcLSpUurQ4fm/28KcPpUJgEYG/fdd18zdbI777yzmQLGjTAJwNhYvXp1tXz58ubWi1KVvPXWW5tbwLgRJgEYK73Vydtvv72ZAsaRMAnAWGlXJ1OVFCZhvAmTAIydUp3UVxLGn7O5WRDO5mYh5LVncs31c5tLAj366KPNLWBcCZMsCGGShbBQ76vF6lvffK768r6nqjde9eI1HRfSmiuX+dzClBImWRDCJAtBmJx/7/7vVtShMn0UV7zxb1SvX3F59Zb/fk31mh95Q7XsVRc1a50+YRKmlzDJghAmWQjC5Pzb+Vt3V//71juaWyc797zzqgf/wxeqV7zygmZOd8IkTC8n4AAsYmvXfWBgWPz7v/DL8xIkgekmTAIsYkfPP6d674d+sbl1wtvWvKu68b0bm1sAgwmTAItcQmNvBfLwN/5zdegbX29uAQwmTAJwUnXyf9vxmep/fOfPVu9751urRz71b5u5AP0JkwAcr05+cPNH60sF5fbW33iw+o1//kvV//pPP1zNPP9CsybAyYRJAGoJj+1+kgmVO3d/sTr0l1+v/s7fWlVfkxKglzAJQK3fxctzgs7/8i9/u/rb791Q/cOb3qHZGziFMAnArFKxTF/K3/rEx6pf/tB7NHsDxwmTAIzkDZdcXv3bT++pL2au2RsohEkARpZm74/86r+q3vsPfrF637uc7Q0IkwB0cP3P/p3qX//+f6ybvX/lw3+//n1vYHESJgHoJM3e/+eu/6c697yXVht+9ierzz+xp1kCLCbCJACn5Rfv/Jd1s/cvb/y56tM7/nUzF1gshEkATluavf/FJx+ufu+Bf1Pd8b53avaGRUSYBGBepNl7+6f+sPrh5VfWP8Wo2RsWB2ESgHn1j/7xr1b/6J/8at3svfO37m7mAtNKmARg3r1tzbuqe3/3/64+86kd9UXOgeklTAKwIJa96qK62fs1P/KG+vaf/Mmf1GNgugiTACyoD27+aD3+iZ/4iWrbtm31NDA9hEkAzojDhw9XDz74YLVq1arqyJEjzVxg0gmTAJwRS5Ysqfbs2VNdd9111SWXXFI99thjzRJgkgmTAJxRW7durR599NFq7dq11ebNm5u5wKQSJgE441auXFnt27evDpWavWGyCZMAnBWl2XvdunV1s/eOHTuaJcAkESYBOKtuv/32ukL5wQ9+ULM3TCBhEoCzrjR7p1KZZu/9+/c3S4BxJ0wCMBbS7J0KZZq9Ey6d7Q2TQZgEYKyUZu+c7b1hwwYn58CYEyYBGDul2fvQoUPVtddeq9kbxpgwCcBYSrN3fjGnNHs72xvGkzAJwFgrzd4503vv3r3NXGBcCJMAjL1UJtPUnTFnV16HSenHmn2dmZmpf8KThSNMAjBxEhJyck6CQhlWrFhRN4mrXi6cnGGfC8wvXbp0ok6MSpeJxWTbtm3HPxf33HNPM3fhCJMATJR8OSbQ3HvvvfXtVCszHDhwoHrooYdcp/I0pYqXENLv0kwXXHBBPV6+fHk9HncJvZMWfOfDrl27mqmq2rlzZzO1cIRJACZGAs7GjRvr6fvvv786evRofaHzDJnOGeC5pFACBHPXDl0lOLYltOc4J6xPQrXv8OHD9bCYKpN5bVKdz1UQEvoTLBc6TAuTAEyMBMVIkLzpppvq6bY0decM8MXWrDlfctym7dgttsrkI488UgfoW2655fhn5OGHH67HC0WYBGAipCqZL8lUx/oFyX7KCRg5EzzTaQIv/SvbASOXHSrNu2XIuoP6X2b9sq0ypL9m7zZnW2eQUe/bb730lxv0GFk/z72sm+myfumDmq4C0d5u7hfleGZf+sl6ox7H3tem3Qc2+zXo2Peum2HQYxSzBeS5bLN3v8tx6veeah/DDINemy7PaZDSrH3DDTcc/+droX/zfuZo6tUwz/JB2P3koebW/Fl9xdJ62962i9NCva9YeGuuXHban9t8Id51113Vpk2bqq1btzZzh8uXdMLnmjVrjoek3M6XdGn+TB/M0nSeL99ly5bVzeWl39ndd99d3XrrrfV05L75oo/2+tle7pNtjrLOIIPu+/TTT9fPp+i336UfaZo3H3/88ZMepxy/6F0/ld6LLrqoeuCBB+rKbvazrBPr16+vj1s5nhlyuaa2uR7H9muze/fu+jHzOO37ZP7q1avr6cixSVjNumnGTd/ZYesP29+i6zbn+p4a9NrM9fGHyT9c2a88Zl7HSPDPfs5lO3MlTLIghEkWgjA5ueYjTOYLN1+wg5q4+8kXf76cI1/46VvZVr58I1/gqS4V7WUlJKSqlC/n7Efv+m1lX4et08+o2y/Pq99zKqGxfZzKc0mQyX3bsiyPUx6r7Hu2m+23tYNUCSsx1+MY7demHX6ihLGEq3YIzLYSSj/2sY+d9BiD1i+P0bv9tq7bjH7Hvyyfy2szl8cfJtXNhNb2a1e2k8fNNVsXgmZuAKZWOZs3EpB6lS/pfLm3v8gjVZxUQaP0OUsQKmEoP/U4m1HWaRt1+6XKddttt9XjtlT38pzvu+++Zs6J59mvopvn2X7u5fGH6W2qHfU4lubyKK9NAm5v0EvQyrKEz/ZjZVtZt/cxyvq9+14eo1/TctF1mxn6vafm+trM9fGH+cxnPlMfz/Y/AWU7CZXDjsPpECYBmFoJIxlSmer3pVwqR5dffnk97nXxxRfX4yeeeKIeR6o8kaboVIJSiepVmpOHrTPIKNsv+53+cVmnPeSxy/MuZnuebaMEjt5jOepxfO655+pxlH0sTfqD9Hvdso8JpuU5f+ADH6i31bvv5TFGCWRz3WaqrcPeU6O+NsWojz9IKpy5PFa7K0FkHxMus2yhTsQRJgGYCCV0tIPdKFKVGST9EOPSSy+tx4OUgBCpJKX/WZofU4VKk2aqSu3Qly/vfuukf9xsRtl+kb5wWad3iGefffZ4EBn1ecaowatt1O33VvIGvTbZh3Jpot7HStDK/W6++ebjz7f0Xey378Ne/6LLNgeFvLL+qK9NzPXx+ynV4VQ5SyBNl4mMi3ZFdD4JkwBMhFLdGrX/WNGvClRcdtll9fiZZ56px4Mk2LUl8GU/su004abqk9DXDov91kkgHjVQzrb9SMhNX9R+Q8JnCSKjPs8YFJLaegNO1+M47LUpVcz2YyUYJWglrKdvZnmumR4W8IY9p67bHBTyyvqjvjZdH78t2yvV8LxH2oE04xLiMx5le3MlTAIwEa6//vr6yzVflun/NYqsn2GQUu186qmn6nGvVAijBNleCQTph5gTKKLfdkZZZ5BB951tv3vNZf1BIamtN5B0OY7ltRkUblKZ7K3gJWDF9u3bT+ljGIP2fdhz6rrNQfs919em6+O35dqSkUDZDq3tIV09YiGauoVJACZCvmjL9Q3Tr7B9MkeRCk3ORi4VvFS+hlW/sm6kebG3GTl90FLZScUoJzEUuU/vugcPHmymXjTKOv0koIxy3xIMPv7xj9fjXtn39jZKiOu3ftZtVzzL5YCGhaHegNPlOJbXpl9YynFIZfLCCy8cKUyVvoj9DHv9hxm2zRi0X+VYjPraDFIef1BobSvXluyt/LaVM+oXoqlbmARgYqR6U84MTnDJ5aJSCcqQ6TQF9+uXN+gLOc3JZXu5b+ljlu2VL988ZluCV9bNOmXdfPEnLOVC0aOu008CyqD75izdEsaynex31i3HIOtm/3M7+16qVZGTMhI0yvrleZZ128Hxmmuuqcc5vlkn4ag3uPcezy7HMQZVjXMcSmWyLb/qEtluHiND+xqOvfs1W/Uz5rrNYrb31KivTe/jl9elPP5sYTrBNI/VexZ3r7wHsk4+H1l/PgmTAEyUNPuWE1QiX4zlyzSXXkmzYe+X6rAv5LK93L/0Mcv2Bm2rLMu4vW76yJXHyf1mW2eQQfftrWa197usm/3Pcck2es/qTR/MNJcnXJXnmfsmqLYrhpkuwTDrJHz0nqXd7zmU/cnxGuU4xrDKX6lMtmXfcvmh8hwyZLs5rnkuvfuV7WcYdsznus1i2Dbn8tr0Pn7WzXp5/MybTfn5xN7Xu593vOMd9TiPM59mjqYhHeZZ/qty0XLm20K9r1h483HRcmA8qUwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMMlEmpmZMSzCAYDxM3P0mGYa5k2++Hc/eai5BSx2a65cVvm6gemkMgkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0NnP0mGYa5s3MzEzlrcVCeOwLh5spJsmaK5f5mwBTSphkQSRMArT5uoHpJEwCANCZPpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHRUVf8/76ZBHolDVTQAAAAASUVORK5CYII=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57620,"title":"Compute frequency factors for the normal distribution","description":"In frequency analysis in hydrology, the streamflow  corresponding to a specified exceedance probability  (or return period ) can be computed as\r\n\r\nwhere  and  are the mean and standard deviation of the streamflow series, respectively, and  is the frequency factor. \r\nWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.242px 8px; transform-origin: 156.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn frequency analysis in hydrology, the streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.95px 8px; transform-origin: 164.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to a specified exceedance probability \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.6667px 8px; transform-origin: 32.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or return period \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = 1/p\" style=\"width: 55.5px; height: 18.5px;\" width=\"55.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT = mu + KT sigma\" style=\"width: 89.5px; height: 20px;\" width=\"89.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eμ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eσ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.592px 8px; transform-origin: 249.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"KT\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.275px 8px; transform-origin: 74.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the frequency factor. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 8px; transform-origin: 373.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function KT = normFreqFactor(p)\r\n  KT = trapz(QT:inf,exp(-Q.^2));\r\nend","test_suite":"%%\r\np = 0.001;\r\nKT_correct = 3.090;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.002;\r\nKT_correct = 2.878;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.01;\r\nKT_correct = 2.326;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.02;\r\nKT_correct = 2.054;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.04;\r\nKT_correct = 1.751;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.1;\r\nKT_correct = 1.282;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.2;\r\nKT_correct = 0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.3;\r\nKT_correct = 0.524;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.5;\r\nKT_correct = 0;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.8;\r\nKT_correct = -0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\nT = [5 10 20 25 50 100 250 500 1000];\r\nKT_correct = [0.842 1.282 1.645 1.751 2.054 2.326 2.652 2.878 3.090];\r\nassert(all(abs(normFreqFactor(1./T)-KT_correct)\u003c1e-3))\r\n\r\n%%\r\np = rand(1,randi(15));\r\nK1 = normFreqFactor(p);\r\nK2 = normFreqFactor(1-p);\r\nassert(all(abs(K1+K2)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('normFreqFactor.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp') || contains(filetext, 'interp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-29T19:23:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-29T19:23:11.000Z","updated_at":"2026-01-04T12:13:24.000Z","published_at":"2023-01-29T19:23:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn frequency analysis in hydrology, the streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to a specified exceedance probability \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or return period \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = 1/p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = 1/p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT = mu + KT sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T = \\\\mu + K_T \\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"mu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"KT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the frequency factor. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59034,"title":"Compute the maximum length of a contaminant plume in groundwater","description":"Problem statement \r\nWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of , and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s maximum contaminant level, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity , the magnitude of the head gradient , effective porosity , bulk density , and soil organic fraction . Along with the MCLs, the properties of the contaminants provided to the function are the half life  and the octanol-water partition coefficient .\r\nCompute the longitudinal dispersion coefficient as , where  is the average linear velocity and  is the longitudinal dispersivity. The variable aL will be specified as either a number or ‘X\u0026E’. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026 Eckstein (1995):\r\n\r\nwhere  is in meters if the flow length  is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\r\nBackground\r\nContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration  of the contaminant in time  and spatial coordinate  can be computed with\r\n\r\nThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where . Retardation is included in the retardation coefficient . The maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a second-order linear ordinary differential equation with constant coefficients, which can be solved with the boundary conditions  and . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 605.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 302.95px; transform-origin: 407px 302.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 151px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75.5px; text-align: left; transform-origin: 384px 75.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 350.983px 8px; transform-origin: 350.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"C0\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.525px 8px; transform-origin: 157.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.967px 8px; transform-origin: 325.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.358px 8px; transform-origin: 114.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the magnitude of the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18.5\" alt=\"|dh/dx|\" style=\"width: 49.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.2083px 8px; transform-origin: 58.2083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, effective porosity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"ne\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, bulk density \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rhob\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.125px 8px; transform-origin: 29.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and soil organic fraction \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"20\" alt=\"phio\" style=\"width: 17.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.217px 8px; transform-origin: 302.217px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" alt=\"T_1/2\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the octanol-water partition coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"22.5\" height=\"20\" alt=\"Koc\" style=\"width: 22.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.875px 8px; transform-origin: 155.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the longitudinal dispersion coefficient as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65.5\" height=\"20\" alt=\"DL = aLvL\" style=\"width: 65.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"20\" alt=\"vL = (K/ne)|dh/dx|\" style=\"width: 123.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.808px 8px; transform-origin: 105.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the average linear velocity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.417px 8px; transform-origin: 136.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal dispersivity. The variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eaL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.367px 8px; transform-origin: 121.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be specified as either a number or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e‘X\u0026amp;E’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.275px 8px; transform-origin: 88.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"138.5\" height=\"21\" alt=\"aL = 0.83(log10(L))^2.414\" style=\"width: 138.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAACGElEQVRYR+1WK0sFQRS+t5u0GRTUYLCKQawKFpuKQUw+kogo6A9Q8BFMPhCDwVezCBoFwUexadBgMimIdv0+OGcZh5md3Xvvwg0z8LG7dx7nO+d858wtl+pklOuERykSsTMRIxIjEqrOqJGokaiRUAQq1Ug/Ns4DLcCX4ADPOaAHGACu8ho314fKtxGLjwESWQZ2gU+gG7iXg37wbJXfK+aSRoQkboBOIbFqWfmVb0aCEalq+IiYJPZgYcphRYkwUjbJ3KR8RC4lHe94djnCzlRxDUcH8JrbsrXBRcQ04vOWWpkEnoHeavVBTi4it/idleCLBtP2BjQAZ8CIIxrtks4FmaOgj4B94MEVPZsID3iRhT4ja5hXAzN430lJy7cQ9uks2WoTmcbMtsy6jJDooxzOZU0paTGdCvYZm4jp7SiMnBreaiWxoTF1qg8abLPWcps6xRT3AamCTouIKVQlcYgDxwH2FqZuAzgHhhy5pxPDQKY+YxMxhUivmFuOMWAFYL/Q/kFPOSbEmHwmD9VHpj7jK98t8ZpqvxDPVe3aY+jppoeEeQVk6jOhu8b2Muv3kkSQUWvOsqkoItqLgmWrJIsgQp19iAG78tQuU8eRNLciiLDTngBpZfuE+VlTX0UQ0bJ16YPRYsNkX/l3mdaSCI2wb6wDvIc47oBreeefp0GZ45pFU8S1JJKlOLxrIhE7NDEiMSKhkvoDUHNpKZCsq0AAAAAASUVORK5CYII=\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters if the flow length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 8px; transform-origin: 250.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8px; transform-origin: 383.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.0083px 8px; transform-origin: 84.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the contaminant in time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 8px; transform-origin: 72.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and spatial coordinate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.1667px 8px; transform-origin: 15.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.95px; text-align: left; transform-origin: 384px 19.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"170\" height=\"40\" alt=\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\" style=\"width: 170px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 108px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 54px; text-align: left; transform-origin: 384px 54px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.05px 8px; transform-origin: 311.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKMAAAAoCAYAAACSG0qbAAAG7UlEQVR4Xu2bS+hvUxTH752T14iJGwaUpOQRMTCgRJLyTgbyKhl4hMHtn0RhIuUVkgw8MpBSJAMiz6IUA4oSI6+Y8/1cZ13rd+4+56y9z/md//n571+t7u/+ztl7r73Wd6+19lrrv3tX/VQJLEQCuxfCR2WjSmBXBWMFwWIkUMG4GFUUMXKPRj1YNHKBgyoYF6iUIEs36b2HRQcH31/8axWMi1dRJ4Nv6cn3ohs3dwurnO80MB6r7V8mekr06wYr8XDx/ovoNNGnG7yPFdZzwYgSrxL9KDphQ4Rwnvi8VHSO6PiG57mUCGjuFl3k1v5Z398X3TziQBAr3io6KqED3PcTI3QDfyeO4K146Rwwtjd5r1bdhOD5VPF5mOh50ZEzgpF1X3drtpX0l344WfRdgfa+1pg3RHclxr6s37D+b4ueE33m1vhT3w9qxnAYnmy+w+sLIg7rK6LLC3gaPSQHjD9ptcdEWMcfRB+Kzh/NwXwTPKSl7myWm8MyAphDRC+K3mnWxULjWQwQADL3AkKo8a3oOAcyL0X0lLK8AO4T92J7vM3rQTqfdrRSFIxs5H4HPk7fSaJNcdUIdU4wmhu9WOu2Yzpc91cis9K5ymcfuP2U7M0an50Aqt//N3p+lqgdN//dA/K1AzMKRk7Nb475PoGsnenCBeYEI9bpPpG5wTbLPuTJdYt9c+NejxGlwqeP9PvpDSNP69/ULRxrngJpocjzhkXB2J61grFbzhxc3GTqcmGj7DbM/4ntouGOudojElZtSPNYPftcoS94t0V9Khj/VQfgIOi/RHSmiDiOW/jtzb+8g2u7UFRy4Ugp3cDRZaVSYwDQoRngtTnYC3lJPsSpR4sWl9oqBSMmn0vMtty6Co9zl5smvuNWCxhNWaRGiMvea36zS8dUivSWMcdKcRu+XpRr1fzeP9b4MwpluNZhJWC0jeWcaL8J7y5KN5fj2myNoZiReMnykMx/pbMePsbLvXCk9sghfklETq/PnfuxjHlGlHv7Zg6/N0qIqZRQqS4mG5cLRm/u/29gtAA/lW7xliz3wpFSluUCc6wibvZ3Ua438rzDC/Eph21xnxwwsilcs+XISsG4XUIYsox9YIRns+glVtnv2fJ5OfOMKf+ZFYaHOaorhD2flwA+B4ycTCwjG/pDtCXKjV22C4isuxQwAno+F4iilwjChL2iqEv3cqZIcUPzQ84BKNVVcXooCkbQ/kDDHa6F2KUkkC7d4BTjlgBGeLhGlEqG9+2xr/w3JBsfL+aUcLHGXORyihuknu4Q+VDC5iERT6KfMIh5D4hbI2D0ZSSLl3BZOfHOkMDmeL7dYDTrlgvEofJfn+xsrL3TVUL0cwAeEuLXirjQkdKKVtqwwu+KzGMy1wcishKviU4RcSAI9Q641Q+B0ZeucM9WZhoDxqXeptcZM5YCEZCMKTD4LEBXCbANZnROYwlAJjTLASNW2AMXj7qnAbet443bSo/AEBjt1sdEZgnttHnLyG/RZPBOA2MEiACgK360BpWSDimvv9wsgGVOomDENZ/bAh5gviWBDQsdVrxrHxi76qfGpE3Ee9RDF5m7csd+O9y0NS5cJz660inmylI14THlP7YOkK0hIzesygUjwH9EFGn2NS8UsowIAd+Pb2+XwYxJThoJYDpQcuMgh5HZvs4NRpPhm9rhsx27xB1uiYipUo0LxGB7RNHatV+m3TKWW8/OAaMdqGhsySHhs9LE22UZ/Q2snSRtB8UEojlpitnQ11rId62krIS3Im3F+WR/xG35wzy0X26X9DmmLCflP3owu7p/+ua2VJy9s04w4h05WJFQorNvMgVGH2d0JbbtHYB4tSgaLw4pZh3PEdRtIiv1sQYAwGLhVhAi7V7WXsVzLms0EiNcgnC7ARp/7Ju2/5RLQthfiKw4MLSnLnCXlP9YGwvr/8zB1mcdusNp9I1UYHIsIwc9igNr9vDl1n08Dl1ghgRZn69PApYeyS3/TcVRFIwcgMdFkVCCOR8VJbufKhinUt2081j5bzvryFEw4jlovB4KJazPM9WFXi3jtPiZdLYx5b+pGImCMVL+43ARFlHS7AwRqmWcSnXTzkMM9mUT/007c3y2CBhT5b/2CnbT3tKDdi8DGY5XRfti7wrGuHLmenNM+W9KHq3bpy970C7/pdb3fyXpn9NtDu3PxFQwTqm+aeYiBqMuHM3ZTbPqf7PYn2D4DAQNufstmFuQdFhfJ5HPzKT4XGncqGCcWpXj58M9ciGIVDLGr1Y+Q6r8Vz5bddOjZLfTB+eU/0KyqpYxJKb6UksC1s1V0uzbKcwKxoqzEgkQStCbGCn/heevYAyLqr64bglUMK5bwnX+sAQqGMOiqi+uWwL/APsLujiQmfdNAAAAAElFTkSuQmCC\" width=\"81.5\" height=\"20\" alt=\"lam = ln(2)/T_1/2\" style=\"width: 81.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Retardation is included in the retardation coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"20\" alt=\"R = 1+rhobKoc phio/ne\" style=\"width: 122px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 8px; transform-origin: 151.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which can be solved with the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" alt=\"C(0) = C0\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18.5\" alt=\"C(infinity) = 0\" style=\"width: 66px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Lp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\n%  See the text suite for the definitions of the parameters\r\n   v  = K*dhdx/ne;\r\n   Lp = (C0-Clim)/v;\r\nend","test_suite":"%%  Dieldrin and styrene\r\nC0   = [1 15];                  %  Source concentrations (mg/L)\r\nClim = [2e-4 0.1];              %  Maximum contaminant levels (mg/L)\r\nK    = 87.5;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.002;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.25;                    %  Effective porosity\r\nrhob = 2.5;                     %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [25120 380];             %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [1825 182];              %  Half lives (d)\r\nLp_correct = [20.76 58.95];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene, toluene, ethylbenzene, and p-xylene\r\nC0   = 30;                      %  Source concentration (mg/L)\r\nClim = [0.005 1 0.7 10];        %  Maximum contaminant levels (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.04;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.22;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [97 242 622 552];        %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [300 20 120 190];        %  Half lives (d)\r\nLp_correct = [1501.21 20.69 54.12 24.98];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Glyphosate\r\nC0   = 13.9;                    %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 30;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0005;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.18;                    %  Effective porosity\r\nrhob = 1.9;                     %  Bulk density (g/cm3)\r\nphio = 0.001;                   %  Soil organic fraction\r\nKoc  = 4e-5;                    %  Octanol-water partition coefficient (mL/g)\r\naL   = 2.8;                     %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 115.59;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  1,4-dioxane\r\nC0   = 10;                      %  Source concentrations (mg/L)\r\nClim = 3e-4;                    %  Limit set by Massachusetts (mg/L)\r\nK    = 7.77;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.01;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.21;                    %  Effective porosity\r\nrhob = 1.8;                     %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = 1;                       %  Octanol-water partition coefficient (mL/g)\r\naL   = 3;                       %  Dispersivity method\r\nTh   = 1;                       %  Half life (d)\r\nLp_correct = 16;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene\r\nC0   = 2;                       %  Source concentrations (mg/L)\r\nClim = 0.005;                   %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 97;                      %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 263.93;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  p-xylene\r\nC0   = 200;                     %  Source concentrations (mg/L)\r\nClim = 10;                      %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 552;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 190;                     %  Half life (d)\r\nLp_correct = 26.74;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Ethylbenzene\r\nC0   = 100;                     %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 622;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 120;                     %  Half life (d)\r\nLp_correct = 29.83;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Nastene, phylthene, siccanol (fictitious chemicals)\r\nC0   = [10 10 20];              %  Source concentrations (mg/L)\r\nClim = [1 2 0.1];               %  Limits (mg/L)\r\nK    = 0.2;                     %  Hydraulic conductivity (m/d)\r\ndhdx = 0.008;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.08;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = [15 80 2];               %  Octanol-water partition coefficient (mL/g)\r\naL   = 2;                       %  Dispersivity method\r\nTh   = [30 100 475];            %  Half lives (d)\r\nLp_correct = [2.6 1.83 72.39];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-01T15:59:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-01T15:47:36.000Z","updated_at":"2026-02-12T14:03:58.000Z","published_at":"2023-10-01T15:59:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the magnitude of the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, effective porosity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, bulk density \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rhob\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho_b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and soil organic fraction \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phio\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the octanol-water partition coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Koc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{oc}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the longitudinal dispersion coefficient as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"DL = aLvL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_L = a_L v_\\\\ell\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vL = (K/ne)|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_\\\\ell = (K/n_e)|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the average linear velocity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal dispersivity. The variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be specified as either a number or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘X\u0026amp;E’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL = 0.83(log10(L))^2.414\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L = 0.83(\\\\log_{10}L)^{2.414}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters if the flow length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the contaminant in time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and spatial coordinate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t}+\\\\frac{v_\\\\ell}{R}\\\\frac{\\\\partial C}{\\\\partial x}=\\\\frac{D_L}{R}\\\\frac{\\\\partial^2 C}{\\\\partial x^2} - \\\\lambda C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"lam = ln(2)/T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda = \\\\ln2/T_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Retardation is included in the retardation coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = 1+rhobKoc phio/ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = 1+\\\\rho_b K_{oc} \\\\phi_o/n_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which can be solved with the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(0) = C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(0) = C_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(infinity) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57452,"title":"Design a well field in an infinite aquifer","description":"A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand  (i.e., volume of water per time) with the constraint of lowering the water table by no more than , the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity , the specific yield , and the initial saturated thickness ) and the radius  of the well. \r\nThe Gupta/Chin method for designing a well field has the following steps:\r\nCompute , an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance ) is . Compute the transmissivity to be . Evaluate the drawdown at a time  1 year. Realize that for small values of  the unconfined well function* can be approximated and compute the pumping rate from  where  and . \r\nCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \r\nSet the pumping rate to . \r\nArrange the wells so that they are equidistant from the central well.\r\nDetermine the distance  between the central well and others so that the total drawdown at the central well is . In other words, add the drawdown from the central well to the drawdown from the other wells. If , then \r\n            \r\n Write a function to design a well field using this method.\r\n\r\n\r\n*http://www.aqtesolv.com/neuman.htm","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 895.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 447.692px; transform-origin: 407px 447.692px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 43.5px; text-align: left; transform-origin: 384px 43.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.242px 8px; transform-origin: 375.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA well field provides water for a community. The design of a well field involves a goal to meet a specified service demand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_d\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292.875px 8px; transform-origin: 292.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., volume of water per time) with the constraint of lowering the water table by no more than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAoCAYAAABTsMJyAAADSUlEQVRoQ+2Yu49NURTGZ/4AEY9KVB6FaiQeDQoSz6llvKIhnlFQkHgkCsTIjIpBoZF4RZQEBQWReCUUokGmUHoU/gC+H2udLHuOe0/OcU+um7OTL2ffc/Ze61vPvWf6+3po9PeQLX2NMd0azSYyTWRq8ECTZjU4uZSKJjKl3FbDpiYyNTi5lIqikVlq0t/p+UUYED7ZvJTiTmxqZ8xJKT0svBRuCTuEb8JCYfr/ZMwGkb0ufBDmmCen6fnM5v6uE04uJbNVZO5J4mqLypoQBaK1SlhUSmMHN7UyZkx6d5vuZXo+sTn1Mk+40UFepUS3Moaif2xSqZkh4WMpLTVtatcA8D5GMC4Ix0K61USxuJp2xnjBzzaRh/Q8U1x8vSvbGQMbauS10aItz+3W6OQZQ2rtTQjHZjCob3fr9XkxbakxpNVnYb7wJoiIzSB2tqgl3gpm6cMMwW8MrMt7V4zl71XInyR4V4UrXTXTkRrjpE9p0ZGgaZ3mdwTSbGpi5Cb99hbOreCA/Z6iJ3LOCucFzibepXUHKfZQlxzQrGEtHZSDGyesFLYL3Dxw5nfhtu3J5KXGRNJbtJh0QthNE5RGDLu8pu5rTuseF54KtHUUrRf2CzMFbhTRUex9JJwWLgvc+7yDbrQ5Ohg7hYu2f4Gee0yff5/wfzM8MVl4K6wV2MR4Zcryzhm/9uDJBwIRPSgMC7wbNVJ+o/Cac0Oe6/tmMwRdvi69+8VGlFu3RbpZZvlfJt4cIO7XHvcuZxMeZPywp5N00mm0v2od6ZZ3XUJGvCv+QelfGPNeEsn32BggRO47ca9FDIakpzOpiQN8eJTTmuV7PPPQNyFLqhrjoXeSKHXi1BnkGDHfSUP/02KX5pdsTSSbl0ZEGyNoAmk9/RJR1RgnGTuU10sk5GnHuyUCtciNPJIiXeliEAaLBb/MEsmtwjmBxuJXq22aZzeSqsY4yZj3L8x7sYBJO0CDGLdI0CCIHgSPCieMKDXBEXBc2Cc8FOiIno6cg3xH9zXBz53KkaGIyV0vclLlavIO7u7hK5rT7lmHV1fYWlKNQ9rXYSCHIecTThixdcgiG5YLrMkM4UPVyCCja0ZjTNeEIiHSRKaJTA0e6Kk0+wkqfbwpJSm+TQAAAABJRU5ErkJggg==\" alt=\"s_max\" style=\"width: 25.5px; height: 20px;\" width=\"25.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8333px 8px; transform-origin: 47.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 8px; transform-origin: 57.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the specific yield \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S_y\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 8px; transform-origin: 50.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"r_w\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the well. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.008px 8px; transform-origin: 226.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Gupta/Chin method for designing a well field has the following steps:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 231.783px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 115.892px; transform-origin: 391px 115.892px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 104.05px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 52.025px; text-align: left; transform-origin: 363px 52.025px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 30.3417px 8px; transform-origin: 30.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_w\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292.492px 8px; transform-origin: 292.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"r = r_w\" style=\"width: 40.5px; height: 20px;\" width=\"40.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAoCAYAAACGohY/AAAE+UlEQVRoQ+2at6sVQRTGfX+AGCuxMhRWCoZGLRTMYCNixEYxYqGgYgLBgIpaiBG0ESNiIyhqoYUimEALsTDwCksT+Afo95M5Mm/ubLh3x/fU3YWPu2929syZb8+cMPO6+jVXZQa6KktoBPRrSExgBHUk8ZR4OyJ8SMDfLxF1I3Gs5vxSGNmQ2LkJ7XcELu5cROubdbPEd6Jgl3C1gMQp7vl3/b4qIrxOJM4VGbeEocLnCDFD1LZXWBc8+6q/twtns8isE4kEFK71ETJGqO25MCjH6g7o2c7Y8zqR+EUELBduR4i4o7ZRwVInCK0JLHNe7P26kEggwRIHRwhkmV8Upgkx/7dV7Yfce9f02xKU6kIigeR9xnLk2QMhy+fhKz85EvGPLR+iDiQaCeMyLK1M8s1ynyVUItFC/hsJIrLhLz66+5iv/Zva8GtbnM/rVC8j8a4EzA6FFFkiyekOgch1XVjtvsYE/WalCp0q+qfeeybB53KWa5lxyS+pctbG5OSRiAO9IuBLiFxcLI0n7t7ayijRV31IXdC/SplnMpAzU2ipufNINBPGCjFhS1CxToRN7Ctm2hgXXcc7/dt4rUdXi85RK6RnHok4XMvep+r+kRONPxwjFJVOnSqd8r2yZV7WmKy8t8LTvA+RRyLB5KGTjjUuiplyyhknlmX6V/HdGAquwF+JLWoWBRaEQB7XaWG3EKs7E88/ibi8Mq/MABbVF6hz7iZEEYkWSPgaXNuEw2U0+Av65JV5ReoRVPcJhQQiqIhE+thGJvckm6P/AWvMK/OSEphFIkt4Q0CUH2SiRXiRZr38nDlgibEdmzxVqKOPF1ggRsU+4+9UJ7TErBLJDzJ+pPYV8qsYcqthglU49Iu1tcMt8vsLliWgK1mCPwbyisq8rDGRTw093xsj7ItsUr8eQTYk0cgK985sQzOsHem/VLBUiEi42f3N3hxyjgknBXJL2kK/imK8g98loaUPfckIWJaQP0NYJVAp8RGxhBvunVCe+bN2igEjkPGpzLIuKjbSph6lX0iiT5btvTEJtoCYQKyIN59JXYmJdwuPBdIjJrhQ2CQMF6iA/A9kyh9U+3mByG8ZwRJ3bxMiWp5x75NAs1RjJ3aUeRBRNgCaDnkbsj6pLe4sJJGvOEB4LcwRUJbrhZtkTGkrD7GcewK7v5bl03bUkWEVkClhypPILnMEMpb1C/M7P8Bl+eVOyjw+2kCfpZz7b3oWxotS0blIvgUdvzw0ayK3NOf+wwkycoys0LoJCCyrWFmJDL+WD3Xj42H5vVqSlklxiki0HQ4/4EAEy8MIM18L0UzQ3Ea4tWRWHTvP8HPWrA2FqmVe0Vyjz6uSaEvMyGEQI8zfSvf9Gcvdttj8ot4nKbZcrQTDN4f+knFNlyplXp+QaOT4EdL8oU+ELW/aJgv4WnaKfTJwC0RlrAxMEmyTA8tdIZwQCFhWgq7UvQUQO0NJejBfhtWqlmjk+H6N6Bhu2rK8AYGn2ynG4Q/WCjEcqFNmQRA+j1Rqj7BRuC/g5yyt4LyD54x9WbC8sUqZV4arzD5VSSQ4ELEteLAkLwVtDG4WdUH3HFnSDyua7vpySESRb/0gliSa/BJy/H9Awvo5maOPEYgLuSnETvMqEVTm5aoklhmjN/rwUUjNkv2nVztK/y8ktjPn5H0bEhNQ2pDYkJiAgQQiGktsSEzAQAIRPwGdACk4sCMOPwAAAABJRU5ErkJggg==\" alt=\"s_max/2\" style=\"width: 40.5px; height: 20px;\" width=\"40.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.342px 8px; transform-origin: 107.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the transmissivity to be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAAAoCAYAAAAbg93yAAAJz0lEQVR4Xu2c6etuUxTH7/0DlOmVoW6GooiMJRRlLpG6iKTInBcUZYgyZMoLGYu6L5Q5UmSKMpWpyAvK8ELyypg/gPXJ863Vtsdznuc553fvPrXq9zvPHtZZe333GvY6Z/OmfnUJdAnMWgKbZ81dZ65LoEtgUwdpV4IugZlLoIN05gvU2ZtcAscaB8cY3TcVJx2k65X8ITbdVqOb1zttn22EBJ61vr8bXTViDN/1BvvnY6MPa8frIK2V1Ph2APReowuMfhs/XB9hDRLYzeb41ehQo6+WNB9jPmL0ihEbQPHKgRQzP+b6xTr/OGaANfXdx+bZozCXdr2cTL7JgA+AvmR0dAVAabun0UFGk7lYa5L93Kc5zxi802i/AqNeh3J6oGEA6htGtxm9XhJCCqQoypeu8x/296eL/2F4X/fbm4n7tNkoID3AeL3W6JRAYOfb/whduyggPc3opuD5WciU+8KCfLIYP7cgj1qbk51skeuppQXsv69UAp/Z6G8ZpcKT0+23hwI8wBBrh3uc03+A/bnRESWcpEB6uXV83Oi5hUL6ydgBpMx3Bw/AzvPMYvIjVyq+5Q8OAD9wwx6XAJ5kQ1NAXHJZAB8LUgM4z8ON1qdb0uWvc+2IrNkPCwDGwHbXAhup8TBsJQASn55Y0o0USFG8nSOd5aOLsTPsj9A6lHafWiGtu502GOZlcWIujtqwACcYleIULXQK8OEzsjO/trhZ22fdctpR5mMzvtQoZmy0mT5mvz9gBIjBxklGeFXyNLGUOWMlPGU3+xRI/7HBdzcKExxeiVisWH8sLS5A0dee2WqzMZ274Cn0ELgtC4orU5v8wYqySLVeBe2vNGIT2HVm8tnR2PneHvh+oyciD44hgmIZX4D3ndEui36lpFNRR2IgY/c/yijmxnkTn4qZaLMRjxhIs0uw3kNA6HcswBMDb0p5tUu2uK0oBrswYQZWu1/TSEA5mZihqkkCepxckQC6nkyGLwnm1iMYdg/8bK4W5ZtG1PWzhokyLY4WBOC0up9yjWv7eR5KC1v/ZL3lEAkAMtY8tlECqr0LwPO5hdJaFjfzFpCG8WjJjA8RzlR9COA5w+SShyD3lviUrGtrplqua62MfULKZ8YB705GfxuVYuCp5BfOqyMJ8Yzu7LWB+FfxQikpmJK3B2nNJo0HBUWTi7UKBDM+Hl1mzFRzTlmjfDXnU6lxwow1ICE+HeN2MiZhQ21sqZhYSatYer8mtV8jq1W18Z4HoQHhA9YIpUeWGyEMQu5PN6xbTJbyoljLmrPxrK60gFSWAabGKG/4UN6KjVGeMZadRJkuNiCUi8wcO9vQ6iDGbDnrFA8o99dGyJvExM9G1xgpqbVM2Y+Rd6yvYmqfrZSHUHNctWx+hoyH3LnGlAEKK7UhoTboKB5bQKoF4AFKfnaLcNh1Lm7pkGhbOjxOTRFmrAXSsc/ZAlLPAyAFkOEOLPnD3/4jNo8liDo6hHfxPCAVJsWO61bFy9BxxWuNi5qaQ9ldvIcaK8o4MlRRQ1MLUp33ibGNUk1Us1g+E4eVes+IQg6uWnclNk8LSD0PKRB6lzyWdQx5UCxbI4NUm5YQwusIcrzabSQbJeNfWwaYk6kA1wL0bJ9akNYc9I9Rhin7+oy1PATvNbQcu/jnaAGpny/lForP2nyAB/VQ+baGEH7OZXpbQ/lv7Qf/XxgNjZ2VoW917ZcCUh+PUmUxxl9vFdwq24cegpQyTJKVyrvGWFLPQ6pCxWfWa2NSrNfhI4XXGkL4YyQ2kzONql/JGsnr2O6lMsDS+KrRHpIgy54E1FrS1EF/ifGa36fM7noPIbRQ3ioM2ZiwfFylaqOaWmDPZ4sbVSP/ZbfxzzP0+GrZPNWMlysDLPXXWy25YvzcGNK1wYmj1EF/ifHa36fM7uY8hLDgvtX1y2bsnHDULufGyh1uyRbXyn8V7XyJZW2GcxV8tIyZKwPMjTMWoIzNhs4pwuBzUr8zrkJJpszueg8hFkd4ELfU7CJ4ya0EbvGQstbaxOaa1VVVjj/4r3HhWwC06rYyREMSojUvlBA+5WrZyV8kcx817u5G3BVrFjX0EGILFMasLccI6ptLIqSOLcS//70E9ppnXkWbVAmdXLjUxh5WIfGsYVVV7F7tMyiM8hlqxot9jCBXBpibr+Y1RDax441SeRzlP5K6VQJpzatptUKbW7swdkq9fe+taWuBA7sscVmqWN4fvYSLhEK9uhBazWtxU8lX1TJhck3Z6DDLi2dwmRGbItbjeSO+WkFlFkUkHC9xvqiXqWMeBIp90UK2jIM3wttDbGQUf/DK2FlGnDfjbj9lBJ+05eMFoVuJq3uLUUsZoPSCZ/grIfwtC75yeQR0AD6TX38ogdQrKHy0ppYTvE9+W5k4vfeXOw8NX+5lUR40qqlEUsIn5Ub5sSVbLMAlRnz9ARf41sq5phKqwOjfrfQfDYhtUPLOADDvbKKk6BpllFgcAMY5K1+0QHb+XJh21FKfY0Qtszyi8B1g3ceS/2n0sFEs06wywJYCkRAXOdmX3illg7nHKPmCfwqk7HaHGfHid3i9azd+MmrZdaZSoNi8KA1KED4bBfTvu+ei3cFGsWOMsG3u+VDiFzKLgDJtdfOgUBRUvG3UWtQ/hZzRAwBAAb3kyjPkPrSF5cJyAiwAynMSl/E/v/G+7oFGfCnDK7nA4b0OhQSxmE7xfu6su7UMEFDzqZ3aa5s1TGFFxRPZyqSSJa1lpLdLS2BMUmJ7lKuP8+U9+PyAvA4lzAQwgTE8J5bVjsV0iotTnoxK+C40QecSO6tYh+q5O0hXIf7/j8mOeb1R6cx0PdxMO4tCAJ9QEtC8xRPABD651WF8p+OpWKmk3OpUmLaMMsCh0oQ3PIdidVMH6VARt/fDMmwx2l6qtdol8F8PAcdbPgHSZ7DlqgI+Lr5/G+YOBO5Y3KfiBBJaqeOtaqAMfdhEP3jDe6jShQ7SJUu/MFwpHb9ebqaZDfBx+UQN8agHmtxf7pFYIta9fQFSZUFp86QRIMQCf2T0rRHxLS41bjFZXIGbfr7QX273uo+2lOsoWlAtTwfp+hWVWKQmM7x+zlY/o8Dn40qdE3pXVxYSCwiYyHS/Y8QRDRaYz5cwFscz/MZ4ulSKCLjJ/spN1lGJsqhjygDHSIrnaUoIdpCOEXfv2yoBVZf5j4kDlrON/D1lUDlJeHGh1CSOePmdrPw2I7LfZEXJtNKOs9DrjEgS+eMW+nEGSh+fZcXFftko9jXA1udaafsO0pWKtw8+YwlgiTfEN6M6SGesRZ21LgEk0EHa9aBLYOYS6CCd+QJ19roEOki7DnQJzFwCHaQzX6DOXpdAB2nXgS6BmUvgXwunckezlzbWAAAAAElFTkSuQmCC\" alt=\"T = K(b-s_{max}/2)\" style=\"width: 116.5px; height: 20px;\" width=\"116.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.35px 8px; transform-origin: 107.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Evaluate the drawdown at a time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"t = \" style=\"width: 22px; height: 18px;\" width=\"22\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.175px 8px; transform-origin: 50.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1 year. Realize that for small values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u = S_y r^2/4Tt\" style=\"width: 81.5px; height: 21px;\" width=\"81.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 243.133px 8px; transform-origin: 243.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the unconfined well function* can be approximated and compute the pumping rate from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max/2 = (Q_w/4 pi T) W(u_w)\" style=\"width: 111.5px; height: 38px;\" width=\"111.5\" height=\"38\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 22.95px 8px; transform-origin: 22.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"W(u) = integral(exp(-x)/x,{x,0,infinity})\" style=\"width: 112px; height: 35.5px;\" width=\"112\" height=\"35.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u_w = S_y r_w^2/4Tt\" style=\"width: 89.5px; height: 22px;\" width=\"89.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.15px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.075px; text-align: left; transform-origin: 363px 21.075px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 356.708px 8px; transform-origin: 356.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ceil(Q_d/Q_w)\" style=\"width: 88.5px; height: 20px;\" width=\"88.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.7167px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSet the pumping rate to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q_0 = Q_d/N\" style=\"width: 73.5px; height: 20px;\" width=\"73.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eArrange the wells so that they are equidistant from the central well.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 43.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.7167px; text-align: left; transform-origin: 363px 21.7167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 73.9083px 8px; transform-origin: 73.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 261px 8px; transform-origin: 261px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between the central well and others so that the total drawdown at the central well is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s_max\" style=\"width: 25.5px; height: 20px;\" width=\"25.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In other words, add the drawdown from the central well to the drawdown from the other wells. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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alt=\"u_R = S_y R^2/4Tt\" style=\"width: 91px; height: 21px;\" width=\"91\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3px 8px; transform-origin: 23.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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style=\"width: 227px; height: 38px;\" width=\"227\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.133px 8px; transform-origin: 174.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Write a function to design a well field using this 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\" 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style=\"\"\u003e*http://www.aqtesolv.com/neuman.htm\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b)\r\n  % Q0 = pumping rate (m3/d)\r\n  % N = number of wells\r\n  % R = distance between central well and other wells (m)\r\n  N = randi(10);\r\n  Q0 = round(Qd/N,'up');\r\n  R = b;\r\nend","test_suite":"%%\r\nQd   = 7000;          %  Demand (m3/d)\r\nsmax = 3;             %  Maximum drawdown (m)\r\nK    = 50;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.2;           %  Specific yield \r\nb    = 30;            %  Initial saturated thickness (m)\r\nrw   = 0.3;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 1400;\r\nN_correct = 5;\r\nR_correct = 189.4;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 6000;          %  Demand (m3/d)\r\nsmax = 2.5;           %  Maximum drawdown (m)\r\nK    = 60;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.22;          %  Specific yield \r\nb    = 20;            %  Initial saturated thickness (m)\r\nrw   = 0.25;          %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 857.1;\r\nN_correct = 7;\r\nR_correct = 297.6;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 10000;         %  Demand (m3/d)\r\nsmax = 4;             %  Maximum drawdown (m)\r\nK    = 80;            %  Hydraulic conductivity (m/d)\r\nSy   = 0.18;          %  Specific yield \r\nb    = 25;            %  Initial saturated thickness (m)\r\nrw   = 0.4;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 2500;\r\nN_correct = 4;\r\nR_correct = 117.6;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)\r\nassert(isequal(N,N_correct))\r\nassert(abs(R-R_correct)\u003c1e-1)\r\n\r\n%%\r\nQd   = 12000;         %  Demand (m3/d)\r\nsmax = 3;             %  Maximum drawdown (m)\r\nK    = 140;           %  Hydraulic conductivity (m/d)\r\nSy   = 0.2;           %  Specific yield \r\nb    = 25;            %  Initial saturated thickness (m)\r\nrw   = 0.4;           %  Radius of the well (m)\r\n[N,Q0,R] = wellfield1(Qd,smax,rw,K,Sy,b);\r\nQ0_correct = 3000;\r\nN_correct = 4;\r\nR_correct = 78.2;\r\nassert(abs(Q0-Q0_correct)\u003c1e-1)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-23T22:33:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-23T00:54:17.000Z","updated_at":"2026-02-12T15:43:55.000Z","published_at":"2022-12-23T00:58:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA well field provides water for a community. The design of a well field involves a goal to meet a specified service demand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., volume of water per time) with the constraint of lowering the water table by no more than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the specific yield \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S_y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the well. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Gupta/Chin method for designing a well field has the following steps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r = r_w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er = r_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the transmissivity to be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = K(b-s_{max}/2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = K(b-s_{max}/2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Evaluate the drawdown at a time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = \\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 1 year. Realize that for small values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = S_y r^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = S_y r^2/4Tt\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the unconfined well function* can be approximated and compute the pumping rate from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max/2 = (Q_w/4 pi T) W(u_w)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{s_{max}}{2} = \\\\frac{Q_w}{4\\\\pi T} W(u_w)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"W(u) = integral(exp(-x)/x,{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eW(u) = \\\\int_u^\\\\infty \\\\frac{e^{-x}}{x} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u_w = S_y r_w^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_w = S_y r_w^2/4 T t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ceil(Q_d/Q_w)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = \\\\lceil Q_d/Q_w\\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSet the pumping rate to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q_0 = Q_d/N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0 = Q_d/N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the wells so that they are equidistant from the central well.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between the central well and others so that the total drawdown at the central well is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s_max\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In other words, add the drawdown from the central well to the drawdown from the other wells. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u_R = S_y R^2/4Tt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_R = S_y R^2/4Tt\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{max} = \\\\frac{Q_0}{4\\\\pi T}\\\\left[W(u_w) + (N-1) W(u_R)\\\\right]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Write a function to design a well field using this method.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"374\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"389\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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the head for steady 1D flow in a homogeneous aquifer","description":"Problem statement\r\nWrite a function that computes the head  (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations . The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length  of the aquifer, hydraulic conductivity , aquifer thickness  (set to [] for unconfined aquifers), width , and a vector BC, which contains two of three of the head  at , the head  at , and the flow . The function should also return the flow.\r\nBackground\r\nThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\r\n\r\nwhere  is the flow area. For a confined aquifer, the flow area is , whereas for an unconfined aquifer .\r\nThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 738.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 369.25px; transform-origin: 407px 369.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.392px 8px; transform-origin: 247.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.433px 8px; transform-origin: 175.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, aquifer thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (set to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.6333px 8px; transform-origin: 97.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for unconfined aquifers), width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eBC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.183px 8px; transform-origin: 127.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains two of three of the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0583px 8px; transform-origin: 33.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5583px 8px; transform-origin: 43.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.575px 8px; transform-origin: 127.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should also return the flow.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.442px 8px; transform-origin: 381.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAABGCAYAAABc8A97AAAKGklEQVR4Xu2dW+hvQxTH/+ed3B7kEoUHIpTbiZI8UCJFuadT5PYiiZCH8+SaJOUWJXk4CImUSx6IXHMtHlBHLnlA4p31qb1qnTkze2Zff7N//7Vrtf//32/vmTVrvrNmzVpr5rdlwy+XwAIksGUBPDqLLoENB6qDYBEScKAuopucSQeqY2AREnCgLqKbnEkH6ubEwOHS7BOFnks0/yz5/M2aRONArak3puMF4N0stJfQKU01J8v9k+bv++R+qNCxQkcK/dv8/+d0LHUr2YHaTV5Lf/rbBoi/yf0YIQtEwPxG08CP5L61psY6UGvqjel5+bDRqEzrZwfVYQ5833x2h9zvnp6d8hocqOWyWocn/2sacb3cHwsadJ38/2jzmTULqmi3A7WKbpiFiYullh1NTUfI/YegVqZ9pv/vhE4LzIJZGGyrxIG68i6YjYHHpaZrWoD4j3y3h9DzQoC6qsuBWlV3TMrMr1L6AQkgniSff9zUHjMLJmWspHAHaomUlvXMvsLubULnCf0tdIjQTUI67V8if4f+09vls7uaZu4nd7wBlMOC6rIaNK0DdVkgzHHLguh+oZ+FrhTCT2q1Je8rEG1Z6g3APj2qeecVub8ntLcQtisXnoKVBAIcqLmuX873bTaorvZT/lH9HpC/IARI0cJoXusNcKAuBw9VcqpTNxGl44XCFb0F4q1BC6yjH7PgQaFtRnOqNyCljWcRSF+NyqrwAiENuSmzTAsvC4U+ulkaU2ElhCaPE9KpU1kkMvRso72Ynvn+QiG1B/U5VuAvNZot1TwLtNhCyH4f84+qJoann4TeFbJgVm+AmgVjihmTAzs6DD7sVkdXoAJQRpyuHp8yIw+BPCRErLhKX9yYEu5YloYueQ3ZnCsUaj2+0+fQjFdnAKos6DtM6+cIhfF5BsstQrGwqa2Tv1E0l5oyrH2LWRBq445i2OVxHUBFA6AUqKwAiVpcJNQmRJ7bKYQ/roiBIS1d0LsWqKnwJPYg8m0Dcthk68RPlatuqVjYlP76oyk0ZjZYb8DY9qnyRfWxBd4ubS0BKo15XwhNyRVzb9hCdSrhs+pixisAt42hU30sKqQgfUK+BxylWUvWfoyVmzML7EKJuq8N5KPlp7RxX3Gqltf3s4OgBKjquqDQWGNCZq1waOCBfVuzJu9ZMIQmkSqBg6Wt+DG7JoKoVkqZWlaTtw2Q1ACaIlrFwP2i6VtmXq5skCEHVKsdS0eVBWpKAGuCwaJmqLbkYRueZNp+Ugif541CffyTupqPmVlWaymQ4YFggNqaCvSY28rap6rxwEMXjR8TEPIg9/VLIUK6XFkF2AbUEHC5KV+Z6vteUa8v8CHVSlZzqAIAnDcIxRZWJU1VoIWJzoDpfKGjhTR+j9bChNNBkUvrU/tUFRQAJ/E6NA9K+AyxgffhBCHN1srmv7YB1U75pdoUhuxUx/+lAO/S4KU8G0aF6KBnhLD3sd8BbKk9GmtzqDVflYdObwCFZ0HzS+k/3EDUreaFXSjF3FbW/kXjEaEC7EP4xRT5SojZpJOJmAJqqBW7uCasuYBwsyu6pgdCA7svGGvKpbRgQOtxoeHGWmSG8Xj1z97TAErBhuZ+QMiaF7m0Pu0P+EbzaZl9+0XDuzYgoaZLFicpoFq7ikJihniKYWvAd9HE6whUq5WsvDab607dlgDe+mKti6p15Z8Cqi2gi/Pe+uXomJjvru+IXOJ7VmMwbTIz6Up3M5lEzLJkc4X7tKx52bryjwE1BFt2RWYQtET71IKpz2Bgatwz8qI1n3Sxw4KEKBHXZnHd6aItBkQ7i7biLAbU0D7N+rhMJ9lpPxXS6wOGKd+ZCqjWVtdVrY3c0aaxbNUp5TO0bKs128pqXfmXALV0inK31K7dYAetXYzaWae6/fNDURm8ryHe1AK3eOVfMvWXAtWOnD77btZpMRWaT2FH2TVAF9NqZBxNXhzt/FqoLTuqaOVfspgqmfqtG6bvlL9OQLVaM3fYA2jp4lVRdB0kf+w/OdR2r+AX+ej3gnq1P3PuQhsQSa78U0C1oMlpR+vU7pL5U9DWxT5i3Xspz4edgfp4R3Dcszib+6LOezOVqi3+QUabUkzRyj8FVCr6Roi8U66U0x4b40UhG6YbErmYW+hT1Wen9tSCKbTpsxlEAbNoKpznc1/MmMTp2y4dqDltShlhBCwaom0LoaIp2TsDWJm+iB3roVq4HMj2IX+S73R/zdxCq7G+Ll4Ta5+ti7vKmj0lUckwVB/NtstlT9mtt5qPCjhYraLW2XaCaeBadGODwUvUJdxOoiFI3FUkn/AcWoOYvJ6spwMufLbGgViiSfUZtO/TQrGtSXqCIMrOXtF3ckDVAtRmLfUA8B4d0jcraGkd5PxOLIESoKq9gcF/p5BO/22s4T/bLpTaGzRxs7z4AgnQR58uRZm0ARWN+JqQnfK1/dhTpJR9LvSWaSz22VVCbDJjV2WfZOACGfsjPSSA7bhNiJxS+rRLwlCP6sZ9JQVUm31OHiNXaE+lOMHGuHwpI3VccVZfmg1E9HGJrayBqcgUxv7bQuE0D4DPFGKvumaPwzz+U/aDvyOEqeBXvRJQT8Oi8gxKbNR6Re6cdZWAdZ31iYZ1rW+05x2oo4lyEQW1nU9VdQMcqFV3z+jMaUZXLiw+esVDC3SgDpXgct63u05LEo2qapkDtaruGI0ZDXFziB1eG1xS7EAl7M1lQ5s8S3ToDKFThcjbsPYrofSHhfD6rEwTO1BHw0Y1BakdCqhY2RMdtGmY4cZC/Ks/Ch0mpPvsFZCAFE8Oh2Ss9PA7B2o1+BrMCD7S1xOaz67227a+qw2rGzo5sGK7EC5HQEtOx0rC4g7UwfiopgBNl4slrlugtqUT2n1eBARI5xvzqMnewnKg9hZdVS/awyIIyISBmtwZqdoYe4xl350akwjGgTqJWGctVE/HYxGU2n+lOZ+5sKkNsVa1l8uBOiumJqnMTtexjPrcYWghU7o7IQfqSRqTKtSBOqu4J6nMnrEf+2lIu/8tFzYNN1hWg49qGJmkC9e/UKstYz5OaxbkjmbS/W/4WtXf2nUf12QSd6BOJtpZCrar+ZhNGTtrgXf2aVxOyqTuGiWHmGRqPdffurLwxXY9EXs0IThQRxPlSgqyGtUeiaM/DmJ/dY+w6WdCRKjYeaFbhf6Sv/GX2rNT7S+tbG1AvVPuK3NVOVBXgq9RKw3PB8D3eYUQPw/Jb1TtaGoDyPwu6jYhTnvW6Z0NhQQK7CG94ZH4lDX0EN9BjXagDhJfFS+jGR8RYkrnwhbl977Y+annM3DaIGDUkKru4FCXVnguP2UCTrbKY1IMPbd/sKAcqINF6AXMIQEH6hxS9joGS8CBOliEXsAcEnCgziFlr2OwBByog0XoBcwhAQfqHFL2OgZLwIE6WIRewBwScKDOIWWvY7AEHKiDRegFzCEBB+ocUvY6BkvgfyzdX2UpVypGAAAAAElFTkSuQmCC\" width=\"85\" height=\"35\" style=\"width: 85px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.467px 8px; transform-origin: 173.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area. For a confined aquifer, the flow area is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18\" style=\"width: 49.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, whereas for an unconfined aquifer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"18\" style=\"width: 50px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.85px; text-align: left; transform-origin: 384px 182.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"640\" height=\"360\" style=\"vertical-align: baseline;width: 640px;height: 360px\" 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data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Q] = homogAq(x,confined,L,K,b,w,BC)\r\n% h = head at position x\r\n% Q = flow\r\n% x = position at which head is requested\r\n% L = length of aquifer\r\n% K = hydraulic conductivity\r\n% b = thickness of confined aquifer ([] if unconfined)\r\n% w = width of aquifer\r\n% BC = [h0 hL Q]--one of which is NaN\r\n\r\n  h = conservation of mass + Darcy's law;\r\n  Q = -K*dhdx*A\r\nend","test_suite":"%%  Confined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nb = 2.5;                %  Thickness (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = 3.25;\r\nQ_correct = 31.25;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nb = 31;                 %  Thickness (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [43.4 41.4];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nb = 25;                 %  Thickness (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [164 158 152 146 140 134];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = 3.3354;\r\nQ_correct = 40.625;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [43.8839 42.4476];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [138.7047 137.6190 136.5247 135.4216 134.3093 133.1878];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nb = 34;                 %  Thickness (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 193.545];   %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [53.4 52.8 52.2 51.6];\r\nQ_correct = 193.545;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))\r\n\r\n%%  Unconfined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 298.85625]; %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [53.4135 52.8205 52.2207 51.6140];\r\nQ_correct = 298.85625;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-09T15:47:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2023-09-09T15:42:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-09T15:33:16.000Z","updated_at":"2026-02-10T14:45:49.000Z","published_at":"2023-09-09T15:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, aquifer thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (set to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for unconfined aquifers), width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains two of three of the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should also return the flow.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area. For a confined aquifer, the flow area is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, whereas for an unconfined aquifer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"640\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation  above the bottom of the aquifer and the position of a groundwater divide  given the water table elevations  at ,  at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere  is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position  is \r\n\r\nwhere  is the (unknown) flow at . Using Darcy’s law to replace  provides a differential equation that can be integrated using the water table elevations at the boundaries to determine  and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAoCAYAAADpE0oSAAACJ0lEQVRYR+2WOy8FQRiGz/kFEh0lChIFiVtDSSJRiUupEJdKJEgoFQiFQuEShRKdRCT0EteagkJDRQg/wPuczCSze/bY3XNxJHaSJzPWzPd++11mTzpVppEuk24qEf61yCehTkJdsggkxVWy0PoN/7lQt8rDAdEl2sWLqHa8HtJ6XVSJSbEVN1S53nhehm5FvxgzRq3AhP5eE59G+FAzjsQaYaGulLVXY3FH8644Ep3iUXSLG/EWS1Wbw4SxdyfqBeH+EFPiLK6Qf38U4W0n3Lz1eKGinI8iTP72jdiw5oMYwqSqRdSIZkHtZNISRbhW+x6M2ILm5RjCnB0US+JeNNizUYQvtJmWYlyKjhjCbKUAT4UnTWHCqzpALz8Zz6NGyfUNG7PCk6afhPF0T9A65MnmuUdrqpow8jws53RFhbFDC2aGK2wLgb7EKP06YkTcfubyWBHnIqi1uPVmxLug/XjbrBS5wuSBt2R8CQrCLSTbz/yfnt7w/Z/ntF6fmBZEwtYHzs4Z25nJFba5CBJlL23FzcXwO8UzhHrFqFnzzAq3aX2dS9h9HndNf+KM/95+NoYaNXuu1bCqjuoAHwxGk7AFRK6vBIVIQXpGMYTtzeYvIELP5RH42SyGsK0NN8z20uAt60RW2xVDmO/zprA/FogAVW1/QCxqzV2ds6qj5jNon21FOuJEcKcfCy6OoLaL9JEoxKGcZ4sR6rwcS4TzCls+h/5fqL8BFMhkKfmmzHMAAAAASUVORK5CYII=\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAACwUlEQVRoQ+2YPU8VQRSGoYcQsMICCyi0ILEBbSi0gITQ2CiGHqUmkGisJdEfoPILlIRQY6kxASk10UIKjdGKr2iP70vOSc6dnd09e+GyxJ1N3sy9u7OzM8+er9nurnSUEugu7ZE6dCVIDiNIkBIkBwFHl2RJCZKDgKNL0yxpGEyeQleEzRDaT9ATaCePV5MgPQSEF9A2NA3tC5Q3aO9Cq9CDGKimQJrE4jehv9B1aNfAGMDvz9Ag9BhaCUE1BdIvgbCG9l7EWh6JGxIiXVGt7KRrEyCpm3G9C9DLCKQxnPso55+jXbZ9mgCJbkZ34zEO5QXoY+nzFe21pkHSxdOVeiNWpKe28OOG/LlkXa7IkhjQGPVvQRMQA5s1V15ntmCf39DlggnUdYkp/5s8vAqkKdzzViddBIkm2g8dQOtQj4FBQB9kkKvSjqC1WSMGRrPMaaFFs1BkUPu8KpBaxvfGpFeYwLwxRVrQIcS6gm+L0HKLMTP5OiGxPrpZ8HbsGtuCxLT5Wh6gZngf/1tS5WnNowP325fCedON8o5nuLAkF9uCREvZkwFiBVkH1ncmQ56ru3HGXyDGn0yKPJPldGaQ8OV6s5s7cIfT1j1OWQDszHLbH/UPbmXSKZu3lgDsd9vGWG/gDgNuC+kK8z/vwM2p2WKyKAMrzEw544FEk/0uQY1ZjUemdHeCqgOS3ZbMYp70iPCw9VTma4AHEs3wHcT9jMYlm045CW4cL3Kmq7LBDb8SRDe43OzxYN2j1FlpE4KtJQiYgO5AF70csBbcsuWQtSpE16cSuxtmAPsJzUBaSdt6ib57FFx3el0t3dTtwuxc+aMbffM9xH0aXWrOANKVaRbIu14LAedDaVGL0Cj0A+qTdgNt7BPKybCemOR8/v/bLUFyvNsEKUFyEHB0SZaUIDkIOLokS0qQHAQcXZIlOSD9A6nxkiWxjY9EAAAAAElFTkSuQmCC\" width=\"36.5\" height=\"18\" alt=\"x  = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAAC30lEQVRYR+1XTUhVQRTWvW1qZZsWtTDUbBNJ7VwoiCIkVNCysFq2MDJciIiCLsSVP9i+BImoTRkuhMJq0SaojaAgtUoI2tf3wRw4d+7MvWce78kD78DHfe/dmTnf+c6Zc+a1tjTpaG1SXi0VsdTIVIqdeMVuQYEbwCWgQ6nxDp9fAiupCvnzU3OMhBaBdmADeAaQDEc/sOSI/sDzOnBUK0ErsdMwsAzcBP4C94AXAaOcdwC0ASR3sZHEaOyDU4J2bkdICYdVfBhzX57iOVcLOYtiu9j4qtt8Dc/7JYYY0rduzi88zzaCmPaeRroMeaOJkdMFYC+VXJFivoGyEIrtWtdluBcR0yG0qsXNHwA8KDKsDpmI+V4vYNVjYzh0+LnkjCH8ua1jirEUsDTISMmT71gkRTdFaZNiPzGLRZQjpViytPxWFlh8B4xKlxLzN7eUCNm0LvnFzUKh9PPrIeZZe58O4yesG/Ty6wq+zwD7QA/ALsH9c63LQsx6qsrKhLzXB4mFuBvI1ccQMT+UVmK6vLDBs+Hrwbw9BZxTClHBz0AuXWKnUie/JZQT2HzWsQiFkCSfA6HG/s+ty3CJEZvH5HG3IOS9VkK85m80PAT4LUj2Cx0kUToTmRgxhvMbICUjViSZN5sArzl0IJjI+F2MFxHLFPGilkQlXjlyLJQjwBcn1XkXOhZhvnsEhO5noqyFWIZ02bWHyj0BhgF9heZl8SPAazSVKrup1p2YeCw5Yj2hXEdVJddYFhj2olAmKUYD0jfZXiZVOIV06MlTOAXIQahb8ovHb7wQCgnm1WvgK7CllKEqdwFW/FFA/1GhaiwlvZ4nUi4yByyWY/R4HTgE/riN5HpdpBTf0fgdRVbmS23UNqXU5Jp9rPLzXv8+EDYS7gPY5zoBlgkO1q8dYBuInc5YS7qGNZd9R8pOZZk6qe9Jbhpg85bBf1K5/wTHTczsSEXMLJWbWClWKZaqQOr8/+6UrClQAbvIAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n  h = (h0+hL)/2;\r\n  xd = x;\r\nend","test_suite":"%%\r\nL = 10;                                       %  Length (m)    \r\nx = L/2;                                      %  Position where WTE is desired (m)\r\nh0 = 19.11;                                   %  Water table elevation at x = 0 (m)\r\nhL = 19.11;                                   %  Water table elevation at x = L (m)\r\nK = 5e-7;                                     %  Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8;                                  %  Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 2e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 8e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 50;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 60;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.5;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.1;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand;                                  %  Length (m)                                                   \r\nx = L/17;                                       %  Positions where WTE is desired (m)\r\nh0 = randi(100);                                %  Water table elevation at x = 0 (m)\r\nhL = h0;                                        %  Water table elevation at x = L (m)\r\nK = 5;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x  = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58314,"title":"Compute the normal depth of a channel","description":"For steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \r\nAs described in Cody Problem 57969, the normal depth, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) ):\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel, and  is the cross-sectional area of the flow. The coefficient  is 1 for SI units and 1.49 for U.S. customary units.\r\nWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure channelStruct with the following fields and possible values:\r\n\r\nThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 850.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 425.1px; transform-origin: 407px 425.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.017px 8px; transform-origin: 380.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57969\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 57969\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.85px 8px; transform-origin: 40.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.833px 8px; transform-origin: 197.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n) R^(2/3) S0^(1/2) A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow. The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.942px 8px; transform-origin: 155.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the following fields and possible values:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.85px; text-align: left; transform-origin: 384px 64.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 435px;height: 124px\" 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\" data-image-state=\"image-loaded\" width=\"435\" height=\"124\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.15px 8px; transform-origin: 376.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.85px; text-align: left; transform-origin: 384px 169.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 725px;height: 334px\" 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\" data-image-state=\"image-loaded\" width=\"725\" height=\"334\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yn = normalDepth(Q,n,S0,units,channelStruct)\r\n%  yn = normal depth\r\n%  Q = discharge (or flow)\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = 'SI' for metric, 'USCS' for U.S. Customary System\r\n%  channelStruct = structure with with fields 'type', 'size1', and (for trapezoidal) 'size2'\r\n\r\n   C = switch(units,[1 1.49]);\r\n   yn = solve(Q-(C/n)*R^(2/3)*sqrt(S0)*A,0);   ","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 0.61;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.04;                                   %  Manning coefficient \r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 1.12;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyn_correct = 3.58;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 0.72;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.034;                                  %  Manning coefficient (rock)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 1.16;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 2.80;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyn_correct = 3.33;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\nyn_correct = 4.52;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyn_correct = 7.28;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 9.76;                                   %  Discharge (cfs)\r\nn = 0.015;                                  %  Manning coefficient (concrete pipe)\r\nS0 = 1e-2;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyn_correct = 1.36;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T12:36:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-05-17T14:01:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T13:54:07.000Z","updated_at":"2023-05-18T12:36:47.000Z","published_at":"2023-05-17T14:01:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57969\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 57969\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n) R^(2/3) S0^(1/2) A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n} R^{2/3} S_0^{1/2} A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow. The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the following fields and possible values:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"124\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"435\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"725\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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89ZP7662PdFgAAADyyupLvnq/fZM5WnXRb6dGETN+aM95tAUD7Inur+QhywVK2VmF+t7q7WcriKq+g1gAAAEAqyurSlwx92QgjqyuzqZ+rkh3pZnMpi0v73zblatcCAO0jVfbWed0LTPGUdWRvxSDIhTp/vWhK3d0s1Sj43tf+wK4DAAAgnr5k6MuGhoyE+awuPfSlBZlF/d10s7mUxXXLxKG21AcAtJdDry6Pzd7Kv+wmUzSrzPQZPMe1IIwgF+pcP7rInDy6396l0pJaAwAAAOnTkJG4rC5lc+lLi4aeIHOov6t+r6d+cBxlcX37PzEhE4D2ceroq2bX46PN715aEpu9NXTms6agoMC1IgpBLjRw74LJpuLD3ebWyde4FgAAAKSrqawuDT3REBSyujKH+r0fV3xo17uc180uPR/0UikPTdREFheA9qDsLQW4FOgKI3ureQhyoQHdzVJtrr+4Y5xrAQAAQHOlyurSEBSyujKH+r3K0oqioJcCXZqgSRM1AUBbCmZvhZG91TJ51TXcek76/zYfMP9rY6nbiqc/cLqD071nQc4sRetde/Sy6+eqKllnnXXWWWc90eup6G/9n0y90vzptAGuBWgbukMf9QVGdId+wA0rKB7cyf7zsqfMawfy6vrAQeoPX5pfYdb/HVkUANpOU38bLr7hCYJbLUCQywW5wqnJiKe7Wf7zYp111llnnfUkrGuZjrvv+KyZ+vmL3RbQdo4fP26ObC+JnGlRd+s1vPGizy5yLehoe8o+Mn9y7+Om96UjXUs9DWX80TeuZdZxAG1C2Vv7n5sfOTTRZ2/1vnK6a0FzEeTafMD8w9MH3RYAAMhl35szhCAX2tWxvevNgX9vPCW86M79FRN+EjnEEe1vwX0bzJ5D3Rpkc507c8p0P3PAbF71ddcCAC2nzC1lcEVRzS0FuNA6OR/kkp2r89xarbELcv4jAQAgJ9AHQGdQVteHL9wWOT28KKtLNb3QsZ59aa/5q//nddOtx4Wma/eetk1ZXP9l9mBmHQfQKsriPfjCYlNVsc+11CN7q21ReB4AAADoQKqxokLC+lKjLzdhutMfN8sW2o+GI/bKO2Y+PXfGbiuLSwXpCXABaI33tt9l3t04IzLApeytUfPKCXC1IYJcAAAAQCfQlxtNC69himF+xq24YS1oH/d8/SbzySe1QS5zptx872t/ULsOAM2k7K031xWbw2885Frq6QbHVTM2MjyxHRDkAgAAADoJWV2ZRdlceVUf2Syuyopj5otfYLZVAM1H9lbnIcgFAAAAdDKf1aVlGFldHetPbxllKo/uNbdMHMr0/QCaJVX2Vo/8IrK3OgBBLgAAACADKKCiLz/6EkRWV+e588vjTWF+N/PnXx3jWgAgNU0okip7q//Ib5trSsrI3uoAzK5Yg5mVAADITfQBkMnKtpSYY3vXu62G9IVpy4k/N//vL3aZrj162bZzVZWst8F69561AcZPPzlrl/55lixZsoxbyqLivzCDLnjFrnvK3iqevM706n+da0F7I8hVgw4uAAC5iT4AMp2GvijY9cmZ466l3nMnv2/+z4EZbsuYLud1qwvMsJ7eupat4Y/hjwsgtwR//sNBLt2MuGjcfzU9unV1LegIBLlq0MEFACA30QdAUkRlda3d8xfmdfPHbgsA0FkU6PJBLrK3OhdBrhp0cAEAyE30AZAkqbK69KVq0NQnTM++o1wLAKA97N823xzZs8ZtNaTsrSsm/MRtoTNQeB4AAABIABUs1rTz/YbNcy31VOhYRelVnB4A0PZ0o+HVNYWRAa78y24yI2a/QoArAxDkAgAAABJk4MRH7Zep8wuGu5Z6h15dbl7/x0uZgREA2oiyZ5W9pZkTozJpLx+/zAyd+SyZtBmCIBcAAACQMPoydfXtu8wlo+5xLfXOnjpks7o0tBEA0HJH96xJmb0V93sYnYcgFwAAAJBQyiBQVpdqcoWpUL3qzmmIDQAgfcrYUubWvm3zXUtDPnsrKqMWnYsgFwAAAJBgyuq6pqQsNptAX9TiCtYDABry2VtRNwj0+3bw7eVkb2UwglwAAABAFmgqq+uNtcVkdQFADA31bip7S79jCwoKXAsyEUEuAAAAIEukyuryw2/I6gKAhpS9pUk7om4EUHsrWQhyAQAAAFlGGQf6UhY12xdZXQBQq6nsreIp66i9lTAEuQAAAIAspC9lGlqjgFeYz+rSQ1/yACDXHHp1eWz2Vu8rp5tR88pNn8FzXAuSgiAXAAAAkMU0xEaFkqOyuvTlTl/yNFQHAHLB6eO7za7HR5vfvbTEtTSk7K2rZmw053Wn9lYSEeQCAAAAspwKJcdldYmG6pDVBSDbKXvrrcdGmFNHX3Ut9cjeyg4EuQAAAIAcQVYXgFxE9lbuIMgFAAAA5BCyugDkErK3cgtBLgAAACAHKatLX+70JS+MrC4ASZcqe0sZW8rcInsr+xDkAgAAAHKU/6KnoTpRlNWlL4n6sggASaHAVlz2Vr9h82ID/Eg+glwAAABAjtNQnbgvffqSqC+LGvIDAJlMv6/eXFcc+fvKB/UHTnzUtSAbEeQCAAAA0CCrK2r4jjIjyOoCkKn2u8zTqop9rqUe2Vu5gyAXAAAAgDrK6iqaVUZWF4BE8NlbRyJqCJK9lXsIcgEAAABoQDMwpqrVRVYXgEzw1VuuJXsLDRDkAgAAABDJ1+rSl8UwsroAdBafvfXYU2+4lno98ovI3sphBLkAAAAAxNJwH31Z1JfGVLW69KUTANrT8ePHzYEXFsdmb10y6h5zTUn0cGvkBoJcAAAAAJqkL42psrr0pfO97XeZT84cd60A0HZOHNxk9m0oNh/9dqVrqafsreFf2m4uH7/MtSBXEeQCAAAAkLZUWV2H33iIrC4AbUrZW2VbSsy7G2dEBtF99lav/te5FuQyglwAAAAAmkVZXSPu+Cgyq0tDiBTo0pCiU6dOuVYAaD6fvXVs73rXUu/8guF2SfYWgghyAQAAAGi2Ht26pszq0pCi0l9cTVYXgGZLJ3vr6tt3uS2gHkEuAAAAAC3ma3X1H/lt11KPrC4AzZUqe6tn31FmxOxXyN5CLIJcAAAAAFrtigk/sYWfVQA6zGd16csrAEQ5fXx3yuwtBbYU4FKgC4hDkAsAAABAm1Dh5yFffscOJQpTVpe+vOpLrIYiAYCnQPjuDRNis7dGlpRF/l4BwghyAQAAAGgzqtWljIu4rC59iT3w1IjIL7MAcouyt95+apId0pwqe6t7xO8SIApBLgAAAABtTlldmtY/Kvvi7KlDNqOLrC4gd/nsrYr3n3Mt9ZS9pcLyZG+huQhyAQAAAGg3PhODrC4Akm721vkFw11Lx6morDLf+c53TF5enpk+fbprRZIQ5AIAAADQrpSVoawufXkNI6sLyB2psrc0U2tnZm8dOnTITJp4vfn7v/9714IkIsgFAAAAoEPoy6u+xEbNjkZWF5C9UmVvnde9wBRPWWeumrGxU7K35H/8j/9hLr30UrNz506zYMEC29anTx+7RLIQ5AIAAADQYfQlVkORUmV16cuwvhQDSL5Dry43bz02IjZ7q2hWmekzeI5r6Rw/+MEPTElJiamurq4Lch07dswukSwEuQAAAAB0uFRZXfoyrCFNGtoEIJlOHX3V7Hp8tPndS0tcS71g9lZBQYFr7TzK4Fq7dq1dP3HihF1269bNLpEsBLkAAAAAdIpUWV0a0qShTWR1Acmj7C0FuBToCsuU7K2g4uJit1Zzfr172+XZs2ftEslCkAsAAABApyKrC8gOTWVvFU18NGOyt+L4TC5qciUTQS4AAAAAnS6Y1aUvw0FkdQGZL53srb7D5rmWzOUzuajJlUwEuQAAAABkDGV16cuwvhSHkdUFZJ6msreUuZXp2VtBPpPrggsusEskC0EuAAAAABlFX4b1pViFqeOyuuIyRgB0jKqz58x72++K/VlUza1R88ojA9aZzGdyffzxx3aJZCHIBQAAACAj6UtyXFaXzx7RECkAHevEwU3mnf89xBx+4yHXUs9nbylInUTU5Eo2glwAAAAAMlaqrC7RECmyuoCOoewt/cy9u3GGqarY51rrKTA94o6PEpe9FURNrmQjyAUAAAAg45HVBXQun70V9XMWzN7q0a2ra00mn8nVrVs3u0Sy5FXXcOs5a+fqPLdWa+yCnP9IAADICfQBgGRS4Xllk6g+V1jPvqPMwJsetUsArXfq1ClT/uaPYoPICkBfduM/dEpwKy8vz7RFSOOhhx4yu3btMidPnjRHjx41mzdvNkVFRWbq1Kn2+Ysuusj8+Mc/tuvIbAS5atDBBQAgN9EHAJJLw6bef/5PzLG9611LQ5ePX2ZnagTQcsreOvjC4sihiT3yi8ygqU90akC5LYJc+l3ypVtm2sBWnJEjR5rXX3/dbSGTEeSqQQcXAIDcRB8ASD59CS/bUhKZ1aUv4VfesCLR9YGAzqDsrY9+82fmyJ41rqUhBZD7jf5Rpw9NbKtMLmQPanIBAAAASCwFsFToWkOmwpR9ogLZGtqobA0ATVN25NuPXR4Z4FLgeMTsV2ymZNJrbyE7EeQCAAAAkGj6sq2C1yp8HTUDo2oJqWC2sr4ARFP2lrIi4zIjlb015MvvUO8OGY0gFwAAAICskG5Wl77MA6jns7eiatyRvYUkIcgFAAAAIGukk9VV+ouryeoCaqSTvXVNSRnZW0gMglwAAAAAso6yukbNK4+cYZGsLiB19paCWlffvstmbwFJQpALAAAAQNbSl3QNtdKQqzCf1RX1JR/IVqeP706ZveV/Zs4vGO5agOQgyAUAAAAgqykrRQWz47K6/Bd+srqQ7T767Uqze8OElNlbUT8nQFIQ5AIAAACQ9VSrK1VWV6qhW0DSHT9+3Lz91CRz4IXFZG8hqxHkAgAAAJAzUmV16cs/WV3INsre2vtYoal4/znXUk8/D4Nvj65dByQRQS4AAAAAOYWsLuSCYPZWFP8zUFDQeBZSIKkIcgEAAADIScpiuaakzH7ZDyOrC0mWKnsr/7KbyN5C1iLIBQAAACCn6cu+Cm4r6BWmbK5d/9jLHN2zxrUAmUszJ8Zlb53XvcAUTXzUDJ35LNlbyFoEuQAAAADkPBXc1tCtqKwu2bdtvg0eaAgYkIl+99IS89ZjIyKzt3pfOd0UzSozfYfNcy1AdiLIBQAAAABOqqwuBQ80BExDwYBMoeytXY+PNodeXe5aGlL21lUzNpK9hZxAkAsAAAAAAprK6tJQMGV1KbgAdCafvXXq6KuupZ6yt0bNKyd7CzmFIBcAAAAARFBWlwp0x2V17d4wgawudIqmsreKp6wzf/I3x03XHoUmLy8vax+ydetWuwQkr7qGW89ZO1fX/nB4Yxfk/EcCAEBOoA8AIF0KZkUV8xbNVnfxDU8wHAwdQtlbccGtPoPnmAF/uMIWmQdyEZlcAAAAANCEiz67yA790hCwMF+rKy7wALQFDUmMy95SUEt1t5TBRYALuYwgFwAAAACkIRhIiKIMGwUhouojAS116tQpm0UY92+r37B5sQFYINcQ5AIAAACAZtCQsGvmn7XDFMN8to0CXkBr6d9T6S+ujqz95oOuAyc+6loAEOQCAAAAgGbq0a2rGTrz2disLg0pU7CLGRjREsHsraqKfa61nrK3RtzxEdlbQAhBLgAAAABoIWV1jfhPlZHBBmXhvPXYCLK60CzpZm8p0AqgIYJcAAAAANAKPXv2tIGHoomPRhb99lldUfWUAC+d7C1qbwGpEeQCAAAAgDbQ1wUhFIwIo1YXUkmVvdUjv8iMmP0KtbeANBDkAgAAAIA2pGCEMrvisrreXFdsKg+/6FqQy44fP27KtpTEZm9dMuoec01JmenZd5RrAZAKQS4AAAAAaGMaUqbC4FFZXQpm7P7FBDs0TUPUkJuO7V1v9m0otsswn711+fhlrgVtrayszAYZ06X98/LyTHFxcbNe11b8+0+fznDVVAhyAQAAAEA7UGHwVFldGpqmIWrU6sotPntLj0/ONA6WkL3V/rZu3WoGDRpkCgsLmxWw6tWrl+nbt68pKGj889wRunfvbvr06eO2EIUgFwAAAAC0o6ayujRUjayu3KCsrQNPjYjN3hr+pe1kb3WA3r172+XIkSPtMh1nzIU2yFRZWdkpmVx6/27dupljx465FkQhyAUAAAAA7YysrtwWzN46e+qQa63ns7d69b/OtaA9jR071lRXV5vXX3897ays7uakOXPmjM3m6oxMLr2/kMmVGkEuAAAAAOggyurSDIwKaoSR1ZWdUmVvaUji1bfvInsrITozk0v0/mRypUaQCwAAAAA6mIIaKiyuIWphyup6918GmxMHN7kWJNHp47vNuxtnxGZv+X8D5xcMdy2Zbcdb79nC50uXLrVF0BcuXGi3fTH2/3ildnZIPTdu3Li65+bOndvhQaFNmzY1OAd/HhWVVfZ5X8T9lltusdtB2ueBBx5o8Fpds5SXl8dmckW95w9/+MO692xK3DlXnT3n9qh9/7hMrqjXa9v/fwkK/r+U+fPnN3jdypUrbXuU1l5ne8urVo5ejtu5Os+t1Rq7IOc/EgAAcgJ9AACZ4HcvLTGHXl3uthrqM3iOKRy7otMKXaNlFKjU/9eowvLK3iqesi4xwS3v4MGD5nOf+5yd3U+BDgVcFixYYPbv3282b95s91m+fLm55557TFFRkZk6darZuXOnfWj7lVdeafLf8UMPPWRee+01OyxQWUtRy4EDB5r777/fvaIxFZWfMmWKXS8pKTH5+fn2HI8cOWKeeeYZew4KcmnI4vXXX29++ctf2n09BX6WLavNrAtfn+h1/jiegkKLFy+26/49f/7zn9vPKJ1rb845jx8/3n7+QVHvHzzvFStWmEWLFtl1Cf6/fPzxx+3n6l+3evVqu8+SJUsafc6tvc6OQJCrBh1cAAByE30AAJmi8vCLpmxriR2yGKYaXgP+cIUNeCGzKXtLw00r3n/OtTSk7K2ooapJoCCLZiQUBTjWrl1r10XBEh9QefC/fd985y8esOuizCMN8fvVr35lgzRxlLH0pVtmNggoRdEx/mP7i7bOXVjwGDt27Ih9P13L8OHDzezZsxtcRzDYFAyVKBNN165gjo6pY3v+cwm3iw+YrVu3zsyZE/3z25xz1nP6rOPOubS01GbVecHndO4+AOWv3we3gsd7/vnnzcSJE+16+DWtuc6OwnBFAAAAAOhkKjiuwuNRARBlA/mi5Z1VCwhNU/bW7g0TIgNcvvZWUgNcXmFhoQ1yPPzww66llg9szJw5s0GAS7SvginvvPOOa4mmoJUylBRcSvVQgCUqwCVq1wyETdFMhRp2GK5vpawpURZTkAI9CiDp+o8ePdrg5/B//s//aZff/e537TLozjvvtK9Zs2aNa2ks3XPWcRR0ijtnBZiCAS6ZPHly3bUEs7+6du1qr1+zS6565FHXWuvGG2+0/x9lw4YNdimtvc6OQpALAAAAADJEqlpdqQqYo/Moe+vtpybZDK6o4YlJq72VioJVQ4cObTQkzWd4RWUh+YCQZjLsCN/73vfsUnWjVDdMGUhhfqbEcH2rl19+2S6V4RWmAJMeffv2bXD9b731ll0++eST9v2Cj3vvvde+RsMOU0nnnHUcDdmMO+chQ4bYZdiAAQPsMvj5nzt3zl7/NddcY/J79XCt9fT/WN599127lLa4zo5AkAsAAAAAMoiyfpTVpeBImAqYk9WVOVJlb2kmzRH/qTLx2VtBcbP7KStIFDjpbMpE2rJli5k2bZqtL6UAnDKcwoGjuGtJRdlKEvWzp0wqvV/woTYJZ3+FxZ2z6pkFRWWfvfTSS3Y5ePBgu4zzxhtvuLVaqa7fB8w+/fRTuwxqzXV2BIJcAAAAAJCBFBzREDcFvcJ8VtfRPZ0/PCgXnTr6qtn1+OjI7C3VUCua+Ki5asZG07NnT9eaHZStEzW734kTJ+xSgZM4vXv3dmvxVG8qOGtf1CM8JC+Khun54vgarrdv3z4bOAoGjaIyudIVzmQTDaOMGl6phwJsUa8JijpnZXaFA13hc1Yhetm7d69dxrnhhhvcWq1U13/gwAG7jPr/2drrbG8EuQAAAAAgQ2mIm4a6xWV17ds23w6V05A5dAzNhKkAlwJdYcreKppVZvoOm+dasoOKo19aWGUzmaKyf3wAKyqTyz/nA2GpzJo1y85omOoRnCWwKQq4aIZAzS4owbpgUZlMY8aMsctU9cPC2UrpvKY5/Dk/+mhtrSx/XH32KuDf3HP2dbU0K2VQqkwuPwRSxem9tr7O9sLsijXCMysBAIDcxOyKADKZAlkaphgVXJHiKeuYgbEd6XMvffq22Bkwr5zwk6wLbgUpSydqRkLxs/j94Ac/MD/84Q9da62VK1eaxYsX2+wkBW/ak4JPKoL/V8tWmutH19e1C8/+p2tR0fVbb701cqbC8AyC2j9Ydyz4XNxrPD2v7LO4DLS4c/7Wt75lfvrTnzY4Z51DeDbE4AyKcbMrRl2Pn11RgcUnnnjCPRP/mtZeZ0chkwsAAAAAEiBVVpcoAEZWV/vw2VtRAa5szd4Ki5uRUFJlcnUkZUG99tpr5oYxxWbChAm2KLqG/CnAVVRUVDcLpERlMmnIoOpiaYighkbOnTvXDqFUcEnBHT0nwUwuP4Ohf40vHq/XaluBoc2bN7u9Gwues147f/58+54KcAXPWZ9/VCZdcAZFnafe11+3D36tWrXKLr3g7IrK9Apeq39NeBbF1l5nRyHIBQAAAAAJkqpWlwqgv/UYMzC2FWVvvbmu2PzupdogQlCw9lZn1yHqCJqRsKmaXKnqbqVTk6st/OpXvzJ/9md/Zl588UVbFF1BGQ1zVPZSkIb+RV2L6mL5oJGyqBS4Wb58eYPspfD/b2WoqXC8glJ6P1+MXUExva6pIZYqHq9z1mvXrFlj3zN8znEzQkrw/fW+wetWdpcCdEGaXVHXr9kV9f9U5+mvVcfQa4IBQa+119kRGK5Yg+GKAABAGK4IIGk0u58CMOHi55J/2U1mwA0rbAYYmk/ZW1HBLdGw0MKxK3IiuIXsc/DgQfO5z33OFq1XUC+bEOSqceLgJtO1e4E5V/OHQcuufcaZHt26umcBAAAAIHNp6NSR7SX2e00UBbou+mznZ1gkhT7H919aEln7TNlbqn2mIYpAUvmaXFH11ZKOIJej2SIIbAEAAABIqqN71piD2++KzOrqkV9kBk19InKII2qdOnXKlL/5I5vBFUXZWwpwAUmXzZlc1ORyCHABAAAASDIVPlcB9KgsIxVMV+H0uABOrlP2Vukvro78fJS9pbpbBLiQLXxNrqj6XklHJhcAAAAAZBmyutKTTvbWZTf+A0kRQEIQ5AIAAACALNRUra7Lxy+zMzXmKn0uB19YbLPcwqi9BSQTQS4AAAAAyGLH9q43B/59MVldTlPZW/2GzTMDJz7qtgAkCUEuAAAAAMgBZVtKbMArirK6PjP0P5uePXu6luyk7K392+abs6cOuZZ6DOMEko8gFwAAAADkCAV5FOyKy+q68oYVWTlET9lbh7d/PTbIp2GbCvQBSDaCXE0oKyszxcXFbgsAACSR6tJIQUGBXQJArkuV1aWAT+E1f5U1WV0M1wRyRxe3RMiaNWvsdJqPPPKIawEAAEn1+uuvm8LCQrN06dK6gBcA5DIVVb9qxkZbYD1MtapKf3F1bMH6pFD2loJ5cZlrCuZdU1JGgAvIIgS5QlauXGkuvfRSM3/+fFNeXm66dOEjAgAg6c6dO2eXy5Yts8Guv/zLvyTYBSDnaVjiqHnlps/gOa6lnmYcfHfjDPO7l5bYYFHSKHvr7ccuj8xWU/bWiNmvMDwRyEJEcBwf3Fq8eLE5dKhxEUIAAJBcXbt2dWu1/vZv/5bMLgBwfFaXgj9hScvqInsLyG05X5NLNbfGjh1rs7YAAEBueuKJJ8ysWbPcFgDkLmVuKbAVJdNrdaWqvaWgloJ55xcMdy0AshGF52vsKfvI/P3yvzSrV692Lf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RWl2b/GXDDCu5AAgAAOKeP77YZ8criClP2VvHkdaZX/+tcCwAAAOK0eZBLUnXWlNWl4Yu9r5zuWgAAAHLT715aYg69utxtNdRv2DwzcOKjbgsAAABNaZcgl6dOmzpvUfoMnmMKx64wBQUFrgUAACA3qMzDB1smcUMQAACgDbVrkEvI6gIAAKj30W9XmgMvLHZbDekmoPpGAAAAaL4ubtluVH9r0K2/Mf1Hftu11FPdrnc3zrDZXrqjCQAAkK3U13n7qUmRAS7d+FPdUgJcyFVlZWVuDUAu43cBWqvdM7mCKg+/aMq2lsROiz1o6hOmZ99RrgXtYdrCn5nDRyrcVvN073G+eWktM2QCANBcx/aut5ntUTQxz8U3PEEJB+SklStXmqVLl5pFixaZ+++/37UCyFVz584127dvN8uWLTNz5sxxrUD62j2TK0gzA11TUmYLqYYp8LXr8dGxNbzQNr5w7UDzmT5XmL5XjjK9Lx5iH+msX9h3oBk17BJ3FAAAkA5lbym4FRfgUvbW0JnPEuBCzlFwq0+fPmbx4sWmvLzctQLIdXl5eWbfvn2mpKTEFBcXm/Xr17tngPR0aJDL00xBV83YaFPzw1SsXsEu1fJC27vjjz5nTlceMV3O62a69yywj3TW5Wu3kmUHAEC6ThzcZPZtKLZZXGHKXL/69l3mos+SIY3cEhfc6tKlU76WAMgwwYFmBLvQEh06XDHK/m3zzZE9a9xWQ5eMusdcPn6Z20JbmfP99eaDivy64FVTzp05Zc6dKDX//v8tdC0AACCOao5+sPM+c/iNh1xLQ+rbqI8D5BLV2Rk7dixZWwBaTL9Dfv7zn9ugFxCn02+ZKKsrrsiqsrpUoJWi9G1r4Zc/bz755Iz59JOzriW1s1UnzX++Y4LbAgAAcZS9pYz0qACX6o+OmP0KAS7kJH0p3blzp1mwYIFraejee++1GRw8ePDI7Ufc74glS5aYZ555hgAXmpQRecGaLnvoHadt4dWwivefM3sfK7TTbaNtTBo/2Jw5edhtpaYsLu37xS8McC0AACCK6opq1uioCXYU2FJdUibYQS7Tl9NVq1aZ0tLSRl9k8/Pz3RqAXFZR0XCSNP2uUAaoJqagfiXSkTGD3/N79bCFV+OyujTdNlldbedrt3zOVJ0qbzKb69NzZ8z066/iFwoAADFOHX3VZm8pAz1M9UeVvUX5BaBeMNilejty4sQJuwSQ23zAW5lbCm7pdwXfRdEcnV6TK4qKzmsWInUaw9RZHPCHK2z2F1quorLKTLnzUZN/8XBbYD7OiQ/eMP/wt7PNsOKLXAsAAPAU2IqbGVqzSV8x4SeRE+0AqKeb2C+//LKZPHmyawGQq7Zu3WrGjBlDYAstlpFBLi9Vx1FBrsKxK/jH3wpNFaA/c+q46dvjuPmXh+5wLQAAQJq6IafM9N5XTnctAAAA6AgZPVev6ldoem0Vag3TdNwHnhphC7yiZb77tRtsAfo4eu7P517ntgAAgKhO6O4NEyIDXKovOuKOjwhwAQAAdIKMzuQKUkZXVK0LUTCs8Jq/Mj179nQtSNe0hT8zp7tc0iibS1lcH584aF5au8i1AACQ2zSk6oMtk2Kzt66c8BPTd9g81wIAAICOltGZXEEq2KrCrVFZXQp+vfsvg03l4RddC9L1jT/+fGQ2l9pumTjUbQEAkNuUOb5vQ3Fs9lbRrDICXAAAAJ0sMZlc3idnjpv3tt9ljuxZ41oaUjBMmV1I36jZD5m+V45qUIBeBef//X99w/To1tW1AACQe5S9Vb5zsS2TEIV+BwAAQOZITCaXp+EAAyc+aq6asTFytiINa3xzXfSdVkS7dfI1pupUuduqHao46IoCAlwAgJxW8f5zNnsrKsDVs+8oWzeUABcAAEDmSFyQy1NB11Hzyu0si2FVFfvMrsdH28KwaNodf/Q5k1f1kdtyBedLKDgPAMhNyt7STbO3n5pkM8jDfAmF8wuGuxYAAABkgsQNV4yiYJY6o1EdUdXJGHDDCjqiTZjz/fXmg4p8u37+p4fM5lVft+sAAOQSZYKXPn2bvWEWprqgg6Y+YbO4AAAAkHkSm8kVdNFnF9mCr1HTdWuowVuPjTBHY2p4odbCL9cWoO/yaaUtRg8AQK7RDTNlgkcFuDQs8ZqSMgJcAAAAGSwrMrmClNV14IXFbqshBcH6TVhnCgoa1/KCMePn1g7vfPrhOXxGAICccfr4blO2pSSynqfqfxZPWRd5Iw0AAACZJeuCXEJntWUe+d8vmUNHT5q/WjjZtQAAkN0OvbrcZnBF6Tdsnp3sBgCCpi38mTl8pMJttV7/fvmUCgGANpKVQS4vVcdVBeufP/u35v/9xS673bVHL3OuqjIn1v2ye88CO5Nil67dTZfzutl9/FI+/eRsg/2bOi7rrLPOOuusJ2096KuX/1cztvf/seuaxZkbYgCi/PVPnzFbX6sw553Xve53SkuXKhdyRUGVWf93jSfTAgA0X1YHuSRVAdnnTn7f/J8DMxoEdtB8Cob5z5B11llnnXXWk7QeNPXifzCzR79vM76V+Q2g9XauznNrta6+fVfiJ4TSDKxTv7ne9L50pGtpudNH3jL/zw9vM8OKL3ItAOK8uqawwWRz2fD7BG0vKwrPp6ICsSoUq4KxYedOH6nr6KLlgp8h67VYr8V6LdZrsV6L9VqZsh58DBz0RZvBRYALaDualTTbqHbtdSOvsCMiWkOvv7z/ZwhwAS102lzi1oB6WZ/JFVR5+EXzzsYZDaK/nv4Aq2NLJBgAgOyj2ZbLtpaYs6cOuZZ6uiE29JZnCW4B7SBbMy/2lH1k/uTex1uVzfVxxYfmR9+41kwaP9i1AEglnBk6dkHOhDLQDFmfyRXUq/91ZtS8cltINkzDGd96bISt4wUAALKHJqN5+6lJkQGuy8cvMyNmv0KAC2gnPfuNcmu1okqIJJGyr1qTzaXX9co7RoALANpYTgW5PM2UFDccQYXqdz0+2s7QCAAAkkt1OV//x0vNsb3rXUs9ZW8Nvr08spwBgLbzSVXDIFDXmv531dlzbivZbpsywlSf+7hRfb90qOD8N/74824LQFNUCy+Im1OIk5NBLtGMScrq0iyLYeoU794wwRzds8a1AACAJPE3raKytxTYUvaW6uoAaF/dQzW5zp05bnp06+q2kk1ZWBd0OWFnSWyOc2dOmTMnD5uvTLvWtQBoSs/zWpY1idyTs0EuTzMoDbhhRaNIsGoH7Ns237wbU8MLAABkHp+9FVV+QPU3FdzSEEUAHaNrj4Z97DNZMlzRu+frN9msrOY4W3XSfO9rf+C2AKTj009Ou7Va2TipBdpGzge55KLPLjJDb/+dyb/sJtdS78TBTbZgZtRQBwAAkDkU2IrL3lI9Ts22rGGKANBWlM2VV/VRs2pzKYvri18Y4LYApCNcz++8UAAd8AhyOT179jRDZz4be3dXRWv1IKsLAIDMojqaCm5piGKYMrVVh1P1OAF0vK4XNJziPxv70n96y6i0s7k0o+ItE4cyXBoA2glBrhDV6dDUxlF3epXN9cbaYpvdBQAAOt9Hv11pZ0fWMMUw1d1U/U3V4QTQ8VRg/rzuvd1WrXMfH3Zr2ePOL4+32Vnp0H5//tUxbgtAS3ULBdABjyBXhPMLhsfW7NDdJ9XpOvDCYtcCAAA6mmZZivt7rOwt1dzUA0DnUYH5XJkBbfr1V9ksrVQ0pHHUsEvI4gJaIFzPr0vX890a0BBBrhT87EtRRe1051iFbaPuHAMAgPaj2Y/3PlYYmVmtrK2iWWWRsycD6HzZWvrj3gU32Sytc2c/di2NfXzioPnOn17vtgC0Rq4E0NF8BLmaoGGLKlSrgFeYCtvG1QABAABtS1+OVR9Tsx+HqbNbNPFRW3+LLAkgc+RKcWhlrSlL69OzVa6lIWVxDbqiwAwrvsi1AGiOMyf3u7VaXS/ob4dEA2EEudKkoYvK6oqKGPvZnMjqAgCgfShrS3Uxo2Y71g2p4bO2m77D5rkWAJlAX0B7XNhwRER4hrRsoiytT0/9zm3V+/STs7Yw/cIvf961AGiOqPp+ouAyEEaQqxnUiR56++8ih0AowKVAlwJeAACg7Sh7S/W3ooY5+ZtQqqcJILPoC+i50M/tJ1XZO1O5srRGDLrYZm0FnauqNL3yjplJ4we7FgDNod8lVSf2uK1aDFdEHIJczdSzZ09byFbDIaJ+sDR0UcEuTWcOAABaTjeQ3lwXnb2lepmaDTmqnACAzFGdf51bq5XNmVxSMmNkg2wun8X1jT8miwtojfDvju4RdbMBIcjVQipsq6yuqGnJ1SnfvWGCLU4PAACa59SpU3bWRN00ivpCrMCW6mWSvQVkvnCNPGVkVlRG163KBsrW6nn+eQ2yufKqPjJfmXat2wLQEqeONCwNFDU5HCAEuVpBWV3K6Bpww4pGWV36A64OuoZXaJpzAADQNGVCl/7i6sgbRerQamiihigCSA6V/Aj69Nizbi073fP1m0yXTyttFlfVqXJz5+xx7hkALaGaXOGSBdzoQhyCXG3gos8ustOVh/+Aiwrlxk1zDgAA6qmu5VuPjYjM3uo3bJ4Z8uV3Iv/WAshs4S+jZ7J8yKKyuSorjtl1ZXHdeuMguw6gZc4d2+HWatEXQCoEudqIUrFT3V1WRpcK52oIBgAAqKfsLQ1NVF3LMGVKK2t64MRHmUUJSKgL+n7OrdUKF5DORt/72h+Yig93m0njBzUasgmgeapONgyMn9eDnynEI8jVxlQnRIVwo6LLKpz79mOXk9UFAICjYYnK3lI9yzBlb42446PI+pcAkiNcIDrbi8/LrZM/a3p062Lumf8HrgVAS5368NdurdaFl050a0BjedU13DramIZdRN2VFgXDCq/5K1vXCwCAXKN6lR++cJupeP8511JP2VvKjFY5AADJpyC2sjVl7Z6/MK9+cotdDzpXVWm69uiVFcvuPQvMubMfm67dLqhbiorR6zkt0z0WS5a5vgxbMmSuGX3z/abvsHmuBWiIIFc70x/10qdvi7xjpQK6g6Y+wZhiAEBOObpnjdm3bb7bMua+/2XMD75Wu55/2U3misn/yk0gIIuoaPSbj3az688c+b/MM0f/L1uUPUqX87rZ5zJ52Z7SPQeWLLN9GebbFxX/hfmjOQ+bXv2vc88ADRHk6iDK6FJmVxRldTFTFAAg26ku5eHtX7fD94PGLTRmxypjZysmewvITq+uKbSzowWDXMEvtQCQig98KZNr4vyXTbeel9htIIwgVwdSLS4Vnw9PfyrK5iqeso6pUAEAWUmBrfe232XOnjrkWuopyFX1+7JGdXsAZA9NwhSsS6sJJai3B6ApmpxGtTs9lTQYNa/cbQGNUXi+A+kPuQroqpBumIY16oc3roYXAABJtX/bfHuTJyrA5TOZCXAB2e2CUHmOjyMmmwCAsHDZn579KPWD1AhydTBNf65p0HX3KoqGNKowp4Z0AACQZMraeHNdsTmyZ41rqae6lJqNWEP2AWS/7hcOdGu1Pj76mlsDgHhnQkEu9R+AVAhydRJldV0z/6wtsBtmZ6D5x152WnUAAJJGN2qUmazhSVETryiwdU1JGUP0gRwSztbUECQAaMqpj37t1mr1vOgLbg2IRpCrEymra+jMZ20trigHXlhs3n5qElldAIDE0I2a/Ruvj5xsRXdfR8x+hclWgBxUnd9wJjT9rgCAplS8/5xbq0V5AzSFIFcG6DN4js3qUvH5MP1Qv/3Y5Y1mogIAINPUDbmP+PKqv3WDvvRW5N86ANmvoKDAFowOChaiB4AwZXyGM8LDAXMgjCBXhlBWV9zdbc3GqIK9epDVBQDINOqEKrgVNXmKvtT6rOWePXu6VgC5qLB4llurRfF5AKmEb5opI1wBcyAVglwZRnVKBt9eHnmnW9lcqtUVTtkEAKCzqH6kZgeOyt5S/cmht/8usv4kgNyTf8U0t1arfO8/uzUAaOzEvl+4tVqFg+e4NSAeQa4MpOi0srriZpxSnS7dLSerCwDQWZS9pb9Hqh8ZpuwtZW5pJmGytwB44Zu41OUCkErlhy+6tVoX9P2cWwPiEeTKYBq6qGBX1DSpqntS+ouryeoCAHQ4ZRbv3jAh8m+QsreKZpXZGlwdraKyyixdutTk5eWZ6dOnu1YAmUIzqob7tdTlAhAlqh5XZ/QtkDwEuTKc7nhpmvWLPrvItdTTD73uokfNYAUAQFtTBrGvEal6kWG6OaPsrc6ol1FWVmYmTbzeLFvGzI1AJisooi4XgKaFMz0pfYB0EeRKiAE3rLCFe8Oz0oiGLsbNZgUAQFtQ9lbcbL+6IXP17btih9m3t5UrV5pBgwaZnTt3mgULFrhWAJmIulwA0hGux9XrYmZVRHoIciWIotcj7vgoMk1TAS4FusjqAgC0JWVv6WZKquwtDa3XMKTOcPz4cTtEUcGt6urquiBXnz597BJAZglP/89NWgBRwvW4CgZ+ya0BqRHkSpge3braYr56xGV1aQijxjADANAa+vKp+o9RN1BUVyfVJCkdRUMjlcG1atUqu33ixAm7PHbsmF0CyCz6mQ0XoKcuF4CgqHpcn1442q0BqRHkSihlc8VNy65CwCoIrGndAQBoCc2aqAzhcCdTFNga8uV3Gn1R7SzFxcVurR6ZXEDm6tmv4e+Okx9sc2sAUPt9NkjfefN79XBbQGoEuRJM07KrTldUVpeGlOgLyrsbZ9ihJgAApEN3TxXcirpRor81+rujIYrKLM5EvXv3tksyuYDMVTDoq26t1u/J5AIQ8Pv3Nru1WtTjQnMQ5MoCyuoaPmt75B11pX/HFQoGACBIQ97femxEZI2cfsPm2bqQmT67kR+uCCBzRdXlUn09AJDj+za4tVrU40JzEOTKEir4q9ooursepqwuP+U7WV0AgDB9uYybvETZW1fN2GgGTnw0Y7O3gnwmF4DMFVWX65PDDb/UAshNlYcbFpwX6nGhOQhyZRnVSdE07lFZXcrmUgHh8BhnAEDu0rDEvY8VRmZvKWtL9R97XzndtWQ+n8lFTS4gs30m9Hvlwzf/b7cGIJeFfxdo1BL1uNAcBLmykLK6Bt36m8gZr1RAWLMvql4XWV0AkLtUe8v/PYiieo+qv6X6j0lCTS4gGXoNvdut1VKgndnBgdxWdfZcozI7vYsYqojmIciVpTSkREMXNYRR07yH6c69srroTABA7lEHUgGuqMxeZQJfM/+svXOaRD6Tq1u3bnYJIDNFDVkM1+EBkFsqD/xvt1ZLJROS2h9B5yHIleXsl5WSMlswOExZXSowrELDAIDspwxeX6Px7KlDrrVe3c2RBNTeiuMzuc6ePWuXADJX/1ENs7kOvfqAWwOQi47sWuXWahUWz3JrQPryqmu4dWQ5zbSoLzYqRB+mYNjAmx6NrOUFAEg+/Q14d+MMt9WQfvdreKKGu3eGvLw805ruyAMPPGBef/11c+GFF9rliy++aIqKiszUqVPt8xdddJH58Y9/bNcBZJadq/PcWq3hX9puevVvOPsigOynSXBUIzSI3wdoCYJcOWj/tvnmyJ41bquhATesMBd9dpHbAgAknbK3yt/8UeTMiaL6jVEz83ak1ga5pk+fbjZv3uy2Ghs+fLjZvn27HR4FILOE+6UafaDZXAHkFvVTgiOMVHJHI5KA5iLIlaNUk0u/RKKyujSbloJdnXVHHwDQNlRzq2xr9NBEdR4HTX0iIzJ4WxvkApBc4SxT1eAZccdHiR42DaD53lxXbMvpeLoBFzWRGtAUanLlKGVraVp4BbTC9KVo94YJNhAGAEgm3chQcfmoAJc6jbo7yhB1AJ2t95XTG0ySpBuw4eLTALKbJkMLBrikoIh6XGgZglw5TNPCa3r4ooiUcHUwNK28anhpqAsAIBk0Df+ux0dHDk9UhsRVMzZ2+vBEAAgqDM2eFi4+DSC7hX/mlYjBqCK0FEEumL7D5pmrb98VeUffTjP/2OV2CQDIbApsKcClQFeYpuDWECBlTQBAJuk79GturZZGFagINYDcEK4XXTjoq24NaD6CXLAUKde08VF395XVpYwuFQYlqwsAMo/S/DU0MViw1VP2lmZO1IMaNwAykfqh4Zutp/dRNgPIBarLF64T/Zkh33BrQPMR5EIDqtOirK5gbQRPEfbSX1xt764BADKDMm3femxE5O9mZW2p/qKyuAAgk/UbsdCt1WLIIpAbjpf+s1urpT4LN+XQGgS50Ijupg358juRs1moIKDPFiCrCwA6j34Ha2iiMm3DlL2lWXJVf0v1FwEg03W7rGEwXn1OymUA2U3DksNDFfuEhi8DzUWQC5EUPdfQRQ1hjMrqUt0XZXVF1X0BALQvXy8x6newhvwUzSqzs+gCQFIUFBSY/iO/7bZqHX71AbcGIBudeO0ut1ZLfRhqh6K1CHIhJf2iGfSltyKHuugOW9wMXgCAtqfsLWVu6RGuXyH+5oS+LAJA0oSHLCqQTzYXkJ2isrguvua/uDWg5fKqa7h1ICXVe9n79G2RX6yU7aVhMUz1CgDtQ1/2dGMhim5IqLC8fgePGzfO7Ny50z2THOXl5QTnANggfjCwpT7mNSVlbgtAtjjwwmLz0W/rJ5hQqYXBXzlk8nv1cC1AyxDkQrMowHXg3xdH3lXTLyZlETBEBgDajrK3jrz8nQYdwSDVT4yaGRcAkigqoD/8S9tN1z7jKEYNZJGdq/PcWi3VEuV7JNoCwxXRLH4qev0S0nqQDYC9sNgWptd09gCA1tGXPdU/jApwKbtBQxMJcAHIJspMLSia5bZq/e43SwhwAVkkXO5G3ysJcKGtEORCi+iXkKaljyoMqGGNuzdMoIYCALSCZrFVNoPqH4bpd7CG7+jLIABkm0vH/sCt1VLfkhuoQHaoOnvOHApNKsENO7QlglxoMU1LrzpcyuoKU1aXL46soTYAgPT4oTpRk3roTmfc710AyBZR2VwaLaAvxwCSrfytBxvUeFbf5jNDvuG2gNYjyIVWU0bB1bfviswoUDbXrn/sZU4c3ORaAABxFNhSgEuBrrB+w+aZUfPKmVobQE4Iz7SobK7qynfdFoAkisriumTU3QxHRpsiyIU2oRm9UtWGeXfjDHsHjqwuAGhMw3BUz1BDFMN0h1OZWwMnPupa0FxlZWV2qvJ0af+8vDxTXFzcrNe1Ff/+06cT0ETuUkA/fANVfUkAyRXO4pLzi6jFhbZFkAttSrN8KdilgshhKpysAspRGQoAkKv0u1F1DJWlEJZ/2U22/iHFWFtu69atZtCgQaawsLBZAatevXqZvn37moKChpOsdKQ+ffq4NSA3XRa6eeprczFsEUieqCyu/iO/3al/Z5GdCHKhzemumwoiK+AVpgLKGorDnTgAuU6Zrcre0u/D8F1NUfbW0JnP2vqHaLnevXvb5fDhw+0yXd27dzeVlZWdksklCsodO3bMbQG56fxLbrajBYL0O5OhTUDyRGVx9f/c3W4NaDsEudBuNHRRWV0aahOmzIW4ujMAkO1Ur/Ddfxkcmb2lGwWDby8ne6uNjB071lRXV5tdu3Y1626xAlzK5uqsO8x6fzK5kOsUzLpiwk/cVi393qTWK5AsumEULsmgLK5uPS9xW0DbIciFdqUvayqUrILJYX4GsagaNACQjZS95WeePXvqkGut528OkLrfuc6YC22A68yZM52WyaX3J5MLiK7Npd+hFZVVbgtApjuyvcSt1SOLC+2FIBc6hAoma9r7qKyuutnEar78RQ3ZAYBsoOwDZW8piytMdQw1S23UMO/O4AufL1261K4vXLjQbvti7Grz+40bN67uublz53b4BCMbNmxocA7+PHxwyl+L2sK0z0MPPdTgtbrm6qqjNpNKQxajAo5R7/nDH/4w7YBY3DkHv7SnyuTS6ydMmNDg9Trezp073R71drz1nn1e1yV33HFHg9etXLnStkdp7XUCbUXDt4PUX6x8p2GGF4DMpMzLcPalfqbJ4kJ7yatWDj/QgVSDJmqIjugXHkN0AGQTBX3K3/yRDehHUWCr3+gfZVSNGQWGNMxPs/tt2rTJlJeXmwULFpj9+/ebzZs3232WL19u7rnnHlNUVGSmTp1qAyx6aPuVV5rORlNw5fnnnzf5+fmmoqLCLk+ePGkDS8qgkoEDB5r777/frkfR6ydOnGjXS0pK7DF0jnv27GkQiNO1jB8/3l5LkAI/y5bVFrYOX5+ojtf27dsbXIvOe/Hi2rqS/j1//vOf288onWuPO2c93nxtu70ZtKfsIzNh7LDIc456/+B5r1ixwixaVP93VEW6+10xztx66611/y/961avXm33WbJkSaPPubXXCbS1/dvmmyN71ritWro5EK7ZBSCzvLqmsEEig27sqX4z0F4IcqFTKJNBqeZRNJvYxTc8QecZQOJpWPa7G2dEDk1UJ2/Q1CcaDcPJBAoMKcCjYJMCHGvXrnXPGBv48gGVe++91/z4xz+266LMIwVBSktLbcZXKsHjxFFw6tlt/2Hye/VwLfWU9fSV2V+yx9ixY4fdN4q/ltmzZze4Ds26OGXKFLse7AopS0mzMeo6dEwd29Ox9Fy4XXzAbN26dWbOnDmutaHmnPPIkSNtYCrunMOfcfA5nbv/G6pMruvHDI78fxn3mtZeJ9Ae9POz9+eXNPiybGegnfms2wKQad7bfpc5/MZDbqsWwWm0N4YrolP0GTzHXDP/rO2chCnL68BTIyKH9ABAUqjeoIZiRwW49Dtw0JfeysgAl6eaUApyPPzww66l1qxZs+xSAZNggEv8vk0Fr0RZRQoupXoowBIV4BK1p1uYPaq+1TPPPGOXymIKUqBHASTNbhiuyfXII4/Y5Xe/+127DLrzzjvta9asaZhpEtScc1ZGW9w5K8AUDiJOnjy57lqC2V/9P1Md+/9Sr5k2bZpd19BEr7XXCbQH/fwM+MOGwxbVZzwayu4CkBmUSRwOcKlOMwEutDeCXOg0Gpqju28qtBymL4W+OHNH13cBgNbwk2pEDU/UUDT93iuess707NnTtWYmBXiGDh3aKKv285//vF1qyFqYDwidOHHCLtvbN77xDbtU3SjVDVMGUhRdSzi49PLLL9ulMrzClNWkR7gml3/Nk08+ad8v+FBWm15z5MgRu0+cdM85qiaXf/8hQ4bYZdiAAQPs8vXXX7dLOXfunD2vqP+XMmbMGLt8++237VLa4jqB9qAbBOEbpAe332Wqzp5zWwAyxYEXaoe8e+oDqU4z0N4IcqHTqR6NpsuPymhQNteuf+wVW8MLADLJR79dWTuRxtFXXUs9fTkbObcsMoM1E0VlEqWro4JcykTasmWLzUZSfSkNsQsWxvdaci3KVpKoIuvKpNL7BR9qk6NHj6YszJ7OOXft2jUy++yll16yy8GDB9tlHB+kEl2HHnHX7wNjUVpznUB7iSpCf+hXd7otAJlA3+HC39/CmZhAeyHIhYygu8uaNj8qq0tUrF5Df8jqApCJlJKv31Phu5aiO5dFEx+12VtRM8xmqrjZ/XwAq3fv3nbZUqrJFZy1L+rRVF0vUdDIF1TXcL19+/bZwFFwpsFUMxXG0fEkKvtJwyijhlfqoWBV1GuCmjpnZV9FnbMK0cvevXvtMs6kSZPcWn1WWtz1HzhwwC4VCAxr7XUC7UFDncIz0aogvX4PA+h8ugFy4N8b9od0g083+4COQJALGUWdFgW7VJA5TEN/NP0+WV0AMonuVr712IjI3029r5xuht7+O9N32DzXkgxxmUTig1tR2VrNCXqotpdmNEz1CM4S2BS9t2YI1OyC8s4779jlGXNh5LX4YXp+v7CoTK6mXtNccecsLTnnf/3Xf7VLzUoZlCqTy2d9qTi/19bXCbQ1OyNtqK8YN6ERgI51ctd9DSaIkHAGJtCeCHIh42jYoqaVDd+lE9XqUrZE3FT8ANBRlFnqawdGUYfuqhkbM772VpS4TCJJNRTRB4TSyfJSAGvVqlUpH3fffbfbuzG9l7LBghlb4jOTvO7mZGRNrptvvtkuH3zwQbv0lKGkrKqoTK6413iarTA8VDIo3XP24s5ZRf/D76P3fuqpp2yB+ahZDzUZwC233OK2auk1ag+/prXXCbQ31XW9LJT9r2HiGjIOoPNUHn6xUbF5jdSh2Dw6EkEuZCz9QlRWV9TwHg1dfHNdcWTdGwBobycObrL1AqNmgVWgXtNjX/TZ9LOQMk06mVypdERNLgWfXnvtNVvA3Rdx13LZsmU2K+krfzzd7qdriarJ5WcWVMBJQyPnzp1rA1AKcCnoo+fCdaf0Gg0v9K/x76vXanvKlCkpZ5bUOauuVtQ5q5B/MNCkwFzUOfsZFHWeel9/DL23KDgYRcf/j//4jwbX6l8TnkWxtdcJdAQNfSooqp3t1dOQcYYtAp1DN8je2TjDbdVSxmXh1Y1n6gXaE0EuZDR9WdRQn6gx3FUV+2JnMAOA9uCzt94NdeI8H5xP+h3LdDK5WluTqy386le/qgvGqCi6lhrmuGvXrrobJLqWuJpUqovlg0YqqK7AzfLly20tKunbt2+DTC7R8EIVjlfQyL+vXqugmF7X1BDL0tJSe47hcw5nRikwF3XOwff3heH9MXRsBeiiTJgwwT6v8/TXqmOoLSrzq7XXCXSEvuMbz9Sm38/Mtgh0vNJNX2w0TLF48jqbeQl0pLxqVQ8FEkD1bvY+fVujX56iYoYaGkQqLID2ot9B+7fNtwH2MN2pHDT1ichZYoHOpEy0/v3722L0CuoB2UYZteFh47o5qsk+AHQMJR1opE1Q/5HfNldM+InbAjoOmVxIDAWylNWlQs5h+vKpws9RQ4cAoDWUvaUhMKoHGBXgUv3AIV9+hwAXMpKy2KJqkgHZQgGtcMa/+oPU5wI6hupwhQNc+t5GgAudhSAXEkUFnFXIWVlbUbW6/DAifSkFgNZSbZfSX1wd+WVJv4M0NFFDFEnFRyZLNbsikA2UtRWebZH6XED7U7Zw2daGmZTqH118wxNuC+h4BLmQSCrorKyuqMwJXxBaSwBoKd2VVIZoVPZWv2HzzKh55WRvIRHi6qsB2UQ3QcOozwW0ryPbSxr1k4bU/CyG61kCHYmaXEi8qDHgntLX+0/4WSKn8AfQOTRr6/7n5kfO3qq7k8oYiBo2DQDoXEf3rDH7ts13W7WozwW0j6jvYCrhoAx3oDMR5EJWUDq6hipGfSnt1vMSO7OHxoYDQCoalqghLlEU2IrKFAAAZA5NEHJkzxq3VUtlLjQKAEDbUB2u3b+Y4LZq2frJM591W0DnIciFrKK7CbqrEEWdm35j/htZXQAaUaBcwS1NYhGm7C3dleQLEgBkPg1PfOd/D2k0hOrq23cxCzfQBioqq8zen1/SYMZ79ZWKZpUxTBEZgSAXso6yuUqfvo1p/gGkRdlbCpAHO2uenR1o8r8SHAeABNGNC9VUDFIfUDPhMlEI0DqabTp8U3D4l7abXv2vc1tA56LwPLKOAljqxGhMeJgCX7seHx1bwwtA7tAsrBrmrAyuqACXsreUdk+ACwCSRRlbRRMfdVu11Afcv/mLdjY4AC3z3va7GgW49J2LABcyCZlcyGqaYVFfYqO+wCoYNvCmR8nqAnLQsb3rbUft7KlDrqWefieoSDHDWgAg2aLqc1GIHmiZqELz1OFCJiLIhZwQ1cnxlK0RlfUFIPsoe+vIy9+xQxSj8PsAALKH6nOVPvn5RhMT9Rs2zwwMZXoBiBc1MQ91uJCpCHIhZyir692NM9xWQ7oLcfENT/BLGshiSq9XwJt6fQCQOzQ88b2Noxv97tcNDd3YAJBa1HcoBbiGz9pO1jsyEkEu5BTd0VM9hqgZ1IQppoHso+yt8jd/FDvzqr7o9Bv9I4oRA0CW0tD0Pb+Y0CjQRb8PSK3y8Itmd83PTthVMzaa3ldOd1tAZiHIhZykejyq1RVFtRr6T/gZxaaBLJBqtlXdhVRdFjppAJD9NOPi7g0TGtVp5cs6EC1qllLhZwaZjiAXcpayO/ZvvL5RnQbp1vMSc8WEn9iAF4BkiiqQ6uln+7Ib/4HsLQDIIXxpB9KjnxUNUQzfJNSspX2HzXNbQGYiyIWc19QXYbK6gGSJ65gJ2VsAkNvi6gsNmbHR9Op/nWsBcldcHTsm50FSEOQCauhLsYYvRmV1qSC1ZuBRcXoAmU2z/yhoHR6OIgpsXTbxcYLWAJDjju5ZY/Ztm++2alFIG6j19lOTGtUv1oykl/zBI2TAIxEIcgEB+nIcV5waQDLpi4vuPlJcGADg6abIgRcWu61aurGpoYsEupCLlMH14Qu3NQpwaWSLsuCBpCDIBYSkKlQNIFl69h1lLp3yrCkoKHAtAADUzrh99PUfmw923udaainQVTx5HUMXkXN2PT660agWjWQZOO3fyOBCohDkAiKo43P4139u7/IBSA4FtXwHjdoRAICm7N823xzZs8Zt1aJGF3JJXC1T9alGzH7FbQHJQZALSCGqOCmAzKXO2Hvb7zIDbljBcBMAQJN0Y/PQr+5sFOgSDdFipm1ks1QBLjLhkVQEuYA0qRPkU3VZZ531zF8HACBdukFy+I2H3FY93TShpiOyUeXhF807G2c0mqxHQxSHznzWbQHJQ5ALAAAAQE7TTZLytx60kxCFMfwd2UajVTSzPAEuZCOCXAAAAABQ4+ieNWbftvluq16/YfPMwImPui0guaJmFhX+jSNbEOQCAAAAgBrK6Dp96JnImqyqz1U4dgV1ipBYh15dTrYish5BLgAAAAAIUEHutx4b4bbqaTjX4KlP2BkYgSSh7hxyBUEuAAAAAAhQRld15buRM8/1yC8yg6Y+YWegAzLd8ePHzYcv3GYq3n/OtdS7asZG0/vK6W4LyA4EuQAAAAAgggIE720c3SjQJWTAINOpwPzBFxY3+verTMQhMzaarn3GMSs1sg5BLgAAAABIYdfjo82po6+6rXrU6UKmiqu/5QNcvfpf51qA7EKQC2ilsrIyU1xc7LYAtKc9ZR+Z/oXd+DIBAOhwZVtKzLG9691WPYYvIpOkGp6of6OXTnmWfhSyWhe3BNBMK1euNH369DGPPPKIawHQ3p7d/LgZNGiQeeCBB0xFZZVrBQCg/RVPWWcfYRoKpkwvZc4AnUnZhvs2FEcGuPoNm2dGzH6FABeyHkEuoJl8cGvx4sWmvLzcdOnCjxHQkfRzd88995iBV15qg10qDgwAQEfQ8MSrb98VmbWloWHK9lImDdDR9O9PwdZPzjT896fhiSowP3Dio64FyG58OwfStGbNmgbBLQAdL3j30Qe7Lu1/sQ128aUCANARzi8YbjNilBkTpuGMyqRRwW+gI6j/E5dJqGBs0awyZlBETqEmF9AE1dwaO3YsgS0gwxUWFpp/+7d/sz+vAAB0BAW1Dvz74kbZM8Lsi2hvCqYqezDq398lo+4xl49f5raA3EEmF9AEFZXfvnOPWbBggWtp6N577zWKFfPgwaP9HytWrHA/eQ3NnDmTABcAoMNp+KIyZaKGLx54YXHsrIxAayh7a/+2+ebdjTNihycS4EKuIsgFpGFY8UVm1apVprS01Myb1zA1PT8/360BaG/hYqklJSVmx44d5pe//CUBLgBAp9DfprjhiwpwKdD13va7GFaPNqFhiXsfKzRH9qxxLfXyL7vJ1oxjeCJyGUEuoBmU1fXoo4/aYJfP7Dpx4oRdAmh//gvCtGnTbHBr7dq1BLcAABlBhb2VQaNMmrDDbzxka3UdjQhMAOmoPPyiDZiqwHwUZW4Nnfms6dbzEtcC5CZqcgGtoHpdekyePNm1AGhP+nk7duwYgS0AQMbSDZkj20tii88r20b1ulTAHmiK/j2V71xs679F6ZFfZAZNfSJyyCyQiwhyAQAAAEAbU5Dr4AuLTVXFPtfSkAqD9xp6d6Oh+ICnzL+D2++KLCyvjMFLRt1t/x0BqEeQCwAAAADaiepxabhiFAUqBvzhClvAHvA0NFETF8RNWqB/L4VjVxAgBSIQ5AIAAACAdnT6+G4btKh4/znX0pCGMF4x4ScMOctxGpp44rW7IovKi4YmXnnDCgrLAykQ5AIAAACADqC6Sgf+fXHk8DNRhs6lY39Ava4co+BW5dsP2JkT46iwPEMTgaYR5AIAAACADqQZ8lIFNBTsuvia/2J69b/OtSAbpRPcYqICoHkIcgEAAABAB1O9pf3PzY+tuyQMY8xOGr56+LUHYocliuq1FU9Zx9BEoJkIcgFAG9IdOUm3EGhZWZkZO3as6d27t3nllVfSft2eso/M8EEXm2nTpplNm6KnKAcAAJlPQxjff2lJ7CyMoiDXZeOXEfBIOAW3Pth5n/1/ngpDE4GW6+KWALKEgix9+vQxeXl5jR7jxo0z69en/qOKltu6daspLCy0Dx/sSkd5ebnp27dvs2bI6W5O2vfR/+vWqKis4t8LAACdSEMTrykps1k7cRlbyvZ6d+MMs+vx0ebEQW5uJY3+/5VtKTFvPTYiNsBlZ9q8YYUZu6CaABfQCgS5gCyjQImygqSkpMQsWLDAPpTxs3PnTtvWVoGL6dOn22CIjhulqeezjf/clZl1XrcL7HpTfFDs6NGjrqVeqs+va9eu5syZM+bYsWOupWXye/XosH8vAAAgnoJdI2a/Yq6asdEOU4zig11vriu2dZyac1MNHU8BrbefmmSDk3HBLc2YqODWqHnl5qLPLnKtAFqKIBeQZZSZc+LECRs4efjhh82qVavsQ0PatmzZYve577777BJtS8EtjQDfsWOHDR6lQ1lclZWVNpOrOc6dO2eXrc3kUueYfy8AAGQODUkcOvPZlMEuDW1U8fq9jxXaDKGjKWo7oWMp027/tvlm5+o8+/+m4v3n3DMNKbil7D1l8RHcAtoOQS4gy/jMHAVPwiZPnmyKiorM7t27ufOXQXr16mWXzf1/0r1791ZncvnMP/69AACQWXyw6+rbd5mColmutTFlCO1zQRUFVxjO2PFUa0tBx1fXFNpMu1QF5TUk1Qe3lL0HoG0R5AKyzNlTh8zp06dtACQsmLUTRTWlVIfJ12TSQ9sqjh60cOFC+9zmzZvtdvA1GtrW1PNB6b6nqE3PL1261K7799GjuLi47jVaBo85d+7clEEanYP20/DAsJUrVzb5nM5H/Pnp/aI88MAD9nn/8K/zASZfkyvdz08ZYD6TK/xZNGeIqP5NtOTfCwAAaF9VZ8+Z8wuGm8FTn7BDGfsNm+eeiabgSnA4o4IvaB/qJ33025V2KKJqbenz/uRMfH9TWXnKztP/R4JbQPshyAVkmW49LzHnn3++rdcUpiFoCqiMHz++UZFzBWymTJlSV4cpWJdp0KBB9nnvq1/9qn3eBz+CtZy+8IUvpHx+yJAhtk2a856ejrlv3z47NHD16tV1r1GbXqNAkpaqcaXntN+6devM6NGjYwNdPmNJQaXwPgcOHLDLI0eOxD43e/ZsuxSdX1R2lQJa99xTW0TUn/OyZcvsuXr++Kk+vyuHXWfbLi2sshlg27dvNz169Gj0WSgwlm6gS5lczf33AgAA2l+Pbl3dWm0G0MCJj5rBt5fbwuQa7hbHD2dU8EVBGAVj4vpBaB5lzmkYooaKHnhhsa2TFkfF5BWYHP6l7TYrj9kxgfaXV60CMgCyhmpyDbzyUhucUHAkPz/ftivg4YNJa9eutW2eMpkUbJLS0lKbCeQFn9Mxg8EOZTcpMKQaVAomhaV6viXvqUwpHxQKX4d/L1myZIm5//777br4bKd/+7d/izxPUSaUAkUKiM2ZU3t3TZ1BvZ/OQYLX4Z/TQ+3izy98bsHrCf7KDR5fx/XH8VJ9fnqv4cOH2+BU+P0UHFy8eLENeClQlUrwHNL99wIAADJD5eEXzZHdq0x52YaUWUSeAmWfuXK6ufDSiQRc0qTPuOKD58zv39scW18rTJlavYu+RMYW0AnI5AKyTHC2PAVsFLjRw2f1qE3ZTkHPPPOMXeq5YLBJlOWkoJGEAyZNFT1P9XxL3vOMudBmNyngoyLpQbNm1daqUFAmGOAS7asgzjvvvONaGlOml6xZU19DYe/evfZ1ypCSxx9/3C7FP9evXz/XUj9TYjiTy1+rvyZPwTsF+PQaZZ6F77Cm+vz0WSiTSxlo4SCUgnQ6ZlT2WZjOobn/XgAAQGbo1f86m92lmflU56mpoIqyjjSsTkMaVcNLM/9pmzpe9TTEU5+JPht9Rrt/McFmxTUV4FIAUbMkDr3jdFr/LwC0D4JcQJYJzq6oIIwyh/xDs+Wp9pKGzQVrO7388st2GRxKGDRgwAC7fP311+3Sa6roearnW/Ke3c1Jm7k0dOjQRsPnPv/5z9ulgj5hPtATPv8gZT35wJD3m9/8xi4V5NJzTz/9tN0WBYJk3rz62hj6vPUIB6f8tQaHNXr+NZpdMXxNqT4/fRYyYcIEu4wTPmZYsIbb70+ebvTvRYG08L8XAACQeRRUUXBFwxkVbFHQpSkK3CiAEw56KXspV/jAn4YgqnC8hnimE9QSDRm9fPwyOzmAam1plsR0Z9gG0D4IcgFZpqnZFX/1q1/ZdWUV+eDPSy+9ZJeDBw+2yzg+WNMW9uzZY5dNvecbb7zh1ozp2rVrm8woGEXZZKo9pQym559/3rZt2LDBZo3pHDV0UM9pmKBUVFTYpdqDFAxrzvn57DQF79IZZuDps5Co9/LZWTpmU5lcwRpun5z92LXW0r+Xbdu22fXgvxcAAJC51A9QsEVBFwVfFIRJVb8ryAe9lL2koJcCP9pWHapsCHwpS0tZa7omzUSpoJZqlvlrTKcvFqyzpRkSVR9NkwMAyAwEuYAso0BEqhnxlGWk57SPp+COaAheKpMmTXJrrTds2DC7bOo9b7jhBrdmzLlz5xrMKBjkr8cPvYuS6jnxQx5VzF3BLNXD+spXvmI7izfeeKN97te//rV9TsP4NDQyKlMq1TDDMJ+dpuCdOk3pSvVZiD4PHbOpTK5g5l8UHV/ZXMF/L56f0ZHgFwAAmUnBFwVhFIxRwMsPo0u3z6HAj89y8oEvzdzoA0MqaK+gUab1BXROOjedo7LTdM46d2VpKWtN16SZKNO9waiZEZUdp89QQ0M1RFRDRQFkHoJcQJbxWTxRmVxBwefHjBljl3E1q/71X//VLgcOHGiXXlPBnG7durm1xpp6T2VRSfA9lb2kgEtU9pIPYEUFY7xUz4mvZaXC7T5jy7+/L0b/5JNP1hW4v/XWW+3S02v1uYbPL9W1apZEBaMUsAp3EC+44AK31liqz0L0eUTV+QpLlfnn6fzCz+v/vR+y2dS/NQAA0PkU8PJDGhWoUcBGgZuColnNutGmmRv9ED/NLqigkWYaVBBJwS+f/fXe9rvqgmDBR0sywnwGVvDhg1h6KCtL763MLJ2HzknnpnNUdprOuTkU1FIGnLK1xi6otjMjKjsur9dVbg8AmYogF5CFfBZPlOXLl9ugRDAL6eabb7ZLtfngjqeZAZ966ik7bM8Hejw/E19coOqyyy6zy6jnm3pPBZLC75lOJlcqXbqk/pWnz0NZbfv27TP//M//bNv8cEQ9p7pdyuDyAbjwUEUf7Amfn7/WBx980C49XXfv/p+zr1PAKpx1dfHFF9tl1OeX6rPw2XxRdb7C/L5xmVxR/16UwaUZGVWzS/pdXPv/GQAAJIeCXgrcDJ76hA16aXijAjsKerWUgl8+++vwGw/VBcGCD58RFn4oSKVH1HM+Ayv48EEsn5Wl925O6YcgBbWU8WaHIM4/a4Na2g5na/XoVlsuAkDmIsgFZCFl5mgI3De/+U0bkPAPn32j4uzB2QmDsxkqeDF37ly7/7hx48yUKVNs+6pVq+wyyM9IqACI9lfQJzg7oR/eGHxeWVLSkvdMJ5PLL4N8cObTTz+1y1R8IXl9TgpqBYNEPiNLAbhg0MdToEiP8PnpWnUs1fTS8D5dqz4LXbceei4qk8sXlQ9+fr4AfKrPQuflP4emMrn8vgpk6d/L/Pnz7XvpEffvRf9fduzYUfce4VpeAAAgeVSoXoEdBb2UvaSAjzK9+o/8tg0CpVvXq6UUpNKjPSljTdeia1JA76oZG+sytbStoBaBLCDZ8qo1hRaArKGghgInPqsoSMGKRYsWmbvvvtu1NKQMqq9//es2k8nTzIKaXU+F2aMsXbrULFu2zG0ZG/xQBpbX1PPNeU9lPg0fPtzOUrh27VrXWkvHUXBMgbP777/ftdZSYG3x4sU2Kynu2j29hz4/Ce/v30OU0RXObPOvVVAqfH4S/iz88RW80qyO+mzC4j6/VJ+FKEClc4k6Zpj2bcm/FxXonzhxon1tOOAHAACSq+rsubpgT3BdNNyw6uQ+c6Zin/n46Gvm7MeH0pqJsCMpYNc9v8j0uvgLptsFl9ista59xhHAAnIAQS4AQIsoM02ZdwS5AACAbrR2q9pdN2zw3MeHTdcL+pvKD3/daBhhc4Niyr4K+8wV02qOe8Kc1702s/yCvqNMdf51jfok4SAdgOxGkAsA0CI+s40gFwAACGpuYEmzPXc5+Yo5d+a46dJnkp0YpykErwBEoSYXAKBFouqfAQAANDf4pKCW6mH1vnJ6WgEuIcAFIApBLgBAi6QzoyUAAAAAdBSCXACAZtHMi5ol0hfh14yS2tbwRQAAAADoLNTkAgAAAAAAQOKRyQUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAACAxCPIBQAAAAAAgMQjyAUAAAAAAIDEI8gFAAAAAIhVVlZmjh8/7rY6n84nLy/PTJ8+3bUAQC2CXADQTprbIdzx1nu2w1ZcXOxaWsYfh44fAACIo37K/PnzbZ/BPwYOHGjmzp1rdu7c6fYyZuvWrWbQoEGmsLAwowJd0qdPH7cGALUIcgFISYGSYOcn1WPp0qXuVQh2CNWJTEf/z1Tb/fv27duqTqQ/DgAAQJSVK1fafsqaNWvs9tixY+3jwIEDZt26dWbcuHHm0KFD9rnevXvb5fDhw+0yU6ivc+zYMbcFALUIcgGIpUDLmDFj6jo+/uGF26+99lr3DDx9LulmZp07d86Ul5fb9YKCArtsCR2nsrKSu5sAAKAR3YhbvHixXVdAq7q62uzYscM+tF5aWmpmzpxpzj//fLuP+jJq37VrV6v6J22Nvg6AKHk1v7Cq3ToANElZSers6O6fOkNoO6eP7zaXDfoDe8f0lVdeaXFH0v8/Gj9+vNm0aZNrBQAAqB3ip5tqCnDNmTPHtSYLfR0AccjkAoAMUHX2nPmgvIe9K6nhiq29U6rOK3c3AQBAkLK41EdQgCjdAJcCSipLoVpdQb5d5Sq0riGO2lYGe7Dswvr1622bL2+hul8PPPBA3T46J7VH1RJNVa80LpNL5/Ktb32r7v300LkF64x5/vhNXQOA5CDIBaBFjh49GvnHP1WHR9t+Hz2vdv/QfurkhAWPJwsXLmzwOtWUiKPj+ff3Dx0nfN6p6o4Fz0nrEyZMaPB8XKdpT9lH9vm44u867+Bx7vvBX5ujp7qZXr162efD55juZ6Zg2aWFVdSpAAAAjfzLv/yLXU6dOtUu0xXXr1D7vn37bL0u9YcUPNO2953vfMeUlJTYNi0XLFhg+5D33HOP2bBhg92nZ8+edhklVb1S9ZnC56Rz0Ln89Kc/NdOmTbPvp6Xao/pN/vhR13C4/KzbC0CiaLgiAKSrtLS0uqYzUF3TAXAtDen5mk5HdU1Hprp79+4aDm331frvT56u3rFjh23To6bTUV3T+bBL36bng3Q8tet4fh+t63V+e8mSJW7vev/9v//3RvvrvLVd04lxe9VasWKFfT748K/156N9wscLnve6devsfl7wcwgLHj98HD3Cn+2WLVvqnkv3M9PnHfXeAAAgd/n+Q7jfkkpcv8L30fSI6hf6/ku43yV6Tq/369pv1qxZdjvIv3f4+HHnpGOpzR/b8/24mTNnupZaTV0DgOQhyAWgWdQZ8EGu8vJy11rPPx/XWVBAJlXnQ52voN2lH9YdL9yRCQbMPvjgA9dafw5FRUWupZ4CYtpf7xfHn4t/v+D7hM87GIAKfh7+HMLXE7e/1i+55BLbrvMOPteSz0wBtnA7AADIbS0NckX1adRX8X20YL/F832upt7L97Oi+i0HDhyw76FAWfA94s4pjj/X8P4fl+9KeQ0AkofhigCaraYTYJdxdaNUI6F79+7mmWeecS31xo4da9auXduotkJNp8Omi3fr1s211OpuTpozZ87UvS5IbXqdPPfcc3Ypy5cvt+e4bNky11LvzjvvtMvnn3/eLsP8sEB5+OGH7XL16tV2qQKt4fOePHmyTYWXcOHTqFoR//zP/2yXOsfg56f1X/3qV3Up+cHnWvKZ6fOnJhcAAGgrF1xwgVurpb6WHiUlJZF9wpdfftkuhwwZYpdxTpw4YZdR/RY/Y7SGJobfQ/3DuL6OhjaqFpjKXOjxzW9+055reH9fDzXuGgAkD0EuAM2ioIoeElWTS9QRmT17dsrOQrjz4QNTZ882rn+ggE2/fv3cVkNjxoyxy9dff90u5f3337fLJ598su74wfeR7du32/pVYZpSW+ehgJY//w8//NAu4zppo0ePtsvgOYg+h3CtiIqKCru8+eab7TJO1Geb7mem/z9qpyYXAAAIiuo3pevjjz92a7XOmAttn8P3bcJ27dpll4MHD7bLOJpVWuL6LepPSbhvpP5h1GvUR9J5KXClG5V6qF8n4f11DTp+3DUASB6CXACaRcETPSQuiOWfjxPV+fDZUlF35OJmz5EBAwa4tXo+6KMOTfD4wfdRtlSPbl3tuvfiiy+azZs32/MKzji0bds2uxw6/Bq7jBMstCpRdxibCjzFfbbN+cz8MeI+MwAAkJt8v+npp5+2y3RF9cV8tn1+fr5raWjEiBF2uXfvXruM4zO54ui9Jdw3ijon9ZfUP1IWfGlpqUrz2IfW1Y+Kyn7XceKuAUDyEOQC0GzqJEhUtpGe0yMumOM7H0VFRZGdj6jXRWVEeQcOHHBr9XwHZseOHXXHDz/0XNgf/dEf2aUfpuj5GRLf3v2mXcbRNQXF3WGM4z87CX62zf3M/J3V5rw3AADIfr7UgWYRTDVDdZDPdorqV6Tq6/issXfeeccu46gcg85pz549rqVe165d7XsrmBbsG8Wdk8/mX7VqVaMyDxI1YiBVPxNA8hDkAtBsqTK59JwecVlE+/fvt0tN4RzV+Yh7XVy7r/dw7bXX2qWMHDnSLpvqVAUpkKTzDg5T9Pzdvbjj+Smwg+cgUZlcAwcOtMuoY/nPToLnkOozi3oPf2c17jMDAAC5Sf2Ir3zlK3ZdJRpUBiFM9Ul1g2/37t12O1W/Ip1s+wcffNAug9SnUaBNfN9GGfG+TXQen/vc52zfSMG0YN8o7pyigljiSzzEnSt9JiB7EOQC0Cy606aHRGVySaosIt+JCD//yCOP2M5HuF3HUruCT+pwBd9THSQNL1SGU3B4oeqByZIlS+wyLNixEq0rUyo8TNHzheX1fPB1EncOEnV30x9L51ZRWWXXRR05pdZ7wev0hV6jPjN1LsPtuuvZ3CwyAACQG5Tl5PtI6tvk5eWZcePG2YfWBw0aZPs2fphgXL/CZ1nF9TcWLVpkM8fUd9Jx586da28qan3KlCkNbvhpX9E5+P10HqrXpb6gAlrhfmfUOfm+mD+OHup7+hIPcedKnwnIHgS5ADSLAk56SFQml6S6U3bjjTfaZbDzoc5O1EyI4t9LAaCXXnrJdnTU8bnppptsB0nCr9W+CibpjqDvuOk1cR2re++9163VZnT5x/z58+0dTh3PdwaDnS+t+3NQsCss6g6jjqUOn87tMxeeb4+j4J3vyPnZIoOfrW+L+8zC76GZiFL9PwAAALnt/vvvN1u2bKnrYygQpYdu2qkPpZII/uZbXL/Cz3yYqr+hmadXrFhh132tVL2HMquCNwd1PtpP/Ty/n/bRTUAJZ3JJVD9r3rx59vXaX0s9xo8fb8tU6NhR50qfCcgy1QDQDDWdnuqaTkJ1TQeluqZT4FrrqU3P13SaXEtjNR0Ou49+BelR04mqO25JSYnbq9aBAwfqjqdja+lfp3PQ6+LUdN7ssf3+/r1qOjpuj1rBcwk/fvCDH7i9oo+n8406B389cZ/DkiVLGhynpiNn23W8qM821WcWfo/gZwYAAAAAuSJP/6n5wgQAGckP41O209q1a10rAAAAAAANMVwRQEYrdDW5qJUAAAAAAEiFIBeAjKYAl1ArAQAAoOVUz5NH+g8AycRwRQAp8Uc+O/CrHgCA3EafrnnoOwHJRJALQEp0iLIDv+oBAAAAZDuCXAAAAAAAAEg8anIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDxCHIBAAAAAAAg8QhyAQAAAAAAIPEIcgEAAAAAACDhjPn/AcdzesWXWgXpAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/docu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water surface profiles","description":"Problem statement\r\nWrite a function to classify the water surface profile starting at depth  in a channel with longitudinal slope , discharge , Manning roughness coefficient , and cross section specified by a structure channelStruct as in Cody Problem 58314. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \r\nBackground\r\nSections of channels are classifying by the relationship between the critical depth  and the normal depth . Slopes with  are steep—that is, normal flow is supercritical (fast and shallow), whereas slopes with  are mild—that is, normal flow is subcritical (slow and deep). \r\nThe type of water surface profile in gradually varied flow then depends on the water depth  relative to these two depths, as shown in the figure below. Profile S1 has ; profile S2 has ; and profile S3 has . Profile M1 has ; profile M2 has ; and profile M3 has .  \r\n\r\nFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390.35px; transform-origin: 407px 390.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53px; text-align: left; transform-origin: 384px 53px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.842px 8px; transform-origin: 211.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the water surface profile starting at depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.05px 8px; transform-origin: 112.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel with longitudinal slope \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.175px 8px; transform-origin: 36.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Manning roughness coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.183px 8px; transform-origin: 134.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cross section specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eunits\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.408px 8px; transform-origin: 252.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s^2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s^2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.808px 8px; transform-origin: 258.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.617px 8px; transform-origin: 211.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSections of channels are classifying by the relationship between the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58324\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecritical depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 8px; transform-origin: 41.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003c yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1167px 8px; transform-origin: 17.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003esteep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.275px 8px; transform-origin: 237.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003emild\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.55px 8px; transform-origin: 29.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is subcritical (slow and deep). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.292px 8px; transform-origin: 279.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.35px 8px; transform-origin: 99.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yc \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.6167px 8px; transform-origin: 48.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile S2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e y \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 8px; transform-origin: 62.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile S3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e yn \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Profile M1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yn \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7833px 8px; transform-origin: 49.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile M2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e y \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.4px 8px; transform-origin: 63.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile M3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 427.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213.85px; text-align: left; transform-origin: 384px 213.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 440px;height: 422px\" 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\" data-image-state=\"image-loaded\" width=\"440\" height=\"422\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 353.142px 8px; transform-origin: 353.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function profType = classifyGVF(y,Q,n,S0,units,channelStruct)\r\n%  profType = character string--one of S1, S2, S3, M1, M2, or M3\r\n%  y = water depth\r\n%  Q = discharge\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = either 'SI' or 'USCS' (i.e., lengths in m or ft)\r\n%  channelStruct = structure describing the cross section--see CP 58314\r\n\r\n  y = 'S1';\r\nend","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 1.2;                                    %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.7;                                    %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.34;                                   %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 4;                                      %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 2;                                      %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 1;                                      %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 1;                                      %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.75;                                   %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.6;                                    %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 4.7;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 3.5;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 2.0;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.3;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.2;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 3.7;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nfiletext = fileread('classifyGVF.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T21:56:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-23T01:31:32.000Z","updated_at":"2025-07-09T21:56:13.000Z","published_at":"2023-05-23T01:34:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the water surface profile starting at depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel with longitudinal slope \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, Manning roughness coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and cross section specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunits\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSections of channels are classifying by the relationship between the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58324\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026lt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026lt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esteep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emild\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is subcritical (slow and deep). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yc \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_c \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile S2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; y \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile S3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; yn \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y_n \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Profile M1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile M2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; y \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile M3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"422\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"440\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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the critical depth of a channel","description":"Problem statement\r\nWrite a function to compute the critical depth of a channel with discharge . The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . The geometry of the channel’s cross section will be specified by a structure channelStruct as in Cody Problem 58314.\r\nBackground\r\nSpecific energy for a flow is , where  is the water depth and  is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity  and differentiating with respect to depth gives\r\n\r\nThen using the definition of the top width  gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number :\r\n\r\nFlows with depths smaller than critical are supercritical—fast and shallow (), and flows with depths greater than critical are subcritical—deep and slow (). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the field, in the laboratory, and even in a kitchen sink. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.642px 8px; transform-origin: 226.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139.633px 8px; transform-origin: 139.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 8px; transform-origin: 17.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSpecific energy for a flow is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"E = y + V^2/2g\" style=\"width: 95px; height: 19.5px;\" width=\"95\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.7333px 8px; transform-origin: 72.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.908px 8px; transform-origin: 122.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"V = Q/A\" style=\"width: 61.5px; height: 18.5px;\" width=\"61.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and differentiating with respect to depth gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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\" alt=\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\" style=\"width: 257.5px; height: 36.5px;\" width=\"257.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.583px 8px; transform-origin: 127.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using the definition of the top width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = dA/dy\" style=\"width: 70px; height: 18.5px;\" width=\"70\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.6px 8px; transform-origin: 211.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAACRElEQVRYR+1WOy9FQRC+9wdIvCoRBQodBSqVxCM0RIFG6/EHJNQUeq9OI/gBhJpGiFCoPCpReSV+AN8nuzJ3cnbnHO5NbnE2mezu2dnZb2a+nT3FQpW1YpXhKeSArIzkEfpvhFphoMkyElj/xPebrHutlBFQB2QGMqmMn6h5A+bd4tsixmvlBuTt9WFwKox3BbwnqHUHfhT9UaUAzcLwljP+jr4+cpAH3wid10oB2oDheWd8E/2CAWgH6+1ZwVDf4pC3+YZBnZtMo9+PHMa0DRg6we1pAHVi97Ww0Ibxo7JInae/pEgjSwNI8ucSBnqUEUbkDsIbpoFKVXLrWejQiRrImVRKA4jp8Vd+FeNlBYj8YnkYVt/pyDiEXGJU2Uh0tl3IkBuXlIc0gL7EQXMY30KaIS2QfmeY37cVID+9wIDRY3QJ+hhCPnqQJU5agHT9kcWw1xnmwUm80oB4MPUeIIzyipsvof9NtQWIm7iBjWB0Wug9m+aVB0N+vbgJAQ1GdH/ULEA+3NRNegrIrytI6IkYwdqhA8TITECi71sMkPSONpOeC/KBQEOHyIJ6AL0pH7pQHwPEzXtuY+i54O2KXfV7rHvyht6/EmwxQJm9U17LgpoqOhaHpHfWc5GUAVlQU7/8oQgxFSShb7FrHaID+cXiZ/0dpEqZ9I7Asr7c8kJYfwcmIBo7F2T0FTbLv4287qnTlcQh3qwxSK3KwwfmsXqj0+bfMX7XxTR6863CaJWNsq/ngKyQ5hHKI2RFwFrPOWRF6BtBkGQltOJDawAAAABJRU5ErkJggg==\" alt=\"Fr\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr^2 = Q^2T/gA^3 = 1\" style=\"width: 95.5px; height: 36.5px;\" width=\"95.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.283px 8px; transform-origin: 230.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003e 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003c 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.533px 8px; transform-origin: 240.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=qsC9FUYpHqU\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efield\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/5etwhZ0d2GU?t=373\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003elaboratory\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8417px 8px; transform-origin: 47.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and even in a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/OoA1ASjMfag?t=24\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ekitchen sink\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yc = criticalDepth(Q,units,channelStruct)\r\n  g = 9.81*(units=='SI') + 32.2*(units=='USCS');\r\n  yc = solve(Q^2*T/(g*A^3)==1,y)\r\nend","test_suite":"%%\r\nQ = 12;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyc_correct = 0.33;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 10;                   %  Width (m)\r\nyc_correct = 0.74;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyc_correct = 1.26;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 2.34;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyc_correct = 2.84;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 14;                                     %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1;                    %  Side slope\r\nyc_correct = 1.65;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyc_correct = 3.72;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 8;                                      %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyc_correct = 1.1;                           %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T13:28:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-18T13:25:33.000Z","updated_at":"2023-05-18T13:28:20.000Z","published_at":"2023-05-18T13:28:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSpecific energy for a flow is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"E = y + V^2/2g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE = y + V^2/2g\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and differentiating with respect to depth gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dE}{dy} = 0 = 1 + (-2)\\\\frac{Q^2}{2gA^3}\\\\frac{dA}{dy} = 1-\\\\frac{Q^2}{gA^3}\\\\frac{dA}{dy}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using the definition of the top width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = dA/dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr^2 = Q^2T/gA^3 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr^2 = \\\\frac{Q^2T}{gA^3} = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026gt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=qsC9FUYpHqU\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efield\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/5etwhZ0d2GU?t=373\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elaboratory\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and even in a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/OoA1ASjMfag?t=24\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ekitchen sink\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57879,"title":"Route a hydrograph through a river section with the Muskingum method","description":"Problem statement \r\nWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph , the times  at which the hydrograph is reported, the routing parameters  and , and the desired time step . If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph , and a Boolean flag that says whether the time step is within the guidelines .\r\nBonus points to anyone who can solve this problem using the FILTER command. \r\nBackground\r\nHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow  and outflow  are connected to the storage  in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\r\n\r\nThis equation is written in discretized form as \r\n\r\nwhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow  and the current storage . \r\nIn the Muskingum method, the storage, inflow, and outflow are further related by \r\n\r\nwhere  is a time scale related to travel time in the river section and  is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\r\n\r\nwhere\r\n\r\n\r\n\r\nNotice that . With the assumption that the first value of the outflow equals the first value of the inflow, this equation for  can be used to compute the outflow hydrograph. The guideline for  above ensures that the coefficients , , and  are positive.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 882.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 441.35px; transform-origin: 407px 441.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.783px 8px; transform-origin: 383.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I(t)\" style=\"width: 26.5px; height: 18.5px;\" width=\"26.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2167px 8px; transform-origin: 34.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.875px 8px; transform-origin: 187.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at which the hydrograph is reported, the routing parameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the desired time step \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 284.583px 8px; transform-origin: 284.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O(t)\" style=\"width: 30px; height: 18.5px;\" width=\"30\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 234.942px 8px; transform-origin: 234.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2KX \u003c= dt \u003c 2K(1-X)\" style=\"width: 149px; height: 18.5px;\" width=\"149\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.925px 8px; transform-origin: 251.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.742px 8px; transform-origin: 368.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eO\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are connected to the storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.25px 8px; transform-origin: 97.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dS/dt = I - O\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.583px 8px; transform-origin: 141.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis equation is written in discretized form as \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\" style=\"width: 156.5px; height: 38px;\" width=\"156.5\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2333px 8px; transform-origin: 76.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the current storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S2\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.317px 8px; transform-origin: 249.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S = K[XI + (1-X)O]\" style=\"width: 143px; height: 18.5px;\" width=\"143\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.917px 8px; transform-origin: 185.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a time scale related to travel time in the river section and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.75px 8px; transform-origin: 156.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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alt=\"O2 = C0 I2 + C1 I1 + C2 O1\" style=\"width: 152px; height: 20px;\" width=\"152\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.0667px 8px; transform-origin: 19.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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V0zomSCVtlRSbyAfhtJDCEP7PXSWtcYrBU73mDJbLIEPjIW4gS8VVhCaB/xuSuEKMHiATcs2rGfQjiaOlsmsVD69dNIaB7ACFucsUZhZEIen2defBoSAQV/zYF1/TY5XwjkxZCAf1G7kEuhoaAVxHA364R/2BB0a/tEdZQitDb452rC9o+qNrUoQx1g8j50b1Et4T9Zijx67nGv7fuDW2CJBHI2AbSA5NI+sNXwD5V+6iIFXB+JBHB2gbeAVGOMeEmmJfLWBas1SRGhnMDbG04BAEEcDWJE0EAgE/odAEEf0hEAgEGhGIIijGbJ4IRAIBII4og8EAoFAMwJBHM2QxQuBQCDwBBqkyHR7zIhNAAAAAElFTkSuQmCC\" alt=\"C0 = (dt - 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1 = (dt + 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.8px; text-align: left; transform-origin: 384px 17.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35.5px;\" width=\"135\" height=\"35.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 66px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNotice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0+C1+C2 = 1\" style=\"width: 108px; height: 20px;\" width=\"108\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.742px 8px; transform-origin: 289.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.717px 8px; transform-origin: 207.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.892px 8px; transform-origin: 111.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above ensures that the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACBElEQVRYR+2WPSjGQRzHn2dXYjMZGBiUkiilLMxSXsooL5MMxGaiGIxeJlnEoIwoG3lJYWExWIxK7Hy/dVeXnvv/7nf/v3rKXX16/tzb975397tfuVRlpVxlekpJkLQjyaF/4VA9VjkMBkEbaHBW/YXvS/AAakEv6AHvkjO2XnOGKGQRzIAacA12wRl4MQNO43fd1PNfp2AgVAzbhQrqRNs90ALowgpY9UzEtudG1A5+p4oW5E5AMUNm5VnzbKNyEoyCgyIFNWGwe2cLQifoR58T0OxsZ5AuacuezDZxMK39FDQGgg+0dIbW0GDeLItb1a5dbZAlvxplOfTpbNUhvkdiJtD28Qni9d10BuPV5RX+8+ITxJvB4MfC7WrUnoVY5T5BbxjQRuBnfLfGTqDt5xP07QzEiNytHTi2fYgg7XXP0sKLsQHmQMWAGSKoCIcYKBnhGb1ZvAHWJ+gKnbpM5yLOEJ+fW2DHVQtaQmc+oLaEPgHMCPaBL0JHC+LAr4BpBgtTigXhoLLPBWBW4MsEogVxbtp844hgHrTlEWXzoKy0hF1zCbKijvHhxiQ6cAfqQAcYBx9gFkjRPLcgawgd6AOM2O5hf8TfR4BZY8irXpgg4fgEVydBklXJIckhmxKrI7U0sLaeMW0C2LeMz9FypdspJfnaiXO3T4IkC5NDySHJAan+BzypZynpHrrjAAAAAElFTkSuQmCC\" alt=\"C1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t2,O,dtOK] = Muskingum(t,I,K,X,dt)\r\n  y = x;\r\nend","test_suite":"%%  Chin example 5.38\r\nK = 40;         %  Time parameter (min)\r\nX = 0.2;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:600;   %  Time (min)\r\nI = [10 10 25 45 31.3 27.5 25 23.8 21.3 19.4 17.5 16.3 13.5 12.1 10 10 10 10 10 10 10];   %  Inflow (m3/s)\r\nt_correct = 0:dt:600;   %  Correct time (min)\r\nO_correct = [10 10.000 12.234 23.361 35.133 32.120 28.799 26.195 24.294 22.100 20.094 18.259 16.592 14.410 12.623 10.949 10.343 10.124 10.045 10.016 10.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Chin example 5.39\r\nK = 0.604;      %  Time parameter (h)\r\nX = 0.102;      %  Weighting parameter \r\ndt = 0.5;       %  Time step (h)\r\nt = 0:0.5:8;    %  Time (h)\r\nI = [42.4 46.3 51.8 56.2 57.6 65.1 80.3 90.6 103.2 81.5 78.3 65.8 59.6 56.3 50.8 53.1 50.7];   %  Inflow (m3/s)\r\nt_correct = 0:dt:8;   %  Correct time (min)\r\nO_correct = [42.400 43.327 46.510 50.893 54.574 58.266 66.191 77.540 88.774 92.714 84.880 77.757 68.741 62.190 57.167 53.698 52.750];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c5e-3))\r\n\r\n%%  Gupta example 12.7\r\nK = 3.07;       %  Time parameter (h)\r\nX = 0.39;       %  Weighting parameter \r\ndt = 12;        %  Time step (h)\r\nt = 12:12:120;  %  Time (h)\r\nI = [100 300 680 500 400 310 230 180 100 50];   %  Inflow (cfs)\r\nt_correct = 12:dt:120;   %  Correct time (h)\r\nO_correct = [100 222 573 626 373 359 235 197 123 58];  %  Outflow (cfs)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c0.6))\r\n\r\n%%  Homework problem 44a\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 6.424 15.930 23.650 20.977 19.035 17.713 16.841 15.948 14.981 13.746 13.187 12.289 9.465 6.074 5.258 5.062 5.015 5.004];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b1\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 35;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 7.350 18.103 22.845 19.774 17.965 16.839 15.781 14.614 13.436 12.489 9.898 6.283 5.214 5.036 5.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b2\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 10;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 4.223 5.122 7.129 10.048\t13.062 16.139 20.271 22.245 22.793 22.094 21.428 20.785 20.119 19.543 19.027 18.519 18.104 17.751 17.450 17.150 16.850 16.550 16.250 15.950 15.687 15.344 14.948 14.442 14.073 13.796 13.597 13.398 13.199 13.167 12.773 12.140 11.404 10.444 9.334 7.865 6.894 6.252 5.827 5.547 5.362 5.239 5.158 5.104 5.069 5.046 5.030 5.020 5.013 5.009];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44c\r\nK = 35;         %  Time parameter (min)\r\nX = 0.6;        %  Weighting parameter \r\ndt = 45;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 5.711 26.085 18.977 17.719 16.407 15.024 12.997 12.606 8.234 4.247 5.175 4.959];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-02T23:02:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T16:23:33.000Z","updated_at":"2024-11-11T12:36:59.000Z","published_at":"2023-04-02T16:31:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at which the hydrograph is reported, the routing parameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the desired time step \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2KX \u0026lt;= dt \u0026lt; 2K(1-X)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2KX \\\\le \\\\Delta t \\\\le 2K(1-X)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are connected to the storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dS/dt = I - O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dS}{dt} = I-O\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis equation is written in discretized form as \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{S_2 – S_1}{\\\\Delta t} = \\\\frac{I_1+I_2}{2} - \\\\frac{O_1+O_2}{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the current storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = K[XI + (1-X)O]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = K[XI+(1-X)O]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a time scale related to travel time in the river section and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2 = C0 I2 + C1 I1 + C2 O1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2 = C_0 I_2 + C_1 I_1 + C_2 O_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0 = (dt - 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0 = \\\\frac{\\\\Delta t – 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1 = (dt + 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1 = \\\\frac{\\\\Delta t + 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2 = \\\\frac{2K(1-X)-\\\\Delta t}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNotice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0+C1+C2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0+C_1+C_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above ensures that the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56205,"title":"Measure the hydraulic conductivity with a falling-head permeameter","description":"A falling-head permeameter is another device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . Unlike the constant-head permeameter, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area ) that falls. In other words, the head difference , or the difference between the water levels in the tube and the outlet, decreases in time. \r\nThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\r\n\r\nDarcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nDerive and solve an ordinary differential equation for the head difference . Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the previous problem. Use  and .\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 902px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 451px; transform-origin: 407px 451px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82px 8px; transform-origin: 82px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_c\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37px 8px; transform-origin: 37px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Unlike the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003econstant-head permeameter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_t\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147px 8px; transform-origin: 147px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) that falls. In other words, the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145px 8px; transform-origin: 145px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116px 8px; transform-origin: 116px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDerive and solve an ordinary differential equation for the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eprevious problem\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 981 cm/s^2\" style=\"width: 90.5px; height: 19.5px;\" width=\"90.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-2} cm^2/s\" style=\"width: 94px; height: 19.5px;\" width=\"94\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 359px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.5px; text-align: left; transform-origin: 384px 179.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 401px;height: 359px\" 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RJPT4UI7ZUajTR96B8iPf/xjKSkpkQ0bNtCvAgCAgHI2XPzkJz+Rp556ygx8ZWm/itGjR8uIESPk2WefNX9grEePHt5aAAAQRE6GC9s5U+n//n4Vbdu2lXPnzsmoUaPMegAAkJicvFtEaye0P4Wl/Sh08Cu9C+TLX/6ytxQAACQj58KFhgoNF37an0I7bN5zzz3eEgAAkKycahbxN4f46fJ58+Z5jwAAQCpyKlxosNAgEY3eOVJaWuo9AgAAycqZZhENDnpr6f333+8tEdO/wt/HIvIxAABIHMN/AwAAp3J6EC0AAOAe4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE7llVfw5mtUXl6eRO76yWWl8ttPrnqP4nvgvgbyyowHvUfhom0bAADUjLSquRj7aAtvrmqJlAUAADUnrcJFrw5/Y2okqqJltCwAAEg/adfnIkiNBLUWqEnnzp2Txo0bS9euXeXatWve0sTF286FCxdibnv79u3medrcV7duXVm3bp23Jv46xKbnyZ43e+7GjRsnJ0+e9EoASEXahYuqai+otchc169fl/vvv1/uvvtuuXTpkrc0XJAy2Wb//v3SvHlzadKkSaVj1kAyevRouXr1qvn/iSeekN/+9rdVrkNsq1evlj179sjHH39s+maVlZVJz549TeDo3r17zvzcAdUpLe8WiVczQa0FslXbtm2lQYPwYL179265cuWKvP7667J+/XpzYZw7d26V6xDf1KlTpX79+ma+RYsWsmPHDhk6dKh5DCB1aRkuYtVeUGuBbNS7d2/zDfro0aOhC54Vr5qeKvzkFBYWyne/+105fPiwt0SkTp06smXLFvnzn/8s9957r7cUQLLSMlyoaDUU1FoASFWrVq3kpz/9qQwePFgmTZqUUj8aANGlbbiIrL2g1gJq165d5punvyPeokWLol4gtJPkiy++GNZxr1+/fmHfWP1u3bolr7zySlgHye9///umT0MiEt2O7eg5YsQIb8ntfgH63GXLlpnH2qdCH2tflAULFsRcZ/sLBD1Pdt/anKLz9jna6dTf9yCZ7Z0/f16mT58eek6nTp1innulnVO7desWKt+uXbuo+0jkZyAWDRgXL140zVCNGjVK+PkAqlBeS4Lsev/xP5T/7Yz9ZtL5oGrxsBDHX/7yl/KWLVuWV3ygl1d8sHtLw8Ur89prr5n3Nj8/v7ziglo+ZcqU8ooLg1nWpUuX8oqLt1eyvPzgwYOhdX379jVlBw0aFHr+oUOHvJJ3zJgxI7TeX95OkfuIJdHtnD171rzW4cOHe0tuv359bsVF3jzHHsOzzz5bvnPnzpjrdLuJnCe7by1ny+h2/ec/le1FngN9XNW5j9zHhg0bvFKJvZaqnDp1qvyZZ54p79mzp3l+x44dy0+cOOGtBZCKtA4XaurSX5spEUG3jZplg4O+PwUFBeZDPXKyF8zIcGEvWpEXkJs3b4YuTP6L0L59+8rHjh1b6WJhL07+C7nS8tH2W1ZWFnrNQS5eyWwnWriwoh2bFW1doufJlo/2ulQq29Pj8T+nqnOvF/fIQKlByr6Hib6WWPS90LDz0ksvhbazbds28/xooRZA4mo1XOw8dbnKqXjbR2aKti7aZLed6YqKisxx2EkfW+m0LhH+cFHVFPkhH+/iYS860S7OkWKVtduPdmyxLmrRJLOdeK8/3nFHW5foebLLYl1Uk91eIkEl3j78En0t0difwWjvT6zwAyBxadvnwvrq/Z83U67RNuuK9yc0+W8xTHWd3r6YzPOirUtGxYXMtHf7t2mnig9/qfjw90repn0Yzpw5Y+a1R7/eRuif5s+fb45JxyuIbDfXfhdbt26tVNbPbj8/P1+GDBniLU2cq+0kK5XzNHDgwEp3SaSyPX0PI+98adasmTRs2NB7dJv/nLVu3dpbWlkqr8XvpZdekk8//TTq+zNmzBjzut9+++24fUMAVC3twwXc0kGqtDOc/p+JKr61yqpVq8KmNWvWeGvv0IuRdibUwamGDRsWt2w2CnqegnK9PUvfp/fff1/uuusu08kyiGRfiw0osfalt6N27tzZewQgFYSLHKN3MZSWlpr/M41+uz106FDUGg+d/ONEzJ49W5YvXy5dunSREydOhMqcPXvW3B2QzRI5T0G43p6fvaDfvHnT3GlSlVReiw0ysehradOmjfcIQCoIFzlEayv0ljul/2dK7YX90L9x44YJB1Wx31D1QlRcXCzt27f31kSX6PZjcbWdZLnef00cT9B9uHgtuo14Qcb+3HTo0MFMAJJHuMghWluh7c1K/8+k2gs7BsTixYujtqnr2AdVjVipF48VK1ZU6nOhYm1fL0I65kO050TjajvJcnGe/FxvLxob/qLt49133w1tP9XXouFi+PDhJqBov4pIBw8eNP1zZs2alXRNDIDbCBc5wl9rYWVS7YUOkT1jxgw5duyY6RCqg2FpR76JEyeagZQGDBggx48fN2X9F5E+ffqYjnpaTv8wmB14KlKPHj3M35bQ7WuziW5bR3DUToZf+tKXzP6CcLWdZCVynoJwvb1o9K+R+s+Zvl+6Dx2Mq2/fvqHtu3gtdl/z5s0zA5vZkKLBRPvmFBUVyahRo8wyACkoryW662i3kqY62W0j3A9/+ENzXiInXV5T4g2QZVVVRscjsGNh6JSfn28GkSotLfVK3LF27Vpze6Itq+WOHDlith/tdkMdL2HOnDlh216yZIlZXnFBCnQrqkp0O2fj3EYZ7/bLeOuCnqd4+/ZzsT373kY7j3puiouLw94vHQtl4cKFlcom8jMQTbR9JfJ8AFXL038qfrlqnH7TqAgD3iN3+hc0MtuupcNKS1o7ob3jbZOIX9OmTU2Vfb169bwlAACkhnCRA06fPi0bN270HompEtbqX0urgSu+JXqPAABIDeEiB3F+AADViQ6dAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIF8gqEyZM8OaQaXjvgOyRV17Bm69ReXl5svPUZe+RO/0LGplt19JhZYRsPj+895mL9w7IHtRcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwKq+8gjdfo/Ly8mTnqcveI3f6FzQy266lw8oI2Xx+auPYnlxWKr/95Kr3KL4H7msgr8x40HsEP35vgexBzQWQorGPtvDmqpZIWQDIVIQLIEW9OvyNqZGoipbRskAyzp07J40bN5YRI0Z4S4D0RbgAHAhSI0GtBSJdv35d7r//ftMkFG26++675dKlS17pzHL+/HmZPn26CUT2eOrWrSv9+vWT999/3yuFbEW4yAGlpaVSWFgYmpT/8bZt28wyJK+q2gtqLVCVgoIC6dmzZ9j0yCOPeGszy+rVq6Vly5ayfPlyuXLlSuh4bty4IXv37pUHH3xQJk2a5JVGNiJc5AD9Rf7ss89kz549ZlJ2/vTp0+abBFIXr2aCWgvE06BBA3n33XflvffeC5t27Ngh9957r1cqM2iw0OCQn58va9euNZ107fHovH6ZadSokSk3d+5c71nINoSLHFFUVOTNhZs9e7bUq1fPe4RUxKq9oNYCuUKbeebNm2fmX3/9dRk7dqyZ9xs0aJBs2bLFzC9ZsiRjm30QH+EiRwwfPtzUYPg1bdpUnnzySe8RXIhWQ0GtReb7t8t/9ebS165du2Tw4MFhfTa0VvLkyZNeidv2799v1kXrGKq1CVWti1fbsH79eikrK5MuXbrIsGHDvKWV9ejRQ4YOHSpXr16VnTt3ekuRTQgXOSSy9oJaC/ciay+otcgO3/7BEVmy8V/TNmTohX/AgAGyfft2GT16tEyZMsUEC+3f0KFDB9m4caNXUqRbt26mP4Q2uUTWGtggogHh2rVrZt7SddrUMWTIEG9JZfb5Ghzq169v5qOpU6eO+cKjNm3aZP5HdiFc5BB/7QW1FtXHX1NBrUX22P6//q3aQsbNmzfl2WeflalTp4ZN69at80rEpjUR2sdB+22cOHHC1B6sXLlSdu/eHeqsPXny5FCQ0C8UI0eOrFRroE0ab775ppnX7ehk2XUaVHSK5tatW3LmzBkzr51TkdsIFznG1l5Qa1F9bO0FtRbZqTpCht5FsWHDBlm1alXY9NZbb3klYispKTH/v/rqq9K+fXszb2n/hhkzZlQKEracv9bgyJEjpsZCaz309bz99tvemjvrtMYjXo1EIr761a96c8hGDP+dQbSt03aWUhoUbPtnIuu+8pWvyPHjx024cLXNdFo37unZMn7abO9R7fjwd//X/P/V+z9v/kd8+45ekv3HMrNjn9ZOjRvU0nuUGK0RaNu2rfzxj380g2TFuzNE13ft2lX69u0bChRaW/DNb37TNIfs27dPHn74YbPcz9694f+dsdtq1aqVeZ4GBi331FNPmeYS7Yj5hS98IbRu5syZsmzZMhOARo0aZbYRyb6WrVu3xi1n2delNar2eJA9CBc5SD/QsrXWorp+rlD9BrRrnLa/twNnvufN3dG0cT0TLB79WhNvSeJSDRdBnh/tIh4ZSrQDpj7+5JNPTHPKt7/9bdNBVLept43qOvs43mu0IcQfZGJJpCwyD80iOYjmECB5GipmjWoj617qmlKwcEE7Rnbu3Nn02dALfzxazrIdKm3zh46mqX03tCPm5z//ebPONqXYdQMHDqxyzA3b3FLVCJz0z8h+hAsACCCdQoWlIaFNmzYmJJw9e9ZbeodexDdv3mzmIy/iOjqv1kpoM8aHH35oRtK0Zew67ZOhNRm67vHHHzfr4rHP08By+PBhb2llOriW7lc7oepdLsg+hAsAqEK6hQo/OyaF3hESOaaF1jzoRTzauBMtWrSQ3r17ywcffGAu9v4LvV2n/S/0jpWgIUD7cEyYMMGEnT59+oSCjaVhR4cE12YapZ1Qq6oNQWYiXABAFdIxVFgaAuwdIXqb6JgxY8xtrFqLoINq6dgUxcXFle7ysE0j+jy9fdXf7GFrRHSd/pmAIE0i1qJFi0zzigYMDT7aD6pXr15mfI277rrL/DEzpa9Lm3OQnQgXAJDhli5dasa00A6f9pbWAwcOmLs+jh07FvUuEmWbMZS/T4byj9IZpEnE0mCiw3trrYneCqv0tRw9etQ0uyxcuNC8Vq0NGTdunHTq1Im/kpqFuFsEWYW7RTJXOt8tAve0o6iGC/vHFLlrJLtQcwEAqHHar8OOIqo1Lsgu1Fwgq1BzkbmouQCyBzUXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAAp/LKK3jzNSovL092nrrsPXKnf0Ejs+1aOizUMt77zMV7B2QPwgWySoN6eXLtr94DZJT6dUWuXuf3FsgGhAtkFX3vj6z0HiCjdJsqCf/efvbZZ3LPPfd4jwCkC/pcAMhI169fl8LCQvM/gPRCuACQkV555RUpLS01/wNIL4QLABlHaysWLVpk5vV/ai+A9EK4AJBxtLbi008/NfP6P7UXQHohXADIKP5aC4vaCyC9EC4AZBR/rYVF7QWQXggXADJGtFoLi9oLIH0wzgWyCuNcZK4g41ycPn1aNm7c6D0SmTdvnhQVFXmPREaNGiUFBQXeIwC1hXCBrEK4yFzJDKLF7zqQnmgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAgi5w7d04aN24sI0aM8JYANY9wASAnXb9+Xe6//365++675dKlS95SWJwfpIJwAQAZ5NatWzJs2DCpW7euHD582FsKpBfCBcJcuHBBrl275j26jWpWAEAiCBcZRr+1vPjii+Zin5eXZ6Z+/frJ5s2bvRLJ279/vzRv3lyaNGlCNSgAIGmEiwyibaAPPPCALFiwQL74xS/KlClTZMKECbJ3715Tq7Bx40avZGratm0rDRo08B4BULt27ZLCwsJQqNdmiUWLFsWs6Zs7d66cP39epk+fHnpOp06dYjZl6BcHf9nISX/HZ86cKXfddZds3bpVbty4Id27dw+tj/b7H7nNePsHXCJcZJD169dLWVmZDB8+XE6dOiUrV66U1atXm2UjR470SiWvd+/eUl5eLkePHpX69et7SwHo79mAAQPkwIEDMnr0aBPsNYC/8MIL0qdPn0oBQ3344YfSuXNn83uq5QcNGiTHjx835SMv8PaLw/Lly6Vv376mfNeuXc26/Px883j8+PHyjW98w8w3atTIrLOv5emnn5aOHTuaZdbp06dNLWSQ/QOuES4yhH4DsU0fjz/+uPnfatGihfzsZz+TUaNGeUsQxO//6M0AcWhNxPPPPy9dunSRK1eumJCvF+yLFy/KjBkz5NixY7Jlyxav9B0bNmwwQUGfo+W3bdsmr732mqlx0NpHP/vFoaioSPbs2WPKHzx4UIYOHWrWT5o0yXyp6N+/v/zTP/2T+SKgoeO5554zZVesWCHt27c3ZS0NF0H3D7hGuMgQderUkTZt2ph5/dAISqtyBw8eHKoW1Un7aJw8edIrcUeuddz8xQGRYS+KbK34H4hFL9x6gZ41a1ZYjZ7+Tk6bNs3UImzatMlbeoeGkTfeeCPsOdqsouU1SPhrO/T3UcPCkCFDvCW3t6+BQsPA2bNnvaXBJbJ/wDXCRQaxF3391rFu3TozH4+tyt2+fXuo+lSDhfbR6NChg7M+GplMay/mvU7IQHRaY3jmzBkzr7UTU6dODZvmz59vgke0i3XLli0rNS82a9ZMGjZs6D2qXrW9f+Q2wkUG0arQOXPmmG8y48aNMx3KNGRE+waid35oVaq2C584cSJUlbt7925TPaomT57MXSEeQgaqos0cq1atCpvWrFnjrU2NNmno7/Xbb7/tLbnTFKo1Gq1bt/aWApmBcJFhXn75Zdm5c6epgbAhQ6s5I2sySkpKzP+vvvpqpbZY7dilbcVXr14120qF9oj3N7nU9qS6TQ02rfqFKR7GHzLokwFLL/CHDh0yHZ6jTal2grbNFfPmzTO/21or0qNHD3NXiDaVPPzww15JIDMQLjKQdurSGgi9Y8QfMvRCr2xVbrxvPDZwJNJ/IxrdZ7QP29qa1JGVwaYp/9kUr2RoT5FXZoo0/xtvAXKW7euUbL+HIPT39dlnnzVhX28t/81vfmNqRfTOjoULF5p+E0CmIVxksIKCAhMytAe4WrJkiWnm0A+r999/39wP36pVK7MuFi2H2zRUbHlZpGg8wQJ32L5OixcvjtoEqZ2mo3WQDsr+vur4MjpuxuXLl01Q/utf/yqzZ8+uVCNSE4EHSBXhIguMGTPGdN66efOmueNDP3z0/nr7OB4tl+sIFblNawy+/vWvS69evcIm7bOkYUL7OtlbTrUPk222mDhxommK007TWsuQrHr16pnaiY8//tiMS+Fv5tPXobWSkeHF1jzq2Bf6WvSOsOrqoF3V+QGiIVxkoaq+2diOYkprP3JV17aECtymzYM6QJZ/Ki0t9daKLF261HSE1oGt9G4rbbbQQKDjSGi5VMeY0T5SeteJDoSld3XZSWsvtD+V3lbqH/hKg43t3K2vRTtwV2enz6rODxApr9w2VNcwTeU7T132HrnTv6CR2XYtHVa10RoIbY/VQXP03ndLg4JWnS5btsx8AO3bt89Uo+qHjY7Ep9+0tCOav1On3pqq33T85ZXuQz889QPTdghVsZanI33vtT8FMo92sk309zYbftft76r+Xkf7/dJbyrWWQAfYsv2qgHRHzUUG0Y5e2v6rH6jt2rUzVZPar0KDhXbeLC4uDgUFW5WrVZo6poU2nWj1qfZK12ARWR5A7dIB7CLplwfbJJLLtYzIPISLDKEdM7XT1zPPPGNuWbPVlBoStIpUq1Qjb1fzV+Xae/T1OWPHjjXtx9zeBtS+bt26mT5TWkOhY9folwDbp0P7YNhayWHDhnnPANIfzSLIKjSLZK5cbRZRFy5cMH+07J133jFjZlg9e/aUJ598Ur71rW9Ry4iMQrhAViFcZK5cDhdAtqFZBAAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgBkjNLSUiksLAxNyv9427ZtZhmA2pVXXsGbr1F5eXmy89Rl75E7/QsamW3X0mGhlul7f2Sl9wAZpdtUCfR7+9BDD5mQEalp06Zy7tw5qVevnrcEQG2h5gJARikqKvLmws2ePZtgAaQJwgWAjDJ8+HB58MEHvUe3aa3Fk08+6T0CUNsIFwAyTmTtBbUWQHohXADIOP7aC2otgPRDuACQkWztBbUWQPrhbhFklTqfy5N//3/eA2SUz1V81bn174n93j722GNSUlJCuADSDOECWaW6fq5y1Z//9H+k7OwZ+U+du3lLqs+Ado0T/r29fv06wQJIQ4QLZBXChVs3/vpXeeJvO8vlP1yUrxR0lBat20iLVm3kwYd7Vcx/VRp/oYlXMnXJhAsA6YlwgaxCuHDvX9YWy/9Y8JL3KJyGi5Ul7zoJGYQLIHvQoRNAXEMfnxgzPIz6+2ed1l4AyA6ECwBx5deta0JEpF4DviHfGveU9wgA7iBcAKhSZO2FBo4rf/g3+fSTMm8JANxBuABQJX/thc4vfX2r9BwwRJ4Z9ajsfvstsxwALMIFgEBs7cXkGf9gbk0d/ffPybwVP5VXl/2j/GjeTHNnCQAowgWAQLTGQsOEv5+FhoyVJXvl8qWLphZDx8QAAMIFgMCiDaZ1d8P/KP+4Yp08OmKUzBw/VLaXrPfWAMhVhAsATmiNxoL/+TPZ+OqP5b+/OI1mEiCHES4AOKOjeC7f+E5FsLguU7/5dZpJgBxFuADglDaTfH/pqzJq8rOmHwbNJEDuIVwAqBaDRowxtRjaTPLfZk42fwQNQG4gXACoNi1bt5GVb70r+XXrmVqMfz193FuDbHHu3Dlp3LixjBgxwltyx4ULF+TatWveo+ph99+1a9dq3xeCI1wAqFZ6C+v3Xl5hmknm/P1/ka0b13hrUNPOnz8v06dPNxdj/SN/OrVr107GjRsnJ0+e9Eq5sX//fmnevLk0adJELl265C1FriBcAKgR2kyiI3v+YtNP5B+mjaWZpIatXr1aWrZsKcuXL5crV65Iz549zXT69GlZt26ddO/evVpCQNu2baVBgwbeI+QKwgWAGqPNJNoPo/G9TWTqiL7yv98/4q1BddJahEmTJpn5tWvXmj9t/95775lJ50+dOiWPPvqoWe9K7969zbaPHj0q9evX95YiVxAuANQobSZ5rmip/Nc5P5Ciad+Wf1lb7K1Bdbh+/bo88cQTZn7Dhg0yduxYM+9XUFAgb731ltx7773eEiA1hAsAtUL/ZLvWYux5u8Q0k6B6HDlyRMrKyqRLly4ybNgwb2ls2nyifTHmzp3rLQlX1XorVkdPu1yfb/uA2P4fnTp1ksOHD3slw926dUteeeWVUH+RuhUh9fvf/75cvXrVKxHdrl27pLCwMLQPfd6iRYsqdf70vy6dt8/RjqL0GUkc4QJArWl6X0vTD0P/VwcPHjT/w52SkhLz/9ChQwM1T+hFtVGjRrJ169ZKF2C9wG/evFny8/NlyJAh3tLkfPjhh9K5c2dZuXKlTJkyRQYNGiTHjx+XPn36RA0Ys2fPlqeeesqECS2vr/MHP/iBdOzY0fQhiUaD0IABA+TAgQMyevRo8zzt//HCCy+Y/US7u0RflwaKPXv2mP8/+OADbw0SQbgAUKu0mUSbSNRjjz0mCxcuNPNInYaBM2duj5KqTR9BtGjRwvSXOHbsmGzZssVbepuGPw0dGiwefvhhb2lytImmb9++JhhowNi2bZu89tprcuPGDVmwYIFX6jbtM7Js2TITDD7++ONQea2R0U6q0Wjtw/PPP29qbHQf69evN8+7ePGizJgxI+rxKX1drVq1MiFGa33+/Oc/01yUBMIFgLShHQt//vOfm5Dx2WefeUtRk+rUqSPDhw8385s2bTL/W7YW5PHHHzf/p0Iv+m+88UZYbYqtNdHQ4K9VsPvVsOC/0GsQ0hoGfU6kFStWmFAxa9assH3o8U2bNs08J/L4lAYYDS50Qk0N4QJA2mjatKn86le/kgcffNCMv6AXDtS8MWPGmBqBHTt2hPobaMfQN99801x8takhVbr9yAt4s2bNpGHDht6j22ztSyJNMf4aG62dmDp1atg0f/58EzwiQ4waOHAgNRUOEC4ApB2tFtfqaW0nr6rjIGLTb+lt2rQx8zqeRVD16tWTkSNHmqaBnTt3mmW2Y2imXXz152jVqlVh05o1DORW3QgXANJSv3795Ne//rXs3bvXVJd/+umn3hokon379ub/aB0047F3edimA5dNIjVFazsOHTpkxtuINjEGR/UhXABIW9pMsnv3btPx76GHHjJt4UiM7ccQqwNjLN26dQs1jWiNhTaJBL2d1SVb+6IdPc+ePestjS+Z58AtwgWAtKdNI/rNecKECTJnzhxvKYLQOx/0vKnx48ebob4j6XgTequq/++LaNNIUVGRaRrR5ikNGEFvZ3XN1qIsXrw4rPZF7wjR20Wj3Yoa6zmWjn/h+u+p4A7CBYCM0KNHD3M3SWlpqTzyyCM0kyRAB43SUKbf5PWPlOngUL169TKTzmsNxTvvvFNpQCpb66HjRLgY2yJZ+t5rsNHaF3092ilz8ODB0rp1a/nSl75kmtAi6e209pZT7YSqZfR5EydONMesnVJ1XA1UD8IFgIxxzz33yC9/+Uv5u7/7O5pJEqDNBC+//LLpnKmDVSkNDDrp+Bc6JLhehCPHrrBjXqgOHTqYqTbo69fhyW1A0k6Z2ly2ZMkS87oj7zCxli5dan5GtHZD++7o8/T2V21m05A6atQoryRcyyvXXi21QJPjzlOXvUfu9C9oZLZdS4eFWlZdP1eofgPaNU7o91YHdNLqeh2TQe8u0Wp8uDdz5kwzgJXedcHFGEFRcwEgI2lVud5N8tFHH5nqe/0fbrke2wK5g3ABIGNpM4l29NTbI7Ufhv7dC7ijQ2Zn4tgWqH2ECwAZ77nnnjN9MbRNnj9+5ob/j5Rxhw4SRZ8LZBX6XGSuRPtcRKPV+PS9AGofNRcAsgbBAkgPhAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAABOXLhwQa5du+Y9Sm/nzp2Txo0by4gRI7wlcIlwASCrnD9/XqZPn24uHDpiq07t2rWTcePGycmTJ71ScG3//v3SvHlzadKkiVy6dMlbinSzevXq0O/Fxo0bvaXuES4AZA394GzZsqUsX75crly5Ij179jTT6dOnZd26ddK9e3cufEnSvzUybNgwqVu3rhw+fNhbWlnbtm3NX1FF+rF/L8batGmTN+ce4QJAVtBvzpMmTTLza9euNX+n5L333jOTzp86dUoeffRRsx7u9e7d25zno0ePSv369b2lSCdaq6e/J4MGDTIhfMeOHdUWtgkXADKe/sGyJ554wsxv2LBBxo4da+b9CgoK5K233uJPhyNn7d6929Tofec735GRI0fK1atXZefOnd5atwgXADLekSNHpKysTLp06WKq7oOwHfrmzp1r5gsLC007dNeuXcO+ze3atUsGDx4caqfWqV+/fjH7b2h5uy2dtBlBa1T8HR2DlIkl6HOjlVu0aFHMfWzfvl26desWKq/9VGz5mTNnyl133SVbt26VGzdumOYlW86221fVQTKR8+h/b2wfGvucTp06xWyW0Q6lL774Ylh/G91HvGacqiSyzUR+poK+N66OyTaJaJPVgAEDQu/T4sWLA/3cJYo/uY6sUl0/V6h+qfzJdb34LVu2TIqKiswHexD64a8f+nrB27Ztm/lGp4+1f4au0xoO7cNhm1pGjx4tDRs2lA8//FD27NljlmktyahRo8y80irnPn36SH5+vnzrW98y5X/3u9+ZC8u+fftMc0GQMrEEfa593f5yP/vZz8wxagCL3I89f9HK6zFqJ01tn7fL7LnQwPHUU09J+/btQ+ezb9++UlJS4m35tkTPY+R7o9+w9du2HquGIH2degwPP/yw9wyRQ4cOyWOPPWZen74G7fsRr3y812slu80gP1NB3ptE9x+P/dkZPny4OV4NG9/85jfNthLZTlCEC2QVwkXmSjZc2A9J/VYdeZGKx14Ion2oK/thrN/09ENeL6CWfiDrBUTX2YtGkA/rVD7Qgz7XHlerVq3CjkmfP3v2bBMi/OfJHmfHjh1NFbm/2Ui/YX/xi180x17V/u1+Iy/WiZ5H5X9v9GL4xhtvVApO9iJp6X5WrVpljtG/j1jlY71ev2S3Getnyq5P5L1JZP/xaIBcsWJF2Htnt5NIKA+KZhEAOU0vbPot038RUPZD+9VXXw37YFfaIW7GjBnV2madLL2A6MVt1qxZYcdUp04dmTZtmjRq1CjsLgF7nFr17g8Wqn///pWOPVGpnEe9QPuDhdLmBD0GbQbzV+drh1LtyBu5D1s+GcluM9bPVKLvjatj0j5Jb775pnTo0MFMlt2OBnPXTSOECwA5beDAgZUuqvpN8syZM6bquXXr1t7ScPYDX6u8lV4gvve975k+CfpNXb8RfvTRR2adFaRMLEGea1+32rJli0ydOjVsmj9/vrm42QtzkONMRTLn0U/vaIi8QDdr1sw0JcSifRT0Yhl5zKlIdJvxfqZUkPfGL9Vjsn2Shg4dGnY+W7RoYQLMsWPHzGtyiXABIKPpRbdNmzZmPtoFKhl6IXj//fdNnwKtwo5Hy1n6Qa3fwHVsDa1y1udqB0R/p8UgZWJJ5Llava5V6v5pzZo13trbEjnOZCR7HpOh+9KOnzqQl3bqjXXMiaiObaog741ytX9be6R9XPyB5umnn5Y//elPZp3rMS8IFwAynv3266p6VwNL586d5ebNm6adPB4t56dNCXrL3+9//3uZM2eOHD9+3FTv+3v3BykTS5Dnak2B9m/QPizRJjsWRSLHmYxUzmOitF+CDp6m5+LEiROhYz179mzSzSLVsc2g741ysX897zaM7N27NyzQ6GQ71boe84JwASDj2bZjV9W7tjZEmyD0gzySfqO0Ix3q+BnRaPX9yy+/LK+99lrM7QQpE0u051b1uiMlWj5RLs5jELod2/xSXFxcqY9CMlxvM9Fz7Wr/dmwL7bTpDzF20uCnzSWu+w8RLgBkPK1ynzBhgpkfP368Geo7ko6XoB+iQZoflB0HYPLkyZWeox/CWkui3yjtuBraaS7a9v2Pg5SJJehzqxq/QO8A8T/HXrSilX/33XdDZZMNIomeR5f0Am07UbqSyjYTfW+iSWT/WlbDmwaUIUOGeEvD6fuqd50ol00jhAsAWUEHIdJmAr346R8p09uSe/XqZSad186B77zzjvmGFoT2b7B3MmgP+zFjxph2aq0l0dsn7TdKfwe53/zmN6asDnJky+rthf6LZ5AysQR5rn3dWoujdy3YshMnTjTnQQdQ0qYUS8+VhhYtr7U/9jh10Ca9TdNf1gYRDXBaRs9DVX/8KpnzmCh7gdT3Xju76j70eHV8Dj0/yaiObSby3rjYvx3uW8+7TrHotvX34+233w41r2kw0Z8pfV062WAUFOECQFbQD2NtJtBvw3qLozpw4ICZtMpdhwTXD/VExpZYunSpuaVQxyawnfB0e9G2Va9ePfNB/swzz4TatrWsXhDsmAZBysSSyHP9r9uW1Vs6NSyUlpaGjQWi502HRdcLvF7w7HHq+BYLFy4MCzy6LxvgtIy+niB3mSRyHpOlr01v27THoP0MtLOr3imhF85kVMc2E3lvUt2/bRLR8FjVz5YOB67vqwYMDRY6psnnPve5UPOJvs+J/BVVBtFCVqmunytUv1RG6ATgjnYC1TuSfv7znycd/Ki5AAAAIZ988om5RTWV25MJFwAAIOS+++4zA5Wlcnsy4QIAAIToyJ1f+9rXZMGCBd6S23+bJJE+F4QLAAAQop18//mf/9l0trV3i+jtx0H/KKAiXAAAgDB6B4n+eXftZK1T0L++ahEuAACAU4QLAADgFOECAAA4lZXhokePHqFOKEy5NQEAal/WjdAJIDMxQieQPWgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAA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alt=\"falling-head permeameter\" data-image-state=\"image-loaded\" width=\"401\" height=\"359\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n)\r\n  K = f(delta,t,L,Dc,Dt);\r\n  isDLvalid = (Re \u003c 1);\r\nend","test_suite":"%%\r\nDc = 11.28;                                 %  Diameter of cylinder holding sample (cm)\r\nDt = 2.26;                                  %  Diameter of tube (cm)\r\nL  = 10;                                    %  Sample length (cm)\r\nn  = 0.15;                                  %  Porosity\r\nt  = [0 1 2 5 10 15 20 25]*86400;           %  Time (sec)\r\ndelta = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];    %  Head difference (cm)\r\nK_correct = 3.08e-7;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                %  Diameter of cylinder holding sample (cm)\r\nDt = 2;                                                %  Diameter of tube (cm)\r\nL  = 15;                                               %  Sample length (cm)\r\nn  = 0.25;                                             %  Porosity\r\nt  = 0:60:420;                                         %  Time (sec)\r\ndelta = [25 20.63 17.03 14.05 11.60 9.57 7.9 6.52];    %  Head difference (cm)\r\nK_correct = 3e-3;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 7.5;                                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.75;                                             %  Diameter of tube (cm)\r\nL  = 7.6;                                              %  Sample length (cm)\r\nn  = 0.2;                                              %  Porosity\r\nt  = [0 1.25 2.36 3.74 5.40 7.20 9.28 12.08];          %  Time (sec)\r\ndelta = 88.9:-10:18.9;                                 %  Head difference (cm)\r\nK_correct = 5.25e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                                                               %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                                                               %  Diameter of tube (cm)\r\nL  = 7.5;                                                               %  Sample length (cm)\r\nn  = 0.2;                                                               %  Porosity\r\nt  = [0 1.06 2.11 3.62 4.88 6.53 8.39 10.67 13.52 17.37];               %  Time (sec)\r\ndelta = [56.02 50.36 44.7 39.05 33.39 27.73 22.07 16.41 10.75 5.09];    %  Head difference (cm)\r\nK_correct = 3.89e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                              %  Diameter of tube (cm)\r\nL  = 7.5;                              %  Sample length (cm)\r\nn  = 0.2;                              %  Porosity\r\nt  = [0 2.28 5.13 8.98];               %  Time (sec)\r\ndelta = [22.07 16.41 10.75 5.09];      %  Head difference (cm)\r\nK_correct = 4.79e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                      %  Diameter of cylinder holding sample (cm)\r\nDt = 2.5;                                                    %  Diameter of tube (cm)\r\nL  = 15;                                                     %  Sample length (cm)\r\nn  = 0.18;                                                   %  Porosity\r\nt  = 0:7200:50400;                                           %  Time (sec)\r\ndelta = [50 43.15 37.23 32.13 27.72 23.92 20.64 17.81];      %  Head difference (cm)\r\nK_correct = 2.99e-5;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-01T17:35:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-01T17:35:38.000Z","updated_at":"2026-02-10T14:28:46.000Z","published_at":"2022-10-01T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Unlike the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econstant-head permeameter\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) that falls. In other words, the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDerive and solve an ordinary differential equation for the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 981 cm/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 981\\\\rm\\\\,cm/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-2} cm^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 10^{-2}\\\\rm\\\\,cm^2/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"401\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"falling-head permeameter\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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vfvUrWbBggdxzzz3eWgAAsgcjdFaz06dPy3e/+1359NNP5Yc//KH069fPWwMAQHai5qKa2H4VhYWFMmjQIPn1r39NsAAA5ATCRTV45ZVXTBPI9evX5dSpU/Lcc895awAAyH40izi0Z88e0wTStGlT0wRSUFDgrQEAIHcQLhz46KOPTKjQ/hUaKgYPHuytAQAg99AskgLbr+KRRx6R7t27myYQggUAINcRLpJk+1VowNDOmi+88IK3BgCA3FZr4WLChAnenHvVue2DBw/KQw89JJs2bZJf/vKXUlxcbPpYAACA22qtz0VeXp5U166rY9s6ToX2q9Bwof0qhg8f7q0BAAB+NItUQW8nnTt3rmkC6dy5s+lXQbAAACA2wkUcGzdulFatWskHH3xgQoX2q6hXr563FgAARJPT4UI7ZUajTR96B8iPf/xjKSkpkQ0bNtCvAgCAgHI2XPzkJz+Rp556ygx8ZWm/itGjR8uIESPk2WefNX9grEePHt5aAAAQRE6GC9s5U+n//n4Vbdu2lXPnzsmoUaPMegAAkJicvFtEaye0P4Wl/Sh08Cu9C+TLX/6ytxQAACQj58KFhgoNF37an0I7bN5zzz3eEgAAkKycahbxN4f46fJ58+Z5jwAAQCpyKlxosNAgEY3eOVJaWuo9AgAAycqZZhENDnpr6f333+8tEdO/wt/HIvIxAABIHMN/AwAAp3J6EC0AAOAe4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE7llVfw5mtUXl6eRO76yWWl8ttPrnqP4nvgvgbyyowHvUfhom0bAADUjLSquRj7aAtvrmqJlAUAADUnrcJFrw5/Y2okqqJltCwAAEg/adfnIkiNBLUWqEnnzp2Txo0bS9euXeXatWve0sTF286FCxdibnv79u3medrcV7duXVm3bp23Jv46xKbnyZ43e+7GjRsnJ0+e9EoASEXahYuqai+otchc169fl/vvv1/uvvtuuXTpkrc0XJAy2Wb//v3SvHlzadKkSaVj1kAyevRouXr1qvn/iSeekN/+9rdVrkNsq1evlj179sjHH39s+maVlZVJz549TeDo3r17zvzcAdUpLe8WiVczQa0FslXbtm2lQYPwYL179265cuWKvP7667J+/XpzYZw7d26V6xDf1KlTpX79+ma+RYsWsmPHDhk6dKh5DCB1aRkuYtVeUGuBbNS7d2/zDfro0aOhC54Vr5qeKvzkFBYWyne/+105fPiwt0SkTp06smXLFvnzn/8s9957r7cUQLLSMlyoaDUU1FoASFWrVq3kpz/9qQwePFgmTZqUUj8aANGlbbiIrL2g1gJq165d5punvyPeokWLol4gtJPkiy++GNZxr1+/fmHfWP1u3bolr7zySlgHye9///umT0MiEt2O7eg5YsQIb8ntfgH63GXLlpnH2qdCH2tflAULFsRcZ/sLBD1Pdt/anKLz9jna6dTf9yCZ7Z0/f16mT58eek6nTp1innulnVO7desWKt+uXbuo+0jkZyAWDRgXL140zVCNGjVK+PkAqlBeS4Lsev/xP5T/7Yz9ZtL5oGrxsBDHX/7yl/KWLVuWV3ygl1d8sHtLw8Ur89prr5n3Nj8/v7ziglo+ZcqU8ooLg1nWpUuX8oqLt1eyvPzgwYOhdX379jVlBw0aFHr+oUOHvJJ3zJgxI7TeX95OkfuIJdHtnD171rzW4cOHe0tuv359bsVF3jzHHsOzzz5bvnPnzpjrdLuJnCe7by1ny+h2/ec/le1FngN9XNW5j9zHhg0bvFKJvZaqnDp1qvyZZ54p79mzp3l+x44dy0+cOOGtBZCKtA4XaurSX5spEUG3jZplg4O+PwUFBeZDPXKyF8zIcGEvWpEXkJs3b4YuTP6L0L59+8rHjh1b6WJhL07+C7nS8tH2W1ZWFnrNQS5eyWwnWriwoh2bFW1doufJlo/2ulQq29Pj8T+nqnOvF/fIQKlByr6Hib6WWPS90LDz0ksvhbazbds28/xooRZA4mo1XOw8dbnKqXjbR2aKti7aZLed6YqKisxx2EkfW+m0LhH+cFHVFPkhH+/iYS860S7OkWKVtduPdmyxLmrRJLOdeK8/3nFHW5foebLLYl1Uk91eIkEl3j78En0t0difwWjvT6zwAyBxadvnwvrq/Z83U67RNuuK9yc0+W8xTHWd3r6YzPOirUtGxYXMtHf7t2mnig9/qfjw90repn0Yzpw5Y+a1R7/eRuif5s+fb45JxyuIbDfXfhdbt26tVNbPbj8/P1+GDBniLU2cq+0kK5XzNHDgwEp3SaSyPX0PI+98adasmTRs2NB7dJv/nLVu3dpbWlkqr8XvpZdekk8//TTq+zNmzBjzut9+++24fUMAVC3twwXc0kGqtDOc/p+JKr61yqpVq8KmNWvWeGvv0IuRdibUwamGDRsWt2w2CnqegnK9PUvfp/fff1/uuusu08kyiGRfiw0osfalt6N27tzZewQgFYSLHKN3MZSWlpr/M41+uz106FDUGg+d/ONEzJ49W5YvXy5dunSREydOhMqcPXvW3B2QzRI5T0G43p6fvaDfvHnT3GlSlVReiw0ysehradOmjfcIQCoIFzlEayv0ljul/2dK7YX90L9x44YJB1Wx31D1QlRcXCzt27f31kSX6PZjcbWdZLnef00cT9B9uHgtuo14Qcb+3HTo0MFMAJJHuMghWluh7c1K/8+k2gs7BsTixYujtqnr2AdVjVipF48VK1ZU6nOhYm1fL0I65kO050TjajvJcnGe/FxvLxob/qLt49133w1tP9XXouFi+PDhJqBov4pIBw8eNP1zZs2alXRNDIDbCBc5wl9rYWVS7YUOkT1jxgw5duyY6RCqg2FpR76JEyeagZQGDBggx48fN2X9F5E+ffqYjnpaTv8wmB14KlKPHj3M35bQ7WuziW5bR3DUToZf+tKXzP6CcLWdZCVynoJwvb1o9K+R+s+Zvl+6Dx2Mq2/fvqHtu3gtdl/z5s0zA5vZkKLBRPvmFBUVyahRo8wyACkoryW662i3kqY62W0j3A9/+ENzXiInXV5T4g2QZVVVRscjsGNh6JSfn28GkSotLfVK3LF27Vpze6Itq+WOHDlith/tdkMdL2HOnDlh216yZIlZXnFBCnQrqkp0O2fj3EYZ7/bLeOuCnqd4+/ZzsT373kY7j3puiouLw94vHQtl4cKFlcom8jMQTbR9JfJ8AFXL038qfrlqnH7TqAgD3iN3+hc0MtuupcNKS1o7ob3jbZOIX9OmTU2Vfb169bwlAACkhnCRA06fPi0bN270HompEtbqX0urgSu+JXqPAABIDeEiB3F+AADViQ6dAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIF8gqEyZM8OaQaXjvgOyRV17Bm69ReXl5svPUZe+RO/0LGplt19JhZYRsPj+895mL9w7IHtRcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwKq+8gjdfo/Ly8mTnqcveI3f6FzQy266lw8oI2Xx+auPYnlxWKr/95Kr3KL4H7msgr8x40HsEP35vgexBzQWQorGPtvDmqpZIWQDIVIQLIEW9OvyNqZGoipbRskAyzp07J40bN5YRI0Z4S4D0RbgAHAhSI0GtBSJdv35d7r//ftMkFG26++675dKlS17pzHL+/HmZPn26CUT2eOrWrSv9+vWT999/3yuFbEW4yAGlpaVSWFgYmpT/8bZt28wyJK+q2gtqLVCVgoIC6dmzZ9j0yCOPeGszy+rVq6Vly5ayfPlyuXLlSuh4bty4IXv37pUHH3xQJk2a5JVGNiJc5AD9Rf7ss89kz549ZlJ2/vTp0+abBFIXr2aCWgvE06BBA3n33XflvffeC5t27Ngh9957r1cqM2iw0OCQn58va9euNZ107fHovH6ZadSokSk3d+5c71nINoSLHFFUVOTNhZs9e7bUq1fPe4RUxKq9oNYCuUKbeebNm2fmX3/9dRk7dqyZ9xs0aJBs2bLFzC9ZsiRjm30QH+EiRwwfPtzUYPg1bdpUnnzySe8RXIhWQ0GtReb7t8t/9ebS165du2Tw4MFhfTa0VvLkyZNeidv2799v1kXrGKq1CVWti1fbsH79eikrK5MuXbrIsGHDvKWV9ejRQ4YOHSpXr16VnTt3ekuRTQgXOSSy9oJaC/ciay+otcgO3/7BEVmy8V/TNmTohX/AgAGyfft2GT16tEyZMsUEC+3f0KFDB9m4caNXUqRbt26mP4Q2uUTWGtggogHh2rVrZt7SddrUMWTIEG9JZfb5Ghzq169v5qOpU6eO+cKjNm3aZP5HdiFc5BB/7QW1FtXHX1NBrUX22P6//q3aQsbNmzfl2WeflalTp4ZN69at80rEpjUR2sdB+22cOHHC1B6sXLlSdu/eHeqsPXny5FCQ0C8UI0eOrFRroE0ab775ppnX7ehk2XUaVHSK5tatW3LmzBkzr51TkdsIFznG1l5Qa1F9bO0FtRbZqTpCht5FsWHDBlm1alXY9NZbb3klYispKTH/v/rqq9K+fXszb2n/hhkzZlQKEracv9bgyJEjpsZCaz309bz99tvemjvrtMYjXo1EIr761a96c8hGDP+dQbSt03aWUhoUbPtnIuu+8pWvyPHjx024cLXNdFo37unZMn7abO9R7fjwd//X/P/V+z9v/kd8+45ekv3HMrNjn9ZOjRvU0nuUGK0RaNu2rfzxj380g2TFuzNE13ft2lX69u0bChRaW/DNb37TNIfs27dPHn74YbPcz9694f+dsdtq1aqVeZ4GBi331FNPmeYS7Yj5hS98IbRu5syZsmzZMhOARo0aZbYRyb6WrVu3xi1n2delNar2eJA9CBc5SD/QsrXWorp+rlD9BrRrnLa/twNnvufN3dG0cT0TLB79WhNvSeJSDRdBnh/tIh4ZSrQDpj7+5JNPTHPKt7/9bdNBVLept43qOvs43mu0IcQfZGJJpCwyD80iOYjmECB5GipmjWoj617qmlKwcEE7Rnbu3Nn02dALfzxazrIdKm3zh46mqX03tCPm5z//ebPONqXYdQMHDqxyzA3b3FLVCJz0z8h+hAsACCCdQoWlIaFNmzYmJJw9e9ZbeodexDdv3mzmIy/iOjqv1kpoM8aHH35oRtK0Zew67ZOhNRm67vHHHzfr4rHP08By+PBhb2llOriW7lc7oepdLsg+hAsAqEK6hQo/OyaF3hESOaaF1jzoRTzauBMtWrSQ3r17ywcffGAu9v4LvV2n/S/0jpWgIUD7cEyYMMGEnT59+oSCjaVhR4cE12YapZ1Qq6oNQWYiXABAFdIxVFgaAuwdIXqb6JgxY8xtrFqLoINq6dgUxcXFle7ysE0j+jy9fdXf7GFrRHSd/pmAIE0i1qJFi0zzigYMDT7aD6pXr15mfI277rrL/DEzpa9Lm3OQnQgXAJDhli5dasa00A6f9pbWAwcOmLs+jh07FvUuEmWbMZS/T4byj9IZpEnE0mCiw3trrYneCqv0tRw9etQ0uyxcuNC8Vq0NGTdunHTq1Im/kpqFuFsEWYW7RTJXOt8tAve0o6iGC/vHFLlrJLtQcwEAqHHar8OOIqo1Lsgu1Fwgq1BzkbmouQCyBzUXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAAp/LKK3jzNSovL092nrrsPXKnf0Ejs+1aOizUMt77zMV7B2QPwgWySoN6eXLtr94DZJT6dUWuXuf3FsgGhAtkFX3vj6z0HiCjdJsqCf/efvbZZ3LPPfd4jwCkC/pcAMhI169fl8LCQvM/gPRCuACQkV555RUpLS01/wNIL4QLABlHaysWLVpk5vV/ai+A9EK4AJBxtLbi008/NfP6P7UXQHohXADIKP5aC4vaCyC9EC4AZBR/rYVF7QWQXggXADJGtFoLi9oLIH0wzgWyCuNcZK4g41ycPn1aNm7c6D0SmTdvnhQVFXmPREaNGiUFBQXeIwC1hXCBrEK4yFzJDKLF7zqQnmgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAgi5w7d04aN24sI0aM8JYANY9wASAnXb9+Xe6//365++675dKlS95SWJwfpIJwAQAZ5NatWzJs2DCpW7euHD582FsKpBfCBcJcuHBBrl275j26jWpWAEAiCBcZRr+1vPjii+Zin5eXZ6Z+/frJ5s2bvRLJ279/vzRv3lyaNGlCNSgAIGmEiwyibaAPPPCALFiwQL74xS/KlClTZMKECbJ3715Tq7Bx40avZGratm0rDRo08B4BULt27ZLCwsJQqNdmiUWLFsWs6Zs7d66cP39epk+fHnpOp06dYjZl6BcHf9nISX/HZ86cKXfddZds3bpVbty4Id27dw+tj/b7H7nNePsHXCJcZJD169dLWVmZDB8+XE6dOiUrV66U1atXm2UjR470SiWvd+/eUl5eLkePHpX69et7SwHo79mAAQPkwIEDMnr0aBPsNYC/8MIL0qdPn0oBQ3344YfSuXNn83uq5QcNGiTHjx835SMv8PaLw/Lly6Vv376mfNeuXc26/Px883j8+PHyjW98w8w3atTIrLOv5emnn5aOHTuaZdbp06dNLWSQ/QOuES4yhH4DsU0fjz/+uPnfatGihfzsZz+TUaNGeUsQxO//6M0AcWhNxPPPPy9dunSRK1eumJCvF+yLFy/KjBkz5NixY7Jlyxav9B0bNmwwQUGfo+W3bdsmr732mqlx0NpHP/vFoaioSPbs2WPKHzx4UIYOHWrWT5o0yXyp6N+/v/zTP/2T+SKgoeO5554zZVesWCHt27c3ZS0NF0H3D7hGuMgQderUkTZt2ph5/dAISqtyBw8eHKoW1Un7aJw8edIrcUeuddz8xQGRYS+KbK34H4hFL9x6gZ41a1ZYjZ7+Tk6bNs3UImzatMlbeoeGkTfeeCPsOdqsouU1SPhrO/T3UcPCkCFDvCW3t6+BQsPA2bNnvaXBJbJ/wDXCRQaxF3391rFu3TozH4+tyt2+fXuo+lSDhfbR6NChg7M+GplMay/mvU7IQHRaY3jmzBkzr7UTU6dODZvmz59vgke0i3XLli0rNS82a9ZMGjZs6D2qXrW9f+Q2wkUG0arQOXPmmG8y48aNMx3KNGRE+waid35oVaq2C584cSJUlbt7925TPaomT57MXSEeQgaqos0cq1atCpvWrFnjrU2NNmno7/Xbb7/tLbnTFKo1Gq1bt/aWApmBcJFhXn75Zdm5c6epgbAhQ6s5I2sySkpKzP+vvvpqpbZY7dilbcVXr14120qF9oj3N7nU9qS6TQ02rfqFKR7GHzLokwFLL/CHDh0yHZ6jTal2grbNFfPmzTO/21or0qNHD3NXiDaVPPzww15JIDMQLjKQdurSGgi9Y8QfMvRCr2xVbrxvPDZwJNJ/IxrdZ7QP29qa1JGVwaYp/9kUr2RoT5FXZoo0/xtvAXKW7euUbL+HIPT39dlnnzVhX28t/81vfmNqRfTOjoULF5p+E0CmIVxksIKCAhMytAe4WrJkiWnm0A+r999/39wP36pVK7MuFi2H2zRUbHlZpGg8wQJ32L5OixcvjtoEqZ2mo3WQDsr+vur4MjpuxuXLl01Q/utf/yqzZ8+uVCNSE4EHSBXhIguMGTPGdN66efOmueNDP3z0/nr7OB4tl+sIFblNawy+/vWvS69evcIm7bOkYUL7OtlbTrUPk222mDhxommK007TWsuQrHr16pnaiY8//tiMS+Fv5tPXobWSkeHF1jzq2Bf6WvSOsOrqoF3V+QGiIVxkoaq+2diOYkprP3JV17aECtymzYM6QJZ/Ki0t9daKLF261HSE1oGt9G4rbbbQQKDjSGi5VMeY0T5SeteJDoSld3XZSWsvtD+V3lbqH/hKg43t3K2vRTtwV2enz6rODxApr9w2VNcwTeU7T132HrnTv6CR2XYtHVa10RoIbY/VQXP03ndLg4JWnS5btsx8AO3bt89Uo+qHjY7Ep9+0tCOav1On3pqq33T85ZXuQz889QPTdghVsZanI33vtT8FMo92sk309zYbftft76r+Xkf7/dJbyrWWQAfYsv2qgHRHzUUG0Y5e2v6rH6jt2rUzVZPar0KDhXbeLC4uDgUFW5WrVZo6poU2nWj1qfZK12ARWR5A7dIB7CLplwfbJJLLtYzIPISLDKEdM7XT1zPPPGNuWbPVlBoStIpUq1Qjb1fzV+Xae/T1OWPHjjXtx9zeBtS+bt26mT5TWkOhY9folwDbp0P7YNhayWHDhnnPANIfzSLIKjSLZK5cbRZRFy5cMH+07J133jFjZlg9e/aUJ598Ur71rW9Ry4iMQrhAViFcZK5cDhdAtqFZBAAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgBkjNLSUiksLAxNyv9427ZtZhmA2pVXXsGbr1F5eXmy89Rl75E7/QsamW3X0mGhlul7f2Sl9wAZpdtUCfR7+9BDD5mQEalp06Zy7tw5qVevnrcEQG2h5gJARikqKvLmws2ePZtgAaQJwgWAjDJ8+HB58MEHvUe3aa3Fk08+6T0CUNsIFwAyTmTtBbUWQHohXADIOP7aC2otgPRDuACQkWztBbUWQPrhbhFklTqfy5N//3/eA2SUz1V81bn174n93j722GNSUlJCuADSDOECWaW6fq5y1Z//9H+k7OwZ+U+du3lLqs+Ado0T/r29fv06wQJIQ4QLZBXChVs3/vpXeeJvO8vlP1yUrxR0lBat20iLVm3kwYd7Vcx/VRp/oYlXMnXJhAsA6YlwgaxCuHDvX9YWy/9Y8JL3KJyGi5Ul7zoJGYQLIHvQoRNAXEMfnxgzPIz6+2ed1l4AyA6ECwBx5deta0JEpF4DviHfGveU9wgA7iBcAKhSZO2FBo4rf/g3+fSTMm8JANxBuABQJX/thc4vfX2r9BwwRJ4Z9ajsfvstsxwALMIFgEBs7cXkGf9gbk0d/ffPybwVP5VXl/2j/GjeTHNnCQAowgWAQLTGQsOEv5+FhoyVJXvl8qWLphZDx8QAAMIFgMCiDaZ1d8P/KP+4Yp08OmKUzBw/VLaXrPfWAMhVhAsATmiNxoL/+TPZ+OqP5b+/OI1mEiCHES4AOKOjeC7f+E5FsLguU7/5dZpJgBxFuADglDaTfH/pqzJq8rOmHwbNJEDuIVwAqBaDRowxtRjaTPLfZk42fwQNQG4gXACoNi1bt5GVb70r+XXrmVqMfz193FuDbHHu3Dlp3LixjBgxwltyx4ULF+TatWveo+ph99+1a9dq3xeCI1wAqFZ6C+v3Xl5hmknm/P1/ka0b13hrUNPOnz8v06dPNxdj/SN/OrVr107GjRsnJ0+e9Eq5sX//fmnevLk0adJELl265C1FriBcAKgR2kyiI3v+YtNP5B+mjaWZpIatXr1aWrZsKcuXL5crV65Iz549zXT69GlZt26ddO/evVpCQNu2baVBgwbeI+QKwgWAGqPNJNoPo/G9TWTqiL7yv98/4q1BddJahEmTJpn5tWvXmj9t/95775lJ50+dOiWPPvqoWe9K7969zbaPHj0q9evX95YiVxAuANQobSZ5rmip/Nc5P5Ciad+Wf1lb7K1Bdbh+/bo88cQTZn7Dhg0yduxYM+9XUFAgb731ltx7773eEiA1hAsAtUL/ZLvWYux5u8Q0k6B6HDlyRMrKyqRLly4ybNgwb2ls2nyifTHmzp3rLQlX1XorVkdPu1yfb/uA2P4fnTp1ksOHD3slw926dUteeeWVUH+RuhUh9fvf/75cvXrVKxHdrl27pLCwMLQPfd6iRYsqdf70vy6dt8/RjqL0GUkc4QJArWl6X0vTD0P/VwcPHjT/w52SkhLz/9ChQwM1T+hFtVGjRrJ169ZKF2C9wG/evFny8/NlyJAh3tLkfPjhh9K5c2dZuXKlTJkyRQYNGiTHjx+XPn36RA0Ys2fPlqeeesqECS2vr/MHP/iBdOzY0fQhiUaD0IABA+TAgQMyevRo8zzt//HCCy+Y/US7u0RflwaKPXv2mP8/+OADbw0SQbgAUKu0mUSbSNRjjz0mCxcuNPNInYaBM2duj5KqTR9BtGjRwvSXOHbsmGzZssVbepuGPw0dGiwefvhhb2lytImmb9++JhhowNi2bZu89tprcuPGDVmwYIFX6jbtM7Js2TITDD7++ONQea2R0U6q0Wjtw/PPP29qbHQf69evN8+7ePGizJgxI+rxKX1drVq1MiFGa33+/Oc/01yUBMIFgLShHQt//vOfm5Dx2WefeUtRk+rUqSPDhw8385s2bTL/W7YW5PHHHzf/p0Iv+m+88UZYbYqtNdHQ4K9VsPvVsOC/0GsQ0hoGfU6kFStWmFAxa9assH3o8U2bNs08J/L4lAYYDS50Qk0N4QJA2mjatKn86le/kgcffNCMv6AXDtS8MWPGmBqBHTt2hPobaMfQN99801x8takhVbr9yAt4s2bNpGHDht6j22ztSyJNMf4aG62dmDp1atg0f/58EzwiQ4waOHAgNRUOEC4ApB2tFtfqaW0nr6rjIGLTb+lt2rQx8zqeRVD16tWTkSNHmqaBnTt3mmW2Y2imXXz152jVqlVh05o1DORW3QgXANJSv3795Ne//rXs3bvXVJd/+umn3hokon379ub/aB0047F3edimA5dNIjVFazsOHTpkxtuINjEGR/UhXABIW9pMsnv3btPx76GHHjJt4UiM7ccQqwNjLN26dQs1jWiNhTaJBL2d1SVb+6IdPc+ePestjS+Z58AtwgWAtKdNI/rNecKECTJnzhxvKYLQOx/0vKnx48ebob4j6XgTequq/++LaNNIUVGRaRrR5ikNGEFvZ3XN1qIsXrw4rPZF7wjR20Wj3Yoa6zmWjn/h+u+p4A7CBYCM0KNHD3M3SWlpqTzyyCM0kyRAB43SUKbf5PWPlOngUL169TKTzmsNxTvvvFNpQCpb66HjRLgY2yJZ+t5rsNHaF3092ilz8ODB0rp1a/nSl75kmtAi6e209pZT7YSqZfR5EydONMesnVJ1XA1UD8IFgIxxzz33yC9/+Uv5u7/7O5pJEqDNBC+//LLpnKmDVSkNDDrp+Bc6JLhehCPHrrBjXqgOHTqYqTbo69fhyW1A0k6Z2ly2ZMkS87oj7zCxli5dan5GtHZD++7o8/T2V21m05A6atQoryRcyyvXXi21QJPjzlOXvUfu9C9oZLZdS4eFWlZdP1eofgPaNU7o91YHdNLqeh2TQe8u0Wp8uDdz5kwzgJXedcHFGEFRcwEgI2lVud5N8tFHH5nqe/0fbrke2wK5g3ABIGNpM4l29NTbI7Ufhv7dC7ijQ2Zn4tgWqH2ECwAZ77nnnjN9MbRNnj9+5ob/j5Rxhw4SRZ8LZBX6XGSuRPtcRKPV+PS9AGofNRcAsgbBAkgPhAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAABOXLhwQa5du+Y9Sm/nzp2Txo0by4gRI7wlcIlwASCrnD9/XqZPn24uHDpiq07t2rWTcePGycmTJ71ScG3//v3SvHlzadKkiVy6dMlbinSzevXq0O/Fxo0bvaXuES4AZA394GzZsqUsX75crly5Ij179jTT6dOnZd26ddK9e3cufEnSvzUybNgwqVu3rhw+fNhbWlnbtm3NX1FF+rF/L8batGmTN+ce4QJAVtBvzpMmTTLza9euNX+n5L333jOTzp86dUoeffRRsx7u9e7d25zno0ePSv369b2lSCdaq6e/J4MGDTIhfMeOHdUWtgkXADKe/sGyJ554wsxv2LBBxo4da+b9CgoK5K233uJPhyNn7d6929Tofec735GRI0fK1atXZefOnd5atwgXADLekSNHpKysTLp06WKq7oOwHfrmzp1r5gsLC007dNeuXcO+ze3atUsGDx4caqfWqV+/fjH7b2h5uy2dtBlBa1T8HR2DlIkl6HOjlVu0aFHMfWzfvl26desWKq/9VGz5mTNnyl133SVbt26VGzdumOYlW86221fVQTKR8+h/b2wfGvucTp06xWyW0Q6lL774Ylh/G91HvGacqiSyzUR+poK+N66OyTaJaJPVgAEDQu/T4sWLA/3cJYo/uY6sUl0/V6h+qfzJdb34LVu2TIqKiswHexD64a8f+nrB27Ztm/lGp4+1f4au0xoO7cNhm1pGjx4tDRs2lA8//FD27NljlmktyahRo8y80irnPn36SH5+vnzrW98y5X/3u9+ZC8u+fftMc0GQMrEEfa593f5yP/vZz8wxagCL3I89f9HK6zFqJ01tn7fL7LnQwPHUU09J+/btQ+ezb9++UlJS4m35tkTPY+R7o9+w9du2HquGIH2degwPP/yw9wyRQ4cOyWOPPWZen74G7fsRr3y812slu80gP1NB3ptE9x+P/dkZPny4OV4NG9/85jfNthLZTlCEC2QVwkXmSjZc2A9J/VYdeZGKx14Ion2oK/thrN/09ENeL6CWfiDrBUTX2YtGkA/rVD7Qgz7XHlerVq3CjkmfP3v2bBMi/OfJHmfHjh1NFbm/2Ui/YX/xi180x17V/u1+Iy/WiZ5H5X9v9GL4xhtvVApO9iJp6X5WrVpljtG/j1jlY71ev2S3Getnyq5P5L1JZP/xaIBcsWJF2Htnt5NIKA+KZhEAOU0vbPot038RUPZD+9VXXw37YFfaIW7GjBnV2madLL2A6MVt1qxZYcdUp04dmTZtmjRq1CjsLgF7nFr17g8Wqn///pWOPVGpnEe9QPuDhdLmBD0GbQbzV+drh1LtyBu5D1s+GcluM9bPVKLvjatj0j5Jb775pnTo0MFMlt2OBnPXTSOECwA5beDAgZUuqvpN8syZM6bquXXr1t7ScPYDX6u8lV4gvve975k+CfpNXb8RfvTRR2adFaRMLEGea1+32rJli0ydOjVsmj9/vrm42QtzkONMRTLn0U/vaIi8QDdr1sw0JcSifRT0Yhl5zKlIdJvxfqZUkPfGL9Vjsn2Shg4dGnY+W7RoYQLMsWPHzGtyiXABIKPpRbdNmzZmPtoFKhl6IXj//fdNnwKtwo5Hy1n6Qa3fwHVsDa1y1udqB0R/p8UgZWJJ5Llava5V6v5pzZo13trbEjnOZCR7HpOh+9KOnzqQl3bqjXXMiaiObaog741ytX9be6R9XPyB5umnn5Y//elPZp3rMS8IFwAynv3266p6VwNL586d5ebNm6adPB4t56dNCXrL3+9//3uZM2eOHD9+3FTv+3v3BykTS5Dnak2B9m/QPizRJjsWRSLHmYxUzmOitF+CDp6m5+LEiROhYz179mzSzSLVsc2g741ysX897zaM7N27NyzQ6GQ71boe84JwASDj2bZjV9W7tjZEmyD0gzySfqO0Ix3q+BnRaPX9yy+/LK+99lrM7QQpE0u051b1uiMlWj5RLs5jELod2/xSXFxcqY9CMlxvM9Fz7Wr/dmwL7bTpDzF20uCnzSWu+w8RLgBkPK1ynzBhgpkfP368Geo7ko6XoB+iQZoflB0HYPLkyZWeox/CWkui3yjtuBraaS7a9v2Pg5SJJehzqxq/QO8A8T/HXrSilX/33XdDZZMNIomeR5f0Am07UbqSyjYTfW+iSWT/WlbDmwaUIUOGeEvD6fuqd50ol00jhAsAWUEHIdJmAr346R8p09uSe/XqZSad186B77zzjvmGFoT2b7B3MmgP+zFjxph2aq0l0dsn7TdKfwe53/zmN6asDnJky+rthf6LZ5AysQR5rn3dWoujdy3YshMnTjTnQQdQ0qYUS8+VhhYtr7U/9jh10Ca9TdNf1gYRDXBaRs9DVX/8KpnzmCh7gdT3Xju76j70eHV8Dj0/yaiObSby3rjYvx3uW8+7TrHotvX34+233w41r2kw0Z8pfV062WAUFOECQFbQD2NtJtBvw3qLozpw4ICZtMpdhwTXD/VExpZYunSpuaVQxyawnfB0e9G2Va9ePfNB/swzz4TatrWsXhDsmAZBysSSyHP9r9uW1Vs6NSyUlpaGjQWi502HRdcLvF7w7HHq+BYLFy4MCzy6LxvgtIy+niB3mSRyHpOlr01v27THoP0MtLOr3imhF85kVMc2E3lvUt2/bRLR8FjVz5YOB67vqwYMDRY6psnnPve5UPOJvs+J/BVVBtFCVqmunytUv1RG6ATgjnYC1TuSfv7znycd/Ki5AAAAIZ988om5RTWV25MJFwAAIOS+++4zA5Wlcnsy4QIAAIToyJ1f+9rXZMGCBd6S23+bJJE+F4QLAAAQop18//mf/9l0trV3i+jtx0H/KKAiXAAAgDB6B4n+eXftZK1T0L++ahEuAACAU4QLAADgFOECAAA4lZXhokePHqFOKEy5NQEAal/WjdAJIDMxQieQPWgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgVF55BW++Ro0YMUJKSkq8R4A7u05f8eaQSQa0ayy19HEEwLFaCxeFhYWyZ88e7xGAXHf33XfLn/70J+8RgExWa+ECAPyuX78u9erV8x4ByGSECwAA4BQdOgEAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgEMi/x8lhOZy8L/U+wAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57605,"title":"Determine flows of given probability using empirical frequency analysis","description":"Write a function that takes as input  observations of peak streamflow  and exceedance probabilities  expressed as percentages and returns the flows  corresponding to the probabilities. \r\nUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank  (e.g., the highest flow has ). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with . Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return NaN for any probabilities that fall outside the range. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 158px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 79px; transform-origin: 407px 79px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.158px 8px; transform-origin: 109.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e observations of peak streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAAC3UlEQVRYR+2XOYtWMRSGZ/6BoqWV2ggDiriAaGPhuICt2tgILmMnorh0LqDYuoGlov4ARbEQXAp1LCwEwaUQsXP7Bfo+cgK5+XJvTu58DFPcwEtmvnty8uZsOZmcWKBjcoHymhiI1XpmsNh8W2yJNlwVbfqilkCbfB9XLpeyA8IeYYXw2JRvsPme5ivCl7mQrCGGdY4Jp23DfZohEQbfzwlHhF/CbqG3Bb3EVmuTW8I64bOwUfjRYpFPZknktvW1nIcYpJ4Ki40I7uty0yF9v2GyFzWf6ePSEjHc88osgP7Ufbk9N+vH5/ahZN1WziVij7Ry2lbPal7vOH1MDPE1wjvHuoZIF7G9krwbSXs3SIntko6H4yQWghidXmshG8cY/28RqrOzzWKptQ5L+U3nqa9JjpIRxlL90ZbB1TFGfaKA9lEeW5rgX+k8kCvGfkoqlAcq+3ancm4FyIRxXX/MONcWiaXKa2rRCWm/FO3gTZgR7rkYm0tWxW68r92I1V5jnMTShCndEJ2E27Lyb7TKU4fSG6Imi7ME24i9kTQXNsOzSVwiegd8zNBTx0qxErtwLKQg2HUlxfdkW/WOs9BzwbMnWX9coGdjUC/PCnFv10mMuLlqC1FySnhvypZpPi8Q4Fj0qOCp7sG6JyV/2XSFMGgcvtRdsJbysUOgc4Xga+G3QI/2RPC20IFU6u5g9cbvHmJY7o5A+1NTAnZK/oMRR8dHgdsk1XHBDh1bsfgSJx5wFRnKjJVw5/eCpdiMtjr0b6HjyCVSKMpuV3Li23ZKC4fGRCtEWXkmfLMvmzQfFHA592uIu9AUpKUn3DIj93HOleE1ROuC3//YplvNnTmS8W8Nl9iHQCzNXA6Ge0ceLW0xxgMk1w5DmhfSlLBWWGQbv9X8UuB9kMtOrP9AiBsCshFC2ZeUJ/hLFvJ+h9x+gbYIL3wVyOpsmZlPYt4D/JcbiFWZa7BYrbkGi/Ww2D/pSJcpt+GUTwAAAABJRU5ErkJggg==\" alt=\"Qo\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5417px 8px; transform-origin: 94.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and exceedance probabilities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p1\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5083px 8px; transform-origin: 45.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e expressed as percentages and returns the flows \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q1\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.925px 8px; transform-origin: 108.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the probabilities. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 345.033px 8px; transform-origin: 345.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.4917px 8px; transform-origin: 31.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (e.g., the highest flow has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m = 1\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.142px 8px; transform-origin: 311.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 100m/(n+1)\" style=\"width: 115px; height: 18.5px;\" width=\"115\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.2833px 8px; transform-origin: 87.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for any probabilities that fall outside the range. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q1 = floodFreq1(Qo,p1)\r\n%  Qo = observed flows\r\n%  p1 = exceedance probabilities at which the flows are to be reported\r\n%  Q1 = flows corresponding to the probabilities p1\r\n\r\n  Q1 = Qo*log(normcdf(p1));\r\nend","test_suite":"%%  Small sample from lognormal distribution\r\nQo = [27 360 71 8798 58 122 468 638 19 114 3542 781 356 635 6093 748 8305 8 6253 875];\r\np1 = [5 10 20 50];\r\nQ1_correct = [8773 8100 5583 552];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Larger sample from lognormal distribution\r\nrng(1)\r\nQo = 10.^(randn(1,500)+1.7);\r\np1 = [0.2 1 2 4 5 10 20 50];\r\nQ1_correct = [106602 21248 6176 2975 2432 1062 326 58];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Yellowstone River at Livingston, MT\r\n%  Flows from here down are in cubic feet per second\r\nQo = [18300 15400 13100 10600 18500 30600 13500 20400 15800 20600 26800 17500 21400 20000 22800 21200 20400 14900 25800 21900 17100 24200 15700 15600 20400 20200 20200 27900 16000 24900 24600 21200 24400 29200 26700 21100 36300 25700 21400 14200 26000 20100 15000 23800 27900 18600 17900 15200 24000 7450 16200 16200 17200 23000 13800 24000 16900 23700 37100 38000 18800 23400 19300 14800 25900 27200 13300 17900 22600 15200 26300 23500 28100 40600 23500 17900 32700 15600 12800 26300 33600 22800 30600 18500];\r\np1 = [9.58 13.53 50];\r\nQ1_correct = [30000 27900 20850];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Mullica River near Batsto, NJ\r\nQo = [1190 407 815 360 382 350 384 245 287 1170 645 990 1050 435 430 630 489 1380 499 240 857 1840 380 204 420 705 946 143 419 666 269 579 490 565 401 488 578 149 401 473 747 364 335 343 201 509 452 420 449 1320 258 312 867 1860 303 332 537 387 222 342 517 676 249 285];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 1854 1564 1365 1110 747 433];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Charles River near Waltham, MA\r\nQo = [690 1520 1020 1370 2540 1020 2180 1020 1600 555 1470 1180 1000 1240 1360 692 1730 575 869 933 1250 1360 1550 2490 1990 957 1940 1460 1510 1850 1540 1340 890 904 637 1250 2670 1800 1790 1110 1670 1630 1090 895 4150 1610 1740 3480 1140 1220 2960 1970 2410 811 1110 2710 837 779 1240 1030 637 2180 1430 757 1430 2990 2180 1080 1090 2190 721 1170 1510 1510 1590 1250 1390 1390 4270 1770 1080 1570 1460 1640 634 1150 1250 1180 806 1520];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 4172 3166 2974 2482 1840 1367];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Merced River at Happy Isles Bridge near Yosemite, CA\r\nQo = [2500 3320 3180 3800 2720 2720 3240 2620 1240 2620 2240 2820 2050 2520 1870 1350 2570 2520 935 2820 2380 3020 8400 1210 2620 3220 2800 3480 1980 3040 3690 2450 3080 2480 2520 9260 3580 2180 2500 2800 9860 2910 3640 1520 1710 1080 2230 5200 1720 9240 1640 4640 1480 4980 2330 2170 2690 4240 3260 4650 1440 1800 4190 3500 4040 2100 4880 5450 2860 1600 4040 1750 1640 1910 1090 2310 1490 3140 1870 5220 5900 10100 4150 2810 2920 2330 2290 4550 1830 5680 4350 1180 2760 2750 4470 4610 2250 1750 1190 882 2490 5210 8060 4240 2160 1410];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [10083 9776 9005 8281 5213 4247 2700];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct));\r\n\r\n%%  Quashnet River near Waquoit, MA\r\nQo = [41 36 33 41 40 35 28 34 39 42 32 27 39 26 33 40 36 61 83 32 39.2 52 44 42 58 30 32 30.1 50.1 48.4 53.2 40.8];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 76.0 68.7 56.6 49.1 39.1];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end),1),Q1_correct(3:end)));\r\n\r\n%%  Illinois River at Henry, IL\r\nQo = [104000 108000 53700 106000 95200 46300 45100 45000 40200 53700 30900 67000 47000 58900 78000 117000 88900 55000 40400 71800 88500 38400 52100 84600 32400 90300 128000 92400 58300 64000 49000 161000 65400 98500 107000 93100 111000 108000 120000 64200 51600];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 138560 127200 115800 106600 67000];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end)),Q1_correct(3:end)));\r\n\r\n%%  South Skunk River near Ames, IA\r\nQo = [1990 600 3490 2580 3000 2890 3230 2320 3050 2530 4500 8060 4010 2270 6550 2620 3000 3820 5320 1630 980 8630 1340 376 3540 3150 1720 6210 1990 4300 1820 2170 5260 2900 2790 4890 4380 1330 3660 3030 3340 5780 5230 3580 5300 2240 4980 2720 1880 3490 5150 5020 1980 4040 3040 565 370 6600 4700 2350 11200 2340 1640 14000 2080 4760 3630 906 1990 1070 2030 2520 2310 3330 6510 11000 4560 14800 1620 730 6740 9250 11200 6420 1890 4380 6740 3260 455 4210];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 14144 11181 11060 7092 5292 3190];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%\r\nfiletext = fileread('floodFreq1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-21T19:33:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-01-21T19:33:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-21T19:29:29.000Z","updated_at":"2023-01-21T19:33:03.000Z","published_at":"2023-01-21T19:29:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e observations of peak streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Qo\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and exceedance probabilities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e expressed as percentages and returns the flows \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the probabilities. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (e.g., the highest flow has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 100m/(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 100 m /(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for any probabilities that fall outside the range. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49743,"title":"Determine aquifer properties: unsteady pump test in a confined aquifer","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 714.15px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 357.075px; transform-origin: 407px 357.075px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 7.79167px; transform-origin: 382.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.633px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.3167px; text-align: left; transform-origin: 384px 53.3167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.567px 7.79167px; transform-origin: 297.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose a confined aquifer initially has no flow. In that case, the piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the level to which water would rise in an observation well, would be a uniform value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.467px 7.79167px; transform-origin: 124.467px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. A well turned on and pumped at a rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q0\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.9083px 7.79167px; transform-origin: 38.9083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will create a cone of depression; that is, it will draw down the piezometric head to a level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h(r)\" style=\"width: 29px; height: 18.5px;\" width=\"29\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 7.79167px; transform-origin: 24.8917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.2917px 7.79167px; transform-origin: 95.2917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radial distance from the well. Applying conservation of mass and Darcy’s law to this situation leads to a diffusion equation whose solution for the drawdown \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAAAoCAYAAADZs5l2AAAChklEQVR4nO2Z67GDIBCFTw92kAZswApSgR3YgR2khdRgCfZgC6nBFu79gTtsCD5AEZT9Zpy56oVwcGEfAIIgCIIgCIIgCLlQAKgAtAC66e+7kpPWzdQA3gD+2PWIOqJw5KTVix5qUj6xB3ICOWl1glbGK/ZATiAnrZt5Qk/M3X1kTlqdeEFNyggVON2ZnLQ6MUBNTB97ICcQTCulHC3UdlMAaHANSyugt8fGeF5Da7oDQbQW0Jb1gjKGjv3QViPgRrTn8kl3ajbeko3ng+9U6g6GEERrOzUajOeD5dmWfvZepdnxBihvHqf7GmpSaEe7UyQdRCvPN/mqb+Dmc47aCXzcD62CN9RkcC08kq49+k6NIFop0jQbPnCN9OMBPf4WalL4bsL1+ewySxxh+C5zHEwr73h0bZwADfT4B/yuAIp3Rtgp4R+PHOECm59e59mrdbOYAdeqRfMg9m28K1beddDbaQU1eS4f5YidwGXR+WrdDMUGvp3Eyg5GaOs32y75SNo6+UegyDvVLMJX62YK9iM+J1MxsoOKtbNFw3OVNXKB5uELrSaXrOgsfLUuYvtn/iFdV0OM7ICP12Y85CO76b6ALoLx5xyKvlOLjXy1zkIrwYxMubWlNgk2lo5TuY+sp/seSiPl2rYV1bM2KeGrdRb62OZKIJ+Y4nZoslYY4T7yAfXhKejrF9otvYvFHq2z8NIjlYprKBdhFo1SZe041YxR+KRczQj2aJ2lgt7un/g+OLoKPAaxQb7flnFczQj2aBVmoEh6yQhc6gXCBSF3aKuHpJodCAezVifwKrsK12OpYphaeigEgnJpOispoXaAlAJC4SQo8m4gkbUgCIIgCIIgCIKQB/+ZU42DSga/5QAAAABJRU5ErkJggg==\" alt=\"s = h0 - h\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 7.79167px; transform-origin: 79.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as a function of distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 7.79167px; transform-origin: 7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"s = (Q0/(4 pi T)) integral(exp(-x)/x, u, infinity)\" style=\"width: 117px; height: 44px;\" width=\"117\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.9833px 7.79167px; transform-origin: 65.9833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transmissivity, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.15px 7.79167px; transform-origin: 67.15px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the storativity, and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.025px; text-align: left; transform-origin: 384px 18.025px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"u = Sr^2/(4Tt)\" style=\"width: 49.5px; height: 36px;\" width=\"49.5\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 349.917px 7.79167px; transform-origin: 349.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that achieves the objective of a pumping test: to determine the transmissivity and storativity from measurements of drawdown in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 347.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.733px; text-align: left; transform-origin: 384px 173.733px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 497px;height: 342px\" 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data-image-state=\"image-loaded\" width=\"497\" height=\"342\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [T,S] = confinedPumpTest(t,s,Q0,r)\r\n  % t = time, s = drawdown, Q0 = pumping rate, r = distance from well\r\n  T = f1(t,s,Q0,r);\r\n  S = f2(t,s,Q0,r);\r\nend","test_suite":"%%\r\nQ0 = 0.15;                                %  Pumping rate (m3/s)\r\nr  = 100;                                 %  Distance from well (m)\r\nt  = [100 1000 10000 1e5 2e5];            %  Time (s)\r\ns  = [0.0402 1.236 3.664 6.276 7.05];     %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 1.042e-2;                     %  Transmissivity (m2/s)\r\nS_correct = 9.864e-4;                     %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.30;                                %  Pumping rate (m3/s)\r\nr  = 100;                                 %  Distance from well (m)\r\nt  = [100 1000 10000 1e5 2e5];            %  Time (s)\r\ns  = [0.0804 2.472 7.328 12.552 14.1];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 1.042e-2;                     %  Transmissivity (m2/s)\r\nS_correct = 9.864e-4;                     %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.1;                                      %  Pumping rate (m3/s)\r\nr  = 40;                                       %  Distance from well (m)\r\nt  = [300 2000 8000 12000 24000 40000];        %  Time (s)\r\ns  = [0.494 1.749 2.830 3.153 3.709 4.120];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 9.838e-3;                          %  Transmissivity (m2/s)\r\nS_correct = 3.4e-3;                            %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 1e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.1;                                      %  Pumping rate (m3/s)\r\nr  = 65;                                       %  Distance from well (m)\r\nt  = [300 2000 8000 12000 24000 40000];        %  Time (s)\r\ns  = [0.125 1.050 2.067 2.383 2.931 3.339];    %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nT_correct = 9.838e-3;                          %  Transmissivity (m2/s)\r\nS_correct = 3.4e-3;                            %  Storativity\r\nassert(abs(T-T_correct)/T_correct \u003c 2e-3 \u0026\u0026 abs(S-S_correct)/S_correct \u003c 1e-3)\r\n\r\n%%\r\nQ0 = 0.05;                                     %  Pumping rate (m3/s)\r\nr  = 5+10*rand;                                %  Distance from well (m)\r\nt  = [4e5 9e5 14e5 19e5 24e5];                 %  Time (s)\r\ns  = [0.859 0.918 0.951 0.973 0.991];          %  Drawdown (m)\r\n[T,S] = confinedPumpTest(t,s,Q0,r);\r\nlogfit = polyfit(log(t),s,1);                  \r\nTapprox = Q0/(4*pi*logfit(1));                       \r\nSapprox = 2.25*Tapprox*exp(-logfit(2)/logfit(1))/r^2;      \r\nassert(abs(T-Tapprox)/Tapprox \u003c 1e-3 \u0026\u0026 abs(S-Sapprox)/Sapprox \u003c 2e-3)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-04T00:26:53.000Z","updated_at":"2026-01-09T18:01:40.000Z","published_at":"2021-01-04T05:23:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose a confined aquifer initially has no flow. In that case, the piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the level to which water would rise in an observation well, would be a uniform value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. A well turned on and pumped at a rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will create a cone of depression; that is, it will draw down the piezometric head to a level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radial distance from the well. Applying conservation of mass and Darcy’s law to this situation leads to a diffusion equation whose solution for the drawdown \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s = h0 - h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = h_0-h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s = (Q0/(4 pi T)) integral(exp(-x)/x, u, infinity)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = {Q_0 \\\\over 4 \\\\pi T} \\\\int_u^\\\\infty {e^{-x} \\\\over x} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transmissivity, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the storativity, and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = Sr^2/(4Tt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = {S r^2 \\\\over 4 T t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that achieves the objective of a pumping test: to determine the transmissivity and storativity from measurements of drawdown in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"342\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"497\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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an ODE: equation B","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.625px; transform-origin: 407px 106.625px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.358px 7.91667px; transform-origin: 211.358px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\" style=\"width: 181.5px; height: 39px;\" width=\"181.5\" height=\"39\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.0083px 7.91667px; transform-origin: 35.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y'(x0) = y'0\" style=\"width: 74px; height: 20px;\" width=\"74\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1167px 7.91667px; transform-origin: 38.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.275px 7.91667px; transform-origin: 25.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eyp0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.708px 7.91667px; transform-origin: 109.708px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assigned numerical values, and the other will be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.742px 7.91667px; transform-origin: 128.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.9px 7.91667px; transform-origin: 80.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.483px 7.91667px; transform-origin: 194.483px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the applications for this equation is in groundwater. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 0\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.567px 7.91667px; transform-origin: 136.567px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.975px 7.91667px; transform-origin: 141.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the normalized distance from the well, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEB(x,coeff,Xbc,bc)\r\n%  y = values of the solution\r\n%  x = values of the independent variable where the solution is requested\r\n%  coeff = [a p], the two parameters in the ODE\r\n%  Xbc = values of x where the boundary conditions are specifified\r\n%  bc = [y0 yp0 y1] = boundary values (see description)\r\n\r\n  y = f(x,coeff,Xbc,bc);\r\nend","test_suite":"%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [1 NaN 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [1 0.505461057363874 0.265959532078956 0.140787844664873 0.071276733472728 0.029333752731051 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [0 NaN 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000035290165611 0.000065476121971 0.000315436935125 0.000552779648598 0.000757412623201 0.003086031722519 0.012031119481478 0.040129255417251 0.089700339919646];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [4 NaN -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [2.974028994378906 1.041176175714286 0.308462205553512 -0.076175488441917 -0.426089583908447 -0.952692417292867];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [2 4];\r\nXbc = [1 Inf];\r\nbc = [3 NaN 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [3 0.005688558853080 0.000051725255081 0.000000653418086 0.000000009396692];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n%-------------------------------\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [NaN 1 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-0.696760997897786 -0.352185550727323 -0.185310228971762 -0.098095479140575 -0.049662847941353 -0.020438614824974 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n \r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [NaN 0 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000053997354167 0.000075728700374 0.000316920386259 0.000553525214653 0.000757922298088 0.003086129240342 0.012031140116004 0.040129260776539 0.089700342119009];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [NaN 4 -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.047695617799804 -0.816404083826666 -0.431398160565887 -0.374418157507686 -0.532801281305956 -0.958228725044217];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 Inf];\r\nbc = [NaN 3 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.098451806781317 -0.173147136186896 -0.018397012773047 -0.002117248575316 -0.000253600440751];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-16T01:10:22.000Z","updated_at":"2025-05-09T06:39:10.000Z","published_at":"2021-05-16T01:19:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2y}{dx^2} +\\\\frac{1}{x} \\\\frac{dy}{dx}-\\\\left(a^2+\\\\frac{p^2}{x^2}\\\\right)y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y'(x0) = y'0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\prime(x_0) = y\\\\prime_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, one of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyp0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be assigned numerical values, and the other will be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the applications for this equation is in groundwater. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the normalized distance from the well, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAoCAYAAADg+OpoAAACEElEQVRYR+1XuUoEQRTc/QHB4ws8YgU108BI0VTwAiPB4wMUNFVBA0OPwNgj94oMNPIAzdUvUPwErZJ+w3PmdffOOCwG21DMbk/3e13V1a93q5U6tWqd8lQaiQor/W+lGwWlWaAPaAHugHXgNkY1D6NdBFsEFoADYAC4AT6BIeA5lKzWRPeOxQqe2yrgCz53AHvA0l8TCZMHBOpPBbvE92HAevdraIzRPEbvuxk9hjySiEPagA8fq1CidrfSZjxPgEkjSCmJRDLGt9iwX/aoMKNuzHxyDK7wHPFI8uX66Tza3dt80mk2U5h9bESgtK+uv5AZWjH5XQX2LYaH98yN8+1hEsYKwk0/UrLx5FttGp08wGxyiHNJR5km3AxKww23Gs+PNJ9Zgoy0k3wB9P5wMZ1eKu6FJZ04KRRAH2RLNrqWLal/6URSKDkotMHC2rK1ZptUi1CiTSRbMyTRZvGZgPtMRXaAn7JUJJGwiZ4dvch0In2GLEYbmLwKULIuWW3MCBYj9vlKv0jmu+i4yHFgDuANPAacyyIs19Ex1wCr9iDAa1pcxro3E2FC12YY+8oLkzE4HcT2CJwCwesa78W1mUIcu/hqkV+PWcaXLSDjxrITyW+LTEUpM5E41qwoZSaSa4PH4gJoirku777IeNkfJupNu7NMRnQqjUCHHgJvesVlJgoq0UhU1CiNv5aFlat8AyPAcSmMrVi+AAAAAElFTkSuQmCC\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAoCAYAAABuIqMUAAAC3klEQVRYR+2Yu24UMRSGkzfg1oIiLgUVCHFpQgEF4VIhkAJKk45LR0MkoAOikEgpE+gQEgIeAEhSQEFElYaKAsETAAlPAP+38okOZmfXXnknrDSWfs14xmP//n18fM4MDw1wGR5g7kMN+a1avUb5/0X5vSKyJvwU5oQngdhOXQ8mkFx17e/r/orwUriZ8G12k3Zmc169vA49Tek6KzCpy8KIcCMaZV31mfCMtkx0STgqfBVOCD+ymSV80I48g3933+6KBl+IJnBY9U+u/TXdPw71xX6pTv9VG/a3I3NB929cHVN4EeqoviMSCdXHwrPruprpJWiZ1ySFfExgVEN86ECe/bJ9UMn7Vdtys8lV3pN/pRXAzPpSUswmJtDNbDx581a1ksc3j4cR8fvH3OidyPt3fHJSMN9ffAJVysckvDvsRN670WWxPVucseuwU2zjXSJEJgQOmyryvj2H0yXB+//i8+gWmEH0nmB+G/vHFfpTdlr1MwInKoX6fJhoccK+w27krS3hwXFhjzDiyPvQ4KOef66DtJFKJe8n3M3b9FXtXpRvyJdeksZsSiua2l8vyt9W54/CAHibAz14GGL+i8I74YiwTdgvkLiQseGe8W6nBDsrOPVxx7jlb4yfSx6XuSLsc+rk+HXLsjjE7gQSlrz4CPRheH9VV0hT7BDcfJZK/pBT2/H+63YjDFD13ogzcRRsqadiK+mTHnPHfkJ8/0XYXOlU8lWEcp4byTjEtiDQp5uWivr4iO8p5MmtUhd5IxPvEcwQE4ojV7gRWvOOvUA7gj6Lr2olb38k4tzAVGff3I2WkRgKsImfC/w+MVOrlbyZjLdhNuADgT2Ave8WfLJOIo/HQf1bwj95QV1mYxsQIpPCOeGXcFogYmVF3rchz7vKhKYu8iwzSkMcr/RM4HcKK8IEngrmElsmoYK7fNtOcWtQJ3kbs9i1IV9MysyOGuUzBSvWvFG+mJSZHf0BvpeoKQkEiaYAAAAASUVORK5CYII=\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAAoCAYAAAC1mQk2AAADjklEQVRoQ+2Yy+tNURTHf7+ZkbxGYoKJEXlOUJRHTBSFlAyUZwaSt0x+FEPJo8hvhjL2LAYYeBVJDDCSkbc/gO/n1163dbd9zz1Hxz3n3u6ub/fcffZjffd67LXO4ECPtsEe5TXQJ9Ztmu1rrNc1tsARfKPnL+H/DP3+Ej7U5QDymOIUCbtX2B6Evh1+p+n3Tnjm3ULhYbcQQxP3hbHCNWG9E3y8nm8Jc0JfnkPqGO92wiD4cuGbMC4hFdp8LzwT5nZM6hwbZRFDI5/DGlmCPw0meTjHfh0bkkWMQPHAEVuhZwsWXkC0Oixc7ZjUOTbKImZmZsus0sONxJr43ROhNhERGfP6GGPxs8XCyxwHVvmQdsSIii+clPjaurppJ3WK7YgxB1O74iYTBZfVnVweYilytddcXmIpclzYO4VUpKy9j8UC7lPHSde5Tc8XKmeREKCIxmw69xUBhFa7jMOETBE7rpc3hVYJrc9IWGdCHc0xRYwU6ZiQuoztQCyH7CpivyVtO98xYoR+ypfatVhjlkZRc21sYWLeFE9oTCr5ZR0aaRbjpwufwn/6U31FDof1Jwq+2CW3bewRE/OJ734NPJXY7az6KCzR1nxHns3WChY1yS1HC0PCVMECDZH1gECNxwGSXPu2Un82hfWZ9zXsN1O/H4WlwmqBAIaMlwQsiLHkrCPrxcQsnCM0A9n4tPBTmCRsFqjPYlJeMAShHRTILbnrKH9Y67nwQ7ge1oijKodGVrNGICe1lC42eetnze/CGaEp2MXEtmrA6zAIDcwTFglmWgiWFTHNlK34hBRmSPkDCQLTDsEO0JuyWYKvIsyCUibPAaL1pDv8yz02oo4WzeeVaBwf47DOB2JW01nwMRJGIP78YHNTJZOtYfs0iVQ2MTt17592oXvhiLw0uwPRJN9O4g9C79SH4Km70tbdoPd/FbllEzPz8IJAwvuk+Yf5l0XZ2G+9puPvKbzbEg7jXDDv/6Yx79AW6VI+YgLjG6+EUcLlQN7uRNa6GARn3CPhbTBt/BiTZQ+CkgUWMqbG1VOmxkxgf7mz2SHBm6GZEOY6SzgqPBYIBIybLECMip25kLBmtSDaImqaCUOeaNu4nsokBonZgr/Y8TlO2PcREZcIw8JdgbIHze4Sxrh+7sjdwj2Bu2qPgL/50M68I2FOk5+VScwdbPWPfWLV66CYBH2NFTuv6kf3NVa9DopJ8AfAENopI8yaUQAAAABJRU5ErkJggg==\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57635,"title":"Compute the average precipitation for a watershed using the Thiessen polygon method","description":"Several methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \r\nThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \r\nWrite a function that takes the precipitation amounts and the (, ) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.425px 8px; transform-origin: 366.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.458px 8px; transform-origin: 190.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the precipitation amounts and the (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.767px 8px; transform-origin: 156.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Pavg = spatial_average(xd,yd,P,xb,yb)\r\n%  (xd, yd) = coordinates of the precipitation gauges\r\n%  P = precipitation values\r\n%  (xb,yb) = coordinates of the boundary of the watershed\r\n\r\n   Pavg = integral(P*dx*dy)/integral(dx*dy);","test_suite":"%% Rectangular catchment with simple gauge placement and values\r\nxb = [0 5 5 0 0];    % km\r\nyb = [0 0 10 10 0];  % km\r\nxd = [-1 6 6 -1];\r\nyd = [-1 -1 11 11];\r\nP  = [20 20 40 40];  % cm\r\nPavg_correct = 30;   % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.05);\r\n\r\n%% Example 3 from dreamcivil.com\r\nxb = [0 10 10 0 0]; % km\r\nyb = [0 0 5 5 0];   % km\r\nxd = xb(1:end-1);\r\nyd = yb(1:end-1);\r\nP  = [11 15 12 10]; % cm\r\nPavg_correct = 12;  % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01);\r\n\r\n%% Rectangular catchment with more complicated gauge locations \r\nxb = [0 10 10 0 0];\r\nyb = [0 0 30 30 0];\r\nxd = [-3 8  4 13  1 9];\r\nyd = [-2 2 12 21 25 33];\r\nP  = 132+3*(yd-33);\r\nPavg_correct = 77.65;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)/Pavg_correct\u003c0.01)\r\n\r\n%% More complicated boundary\r\nxb = 10*[0.5497 0.4705 0.3840 0.3214 0.2937 0.2882 0.3379 0.4632 0.6271 0.7284 0.7947 0.8241 0.8039 0.8039 0.7689 0.7302 0.6452 0.5497];   % km\r\nyb = 10*[0.1857 0.2512 0.3867 0.5152 0.6717 0.7909 0.9007 0.9591 0.9498 0.8797 0.7605 0.6320 0.4708 0.4708 0.3914 0.2745 0.2194 0.1857];   % km\r\nxd = 10*[0.4 0.63 0.5 0.7 0.8];\r\nyd = 10*[0.9 0.6 0.35 0.8 0.32];\r\nP  = [113 166 140 183 125]; % mm\r\nPavg_correct = 148.271; % mm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% Example 5.5 from Chin\r\nxb = [2.0084 2.4293 2.8156 3.0028 3.2368 3.4126 3.6713 3.8467 4.0235 4.2117 4.3540 4.5197 4.7338 4.9362 5.0688 5.2611 5.4307 5.5418 5.6399 5.7033 5.7094 5.6167 5.4566 5.3269 5.2170 5.1962 5.2033 5.2325 5.2838 5.3351 5.3630 5.3672 5.3594 5.2956 5.1854 5.0638 4.9172 4.7914 4.5239 4.2432 4.0206 3.9153 3.7154 3.4805 3.3047 3.1412 2.9657 2.6980 2.4305 2.1494 1.9034 1.6444 1.3955 1.1317 0.9849 0.8611 0.7998 0.7605 0.6858 0.5893 0.4919 0.3519 0.2515 0.1265 0.0875 0.0801 0.1796 0.3474 0.5154 0.6832 0.7618 0.8867 1.0592 1.2773 1.4249 1.5055 1.5835 1.5910 1.5914 1.6825 1.8099 1.9151 2.0084];\r\nyb = [6.4122 6.4364 6.4348 6.4401 6.4466 6.4391 6.3966 6.4015 6.3566 6.3246 6.2539 6.1839 6.0530 5.9218 5.7761 5.5824 5.3632 5.1423 4.9708 4.7859 4.5496 4.0617 3.4599 3.0456 2.7688 2.6686 2.3950 2.1719 1.9991 1.8263 1.6529 1.4912 1.3416 1.0910 0.8266 0.5494 0.3337 0.2182 0.1485 0.1406 0.1468 0.1439 0.1756 0.2064 0.2139 0.1969 0.1920 0.1347 0.0650 0.0695 0.0751 0.1301 0.2475 0.4890 0.7338 0.9917 1.5500 1.7106 1.8828 1.9921 2.1387 2.5703 2.8288 3.1364 3.2847 3.5707 3.7975 4.1008 4.3918 4.6951 4.8218 4.9746 5.0914 5.2593 5.4377 5.4897 5.6412 5.8032 6.2388 6.3409 6.3942 6.3972 6.4122];\r\nxd = [1.3 1.0 4.2 3.5 2.1];\r\nyd = [7.0 3.7 4.9 1.4 -1.0];\r\nP  = [60 90 65 35 20];\r\nPavg_correct = 59.301;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% C E 372 problem 11\r\nxb = [33.6241 31.3609 26.3820 25.3635 24.0062 22.8754 21.4057 19.4844 18.2414 17.5648 15.1930 15.1935 15.5336 15.8735 15.8742 15.3089 13.6128 12.9347 12.0319 11.4673 10.2237 8.8694 8.0782 7.7400 7.4023 7.4049 7.7466 8.2004 9.6732 11.4838 14.6517 15.7834 16.4627 16.8027 16.8037 15.5614 14.0926 13.0759 12.3981 12.5118 14.5502 15.4557 16.7001 19.1891 22.2439 24.2812 26.3185 27.5654 27.9054 29.1500 30.9595 32.7690 34.5782 36.2742 38.0830 39.1005 40.6836 41.9275 46.9026 47.6937 49.5021 49.8399 49.8383 49.1574 48.2507 46.8905 45.1911 44.5108 44.0567 43.4877 43.0343 42.5763 42.4619 41.2167 39.1791 38.8389 38.8379 38.3850 37.2537 36.0095 35.5567 34.6511 35.2149 35.4394 35.5514 35.5496 35.3221 35.2082 33.7370]; % mi\r\nyb = [5.2159 3.9673 1.3564 0.6755 0.5609 0.7865 1.4650 2.9363 4.1815 6.2206 9.7311 10.2976 11.2045 11.7714 12.5646 12.7907 13.1290 13.6949 15.8471 16.7530 17.3184 20.3766 20.9425 22.0753 23.7747 26.6075 29.1008 30.5743 33.2952 34.3168 35.4529 36.1339 36.9277 37.6079 38.7411 40.6662 42.2512 43.4967 44.4026 44.9693 47.6908 48.4848 48.8259 49.6215 50.7575 52.3458 53.9342 56.8815 57.5617 58.1295 58.0179 57.9063 57.4547 56.8898 56.0983 55.6460 55.3075 55.0821 53.6137 53.0479 51.6898 50.1037 48.4040 46.0238 43.9832 40.8092 37.7481 35.9344 34.1209 30.4943 29.3608 23.4680 22.1081 20.9738 19.0455 18.1387 17.0055 16.5518 16.2108 16.0963 15.6427 14.8486 13.0361 11.2233 10.0903 8.1639 6.8039 5.8973 4.9894]; % mi\r\nxd = [15.9758 6.0340 4.0115 15.4546 38.1999 50.7358 40.6553 33.7370 31.4005 19.7352 28.4331]; % mi\r\nyd = [0.3267 12.1020 26.1511 47.3517 60.0644 40.6995 25.2792 4.9894 45.8937 28.9988 17.5623]; % mi\r\nP  = [29.79 34.97 25.60 24.27 24.60 42.61 42.35 15.51 39.99 43.04 28.41]; % in\r\nPavg_correct = 35.011;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-02-04T01:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-02-04T01:17:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-01T17:01:04.000Z","updated_at":"2023-02-04T01:17:57.000Z","published_at":"2023-02-01T17:03:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the precipitation amounts and the (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. 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