{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-26T00:14:02.000Z","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":"2026-04-26T00:00:00.000Z","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":57844,"title":"Solve an ODE: draining tank","description":"Write a function to compute the time to drain a cylindrical tank of diameter from an initial level to a level . The outflow occurs through a small circular orifice of diameter at the bottom of the tank, and the outflow can be computed with , where is a discharge coefficient, is the area of the orifice, and is the acceleration of gravity, which should be taken as 9.81 m/s. \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: 319.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 159.55px; transform-origin: 407px 159.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.1px; 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 43.55px; text-align: left; transform-origin: 384px 43.55px; 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: 229.742px 8px; transform-origin: 229.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the time to drain a cylindrical tank of 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: 61.85px 8px; transform-origin: 61.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from an initial level \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: 31.8917px 8px; transform-origin: 31.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a level \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: 40.225px 8px; transform-origin: 40.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The outflow occurs through a small circular orifice of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Do\" 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: 130.667px 8px; transform-origin: 130.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the bottom of the tank, and the 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);\"\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: 71.9583px 8px; transform-origin: 71.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = Cd Ao sqrt(2 g h)\" style=\"width: 99.5px; height: 22px;\" width=\"99.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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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\" alt=\"Cd\" style=\"width: 18.5px; height: 20px;\" width=\"18.5\" 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: 82.3333px 8px; transform-origin: 82.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a discharge coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ao\" 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: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the orifice, 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);\"\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: 111.708px 8px; transform-origin: 111.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAmCAYAAADN0BvRAAABE0lEQVRIS2NkoBAwUqifYRgbEA4Mm0IgNoeG0UkgnQvEp9HDDFsYZAAV5QPxRCB+D8RJQOwG1egOpHchG4LNgGdABbZAfBdJ4U6oISDNIEPgAN0AkE3BQJyO5lSQl1YA8Q0g1iTkAmxJA2QwyBUEXYBNM0gMFC7TgbgKiNvJccFKoCY9ILYG4nekGqAM1HAHGngoMQAyiJikfAKobiO602GuIGTATKhC9FjBGY3I3gMFnCMQZ6L7m5gwAGlOAGIvNM1C0NgApQswwOYFWKJZBZR/iGwbkB0DxKA8AooVrAaYAkX3ATEPmkYY9zmQoYPsKkKBiMMchPCoAcQlZbwBORqIo4GIqzwgmAOJKZGINmQYpEQA0UUlJ+mjkqgAAAAASUVORK5CYII=\" alt=\"^2\" style=\"width: 8px; height: 19px;\" width=\"8\" 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. 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data-image-state=\"image-loaded\" width=\"308\" height=\"223\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = drainingTank(h0,h,Cd,Do,D)\r\n g = 9.81; % Acceleration of gravity (m/s2)\r\n t = sqrt((h0-h)/g);\r\nend","test_suite":"%% Rounded orifice\r\nh0 = 3; % Initial depth (m)\r\nCd = 0.98; % Discharge coefficient\r\nDo = 0.1; % Orifice diameter (m)\r\nD = 1; % Tank diameter (m)\r\nh = 2; % Depth in question (m)\r\nt_correct = 14.6440; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Sharp-edged orifice\r\nh0 = 5; % Initial depth (m)\r\nCd = 0.6; % Discharge coefficient\r\nDo = 0.2; % Orifice diameter (m)\r\nD = 2.5; % Tank diameter (m)\r\nh = 4:-1:1; % Depth in question (m)\r\nt_correct = [27.7579 59.2645 96.6372 145.3422]; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))\r\n\r\n%% External mouthpiece\r\nh0 = 3; % Initial depth (m)\r\nCd = 0.8; % Discharge coefficient\r\nDo = 0.1; % Orifice diameter (m)\r\nD = 1; % Tank diameter (m)\r\nh = 2; % Depth in question (m)\r\nt_correct = 17.9389; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Convergent mouthpiece\r\nh0 = 1; % Initial depth (m)\r\nCd = 1; % Discharge coefficient\r\nDo = 0.05; % Orifice diameter (m)\r\nD = 0.3; % Tank diameter (m)\r\nh = 0.1; % Depth in question (m)\r\nt_correct = 11.1146; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Re-entrant mouthpiece\r\nh0 = 4.5; % Initial depth (m)\r\nCd = 0.75; % Discharge coefficient\r\nDo = 0.2; % Orifice diameter (m)\r\nD = 5; % Tank diameter (m)\r\nh = [1.2 0.8 0.4]; % Depth in question (m)\r\nt_correct = [386.0058 461.6427 560.2147]; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-01T12:15:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-28T00:41:34.000Z","updated_at":"2025-03-25T15:09:17.000Z","published_at":"2023-03-28T01:19:52.000Z","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 to compute the time to drain a cylindrical tank of 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 from an initial 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=\\\"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 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\\\"/\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. The outflow occurs through a small circular orifice of 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=\\\"Do\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the bottom of the tank, and the 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=\\\"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 can be computed 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=\\\"Q = Cd Ao sqrt(2 g h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = C_d A_o \\\\sqrt{2 g h}\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=\\\"Cd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a discharge 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=\\\"Ao\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the orifice, 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=\\\"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, which should be taken as 9.81 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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\",\"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":54735,"title":"Solve an ODE: concentrations predicted by the cells-in-series model","description":"One approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume . Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) is and the first-order decay coefficient (dimensions of time) is , the concentration in the th cell is given by\r\n\r\nWrite a function to compute the maximum concentration in the th cell and the time it occurs assuming that the concentration in the first cell (i.e., ) is at time and no contaminant enters the first cell from upstream.","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: 183.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.95px; transform-origin: 407px 91.95px; vertical-align: baseline; \"\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume \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: 237.25px 8px; transform-origin: 237.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) is \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: 173.742px 8px; transform-origin: 173.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the first-order decay coefficient (dimensions of time\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAmCAYAAADTGStiAAAAwUlEQVRYR2NkGCDAOED2MoxaTK2QFwYaFALEa4D4LTZDaRHUEUCLpgGxIBCL0MviVqBFR4F4K9SXdLMYFqr/Ry1GT2C0SFwgO4ZWUIOygxyRGfojUN1MLGrJ8jEoSxgTafE9oLosallMpJ14lZHl41GLSQ0BG6CGw1BNBkD6Ij0qCS+gJTpoFh0D8o/QqwAhGEq0KrlGLcYIgdGgJpgoqKVgNKipFZIEzRkNaoJBRC0Fo0FNrZAkaM5oUBMMImopAACNICMnaBvayAAAAABJRU5ErkJggg==\" alt=\"^{-1}\" style=\"width: 15px; height: 19px;\" width=\"15\" 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: 11.275px 8px; transform-origin: 11.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is \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: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C_n\" 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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in 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);\"\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: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth cell is given by\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=\"V dC_n/dt = Q C_{n-1} - Q C_n - kVC_n\" style=\"width: 170px; height: 38px;\" width=\"170\" height=\"38\"\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: 193.958px 8px; transform-origin: 193.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum concentration in 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);\"\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: 145.85px 8px; transform-origin: 145.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth cell and the time it occurs assuming that the concentration in the first cell (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 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: 11.275px 8px; transform-origin: 11.275px 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,iVBORw0KGgoAAAANSUhEUgAAACoAAAAoCAYAAACIC2hQAAAC0UlEQVRYR+2XOYsVQRSF3/wCcTQymMDRQBAUZtREA00UDQ1cJpls1MBABgXFyAU0NHAJDN1AEATFUVAYTVxRDCZwiQxdAn+Ang/rwn3dr7u6+zXlDHTBofr1q+XUuXWXHuktkTayRHj2OqJtW6pTdLEpulqEVjlSv/X8wf3equcF4cewxJuYns0PCvuF5cIX4XMgslP9L+GVsCK82zQsSebXIbpB4y8IkKGdEO4KXx0RFL4jTIZ3V9QfSUkU9S47Bffq2ZvYc0HJl8J4OMzFVEQheStshpm3CLE7N6MxV4U9wsMURLmPz91GqORNXcSBa/JeWFnhUJXOUXZHMeGnYG4WOyRcq7Tqv0GoWmd86dJlRLmTh8NsPHm0BsnWhxYRRc3vbjc8vBWnaHqCIqLmDLbuRj0UeXnTvWvNKyJ6W6vsWyxmh0cR0Z/Oid7ouZXsUkvCzOAion/cODINsfS/tipEz4vhqRZY4qDrhEZFSkrTW7hrdPAqzsQd3SXE0mZM9N0acFQ4K7yIDc7+X0TU53fmVA1PpM5nwtoWDtbHtSwzvdZIX66djmxOXXBf2C7Uibkc7ltY2wrxnOKxXG/lGqfjbl0XskUJi88KWGEQSV9oU30R6uwdKZr0jAWOCfymGM9lwljhjKeeCQtAlkUfC++EZcKEQCFNgVym+HH9T9HtCVhlRvgjbt9kAzWqtVzBHSMa5vZQbbMwJuwIL9+q/yg8EWKO9igcaJt6M6uRn9O7pwK1hKXuXKVWlagRbtqTQLJFt/kARKfCYS115+reFEQJSw8En+F8deZV5gqANVlFUhA9p01PCgcEFKMZedQkRtPsq2BgQkhB1EzMZwmeTToeRN5/Z63XmL4v3BRE7X4SLeaDqp68OaI5HJGB1leopyCKeoSxSwJfpNzPGwJRwxc7xOFp4V5Qsy+SpCAaBBqu64gOp19+dqdop2jbCrS93l+eEZEp6CMDrAAAAABJRU5ErkJggg==\" alt=\"C_in\" style=\"width: 21px; height: 20px;\" width=\"21\" 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: 24.8833px 8px; transform-origin: 24.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at 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 = 0\" style=\"width: 33.5px; height: 18px;\" width=\"33.5\" 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: 171.133px 8px; transform-origin: 171.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and no contaminant enters the first cell from upstream.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Cm,tm] = CISmax(Cin,Q,V,k,n)\r\n% Cm = maximum concentration in the nth cell\r\n% tm = time at which the maximum concentration occurs in the nth cell\r\n% Cin = initial concentration in cell 1\r\n% Q = river discharge [L^3/T]\r\n% V = volume of a cell [L^3]\r\n% k = decay rate [1/T]\r\n% n = index of the cell\r\n\r\n Cm = Cin*exp(-n);\r\n tm = log(Cin/Cm);\r\nend","test_suite":"%%\r\nCin = 100; % mg/L\r\nV = 100; % m^3\r\nQ = 10; % m^3/s\r\nk = 0.01; % 1/s\r\nn = 4;\r\nCm_correct = 16.8325926; % mg/L\r\ntm_correct = 27.2727273; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 50; % mg/L\r\nV = 1125; % m^3\r\nQ = 25; % m^3/s\r\nk = 0.001; % 1/s\r\nn = [8 23];\r\nCm_correct = [5.4745741 1.6086642]; % mg/L\r\ntm_correct = [301.4354067 947.3684211]; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(all(abs(tm-tm_correct)\u003c1e-6) \u0026\u0026 all(abs(Cm-Cm_correct)\u003c1e-6))\r\n\r\n%%\r\nCin = 100*rand(); % mg/L\r\nV = 1000*rand(); % m^3\r\nQ = 70*rand(); % m^3/s\r\nk = 0.03; % 1/s\r\nn = 1;\r\nCm_correct = Cin; % mg/L\r\ntm_correct = 0; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 42; % mg/L\r\nV = 2560; % m^3\r\nQ = 180; % m^3/s\r\nk = 0.004; % 1/s\r\nn = 6;\r\nCm_correct = 5.5885481; % mg/L\r\ntm_correct = 67.2834315; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 8; % mg/L\r\nV = 3100; % m^3\r\nQ = 124; % m^3/s\r\nk = 0.006; % 1/s\r\nn = 9;\r\nCm_correct = 0.3650487; % mg/L\r\ntm_correct = 173.9130435; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 100*rand(); % mg/L\r\nV = 531; % m^3\r\nQ = 6; % m^3/s\r\nk = 0; % 1/s\r\nn = [7 14];\r\nr_correct = 0.6844581; \r\nCm = CISmax(Cin,Q,V,k,n);\r\nassert(abs(Cm(2)/Cm(1)-r_correct)\u003c1e-6)\r\n\r\n%%\r\nfiletext = fileread('CISmax.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-11T04:58:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-11T04:52:21.000Z","updated_at":"2022-06-11T04:58:19.000Z","published_at":"2022-06-11T04:58:19.000Z","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\u003eOne approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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. Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) 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=\\\"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 and the first-order decay coefficient (dimensions 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=\\\"^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e^{-1}\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=\\\"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 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_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in 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=\\\"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\u003eth cell is given 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=\\\"V dC_n/dt = Q C_{n-1} - Q C_n - kVC_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\\\\frac{dC_n}{dt} = Q C_{n-1} – Q C_n – k V C_n\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 to compute the maximum concentration in 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=\\\"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\u003eth cell and the time it occurs assuming that the concentration in the first cell (i.e., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\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=\\\"C_in\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_{in}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at 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 = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and no contaminant enters the first cell from upstream.\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":57844,"title":"Solve an ODE: draining tank","description":"Write a function to compute the time to drain a cylindrical tank of diameter from an initial level to a level . The outflow occurs through a small circular orifice of diameter at the bottom of the tank, and the outflow can be computed with , where is a discharge coefficient, is the area of the orifice, and is the acceleration of gravity, which should be taken as 9.81 m/s. \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: 319.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 159.55px; transform-origin: 407px 159.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.1px; 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 43.55px; text-align: left; transform-origin: 384px 43.55px; 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: 229.742px 8px; transform-origin: 229.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the time to drain a cylindrical tank of 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: 61.85px 8px; transform-origin: 61.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from an initial level \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: 31.8917px 8px; transform-origin: 31.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a level \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: 40.225px 8px; transform-origin: 40.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The outflow occurs through a small circular orifice of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Do\" 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: 130.667px 8px; transform-origin: 130.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the bottom of the tank, and the 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);\"\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: 71.9583px 8px; transform-origin: 71.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMcAAAAsCAYAAADRhqyHAAAJ20lEQVR4Xu2dWeh9UxTHefNApiceKCQylgwRRaJEQpnTv+iPByRDSJIHxIOkTCHJLCRShhCRMXM88EDiyRTvrE/dr9Z///bZe517z/7de/zPqdX//u45Z++11zzsff9bbjFdEwUmCmQpsOVEl4kCEwXyFJiUY5KMVhQ4wwa+3OCwVhO0HndSjtYU3nzH/9mW/qjB1WMlwaQcY+XcauN9kaF3u8HjBnuuNqprsLvUvvmSbyflGBnnRoLuN4bniwZbGew3EpyF5qQcI2PYmNA9zpB91mBXg9/GhHiK6+Q5xsy91cT9fUPr7THnGiLrpByrKWBjxep/4zWmnGOsIri6eOM1fjCgjDv6a/Ico2fhyiwAr/GKwR4G368MVmsR2cG+2t3goxqO8yoHluFUg/0N9nKTvGqfnze4tzbxSO5DyNMNTjGg6rKTw/tv+/yewecG2xocZXCEwZBJqATukAgzl0zTiNdgPVcYHG6w9QzfD+zfOwyeaoQ/inChwQGOh8xZbU72VQ6UgoUgJE8bPGiAQnCx8DsNUJZvGwhKI9plh0UprjG4eMZEiPmwwWsGsoqq5YvJ0OH4gZFE4A41ONOglfAMgfLBNsiHBiWvcZ/d31iY7H67hxC3um6zga+aDU4PptqcjCoHwnKPAVYUi3lBB7N4jpgTgUFB9m610objwuhHDFBy1nqzwS0d8/HsG7P1Ds1clA+acw099tDkk+J25Rp8/6QBBuQhg98NdjPYYIDy67quQOtFcfb0DHniiHIg8O/OhAUEa1bMW4iWi12UWLn3vbCjGKfNGFqaS+ut0aUPvt7I8F4oDOgzwYDPErZ8Z1DyGn/ZfbrlOc9wrX2PAeL6xWDnAXHzQ6HAGHfm2NegGv5GlEOunYkiFkxxcuvFDk1DmPyZgcKkqLC3SERRuLMdLi2FZlE61rwGFvsyg1I+xj4s5XOtEnoUFN6SDoSqaTXl8F4gqnFeOSB8q8UuytT0fbY8qLgQMQL+fao0Z0WsUQBpWWKUk1BE144DjV9CAY+1vUG02iRcS2EKyvOmQalI4+UsFPIE6OgfUU7Ed+SRoYJRSTlSIe9rSYVc9L2e6x30cZ+sEU4d2ENABkXEBsNT/2lAcu8tKn+r+DH0nIynXIu5q5WcGQIIPttEos934S36t6K9D93CxrqkHD6cinoNFu8TH/4eg3LI5YJv2O02kFDc/QMGxxhQh/c8CFu8OfCCZ5SrMYhcEUWU14g8W0NJnqNWxMGzkbecbLCLwY8G+xi8bEDllItkP+1h4NlZmx8f/O92a15D3y7lSL1GqPQ1Qy4t2UXDAW+9a8Qs3e/rllNlHoLZ8+KPp2A3qxJXT5O+oV4UB9ZPKEVFTp4qYiCG8hrgqZC2ZADwbC8YkJtQ6EHOSKpT/uUU7J8ZMURD3rlhRmv6UwqnN9GHLuVQZi8Ch12RWyjv9vE4y1IOv1bc+rJ2k7L+cw2ONPC9FJVz16Ni5QWtxHNV0yLVvJqSygOVvIav3qWK6w15zrCl9ykhUyA4zwAPI/6v4X2XcvhYt09Dj0X86qjRojFWI3bf++lal9GbUaUs7akso/IX8R4oMhZ30VwDXiGcJxiUFM3nDGlkoB4KY+VCeJ/PMMfDiQFSSL1GOXPKkQp4H3c+xnxDLhfirod1zikvAsJWnFy50+MXDVH7Ggj/vBemnBcd0mtoFy+d61IFSblXzlDXKl0K2eAtecoGAxU2fBVrjZznlCPNN/okgr4cCjJYhGqzZRFODvCuF74+hqDP1HgG4CAD4nu/dSGld2nc9ciHfAiTyzUV/i3arNM8Xc1BTwevHKlnl6fLyVtq6NP1eI+0hrYR5YhWm+Yt/fYRshbProfnwEJdaUCHNlVADApVl659WetVsfK0lTUmDt/G3ZBA1yx9jU/adcGhqMh+Kglx2gzV9127GXzIlVMeVbGyuWYkrIoqh2dipNqREnBZCbnHu1ZKrDG9dF/r8/RUGFqqsK1HxSrFW0ky3/vIYQiv0VcxwMFvYdKWJBSDz+QMGwxyPSBfbMnJsfKNbG4cScgjYZV3T/OGU8tSDo87jIhW5mDYEwbRzjhKSE1eDUZZYba9l3bzprQdIgmOKLnfi0QINYTXiCoGz6XhOAr7jgFNSgHHI/xO6XRdCrlyuUq1a96lHF5Qa17ATwISJxpEtx9EmNT6mXSTX6SnIyaze7drx67HW7GvT/hF41pfZhkVK3D3fMXqkivRG1gk10DhtgsYgzQv04bQn+zd6JkZ7/1yPPUhGYUHLnj5X5jXpRww8ysDbQbrqpKo2qANXXiZVU/Ac8rmBYH7JW+pcxylreyMoQNhfP7DYKOBmCTGRUrdKW6lipUO9jAnh3sWPXimkFOVnptszNC+pAyRVbLluANd7Nx17Iz26fYd5Qa8Q86GYakZ4NoWdY0pHrDWTQ5dlbaP+I4kiRAte7XlYQLCoS3A/Owjix/z5dfLOvCCeIZPDLBkVJpo0uHSaSJ17XPCsLCdgeuSGc2U9BM+fWygIwCR6li0eqidvDpro/dqnr/Es6G8VtpULs2ZMxhpi4D3SaJpkN5qkDPIEv6uRrTyDe7zI25vGWwSBdR25epE3En2olrsQoxYGcsE8cfoLboYBCOONsDV6iAOivKFwXMGxLhd61W4xdjqwPIZ5YAJKMtdBvLI3MObINipJUQwsaQopH8+946EL006pZSL9EcUt897NifdTtRFd32frgFD/JgBlS08DnRNZVF70fzYtS3q8orwJesRa8qhyXKVltoiWVTN9dXGGNt9WSsflvUJoeZZr6xqroGJciy601VHo0MHhOZZQOGdrhDWRy683qTKGFEOWSXc3fUG1V9tsGcg6I0GY0vOF+GtcoOUUUr85rW8NZxk2dMmlmr8TQSnhtQA9yNGxVfyFvGOWXRLygFyLyUuTIPgitg9+qmBL6URCpxvUNsrMwDtVm4IhQ9pZUTCGy0R91mYBAh++A2LjCGjFinF95lzvZ5VtFLLyxSyDu7ZupRD5woonZGAcvmD8CUC4d7PMdjcQirFsGnTjG6yOrvQdcjChRLmtHMsL4a3j/Zh1kvoo/MoXCxV9LT+mgJF59zkua4OObXe1w3SEArmkvxQJqShpfPWuG4SJn6JY0jmz7WoJb0kS63qEJZPhQy+o5zbgj4knlza5qGiAFtSxqoYrMd3xXN9CrUR2JtFeDV4USiScyxJ1kY3rQ9DseT8xy3PzBTia/u31Q+X6XgrBCPUpcrGD0XoMNDoCOkQ9if/MMbQkYtoBmND9bCZMZ6UY8yiM+HelAKTcjQl7zT4mCkwKceYuTfh3pQCk3I0Je80+JgpMCnHmLk34d6UApNyNCXvNPiYKTApx5i5N+HelAL/An9vj0tPX181AAAAAElFTkSuQmCC\" alt=\"Q = Cd Ao sqrt(2 g h)\" style=\"width: 99.5px; height: 22px;\" width=\"99.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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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\" alt=\"Cd\" style=\"width: 18.5px; height: 20px;\" width=\"18.5\" 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: 82.3333px 8px; transform-origin: 82.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a discharge coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAACDUlEQVRYR+1WPS8FQRR9r6eholFoaND4SEQjwj/wFaUEP0DhD5DwA3xEISo0ChU98dHoKCgo6CRCzzky9+Xu2N3ZtbP7XmQ3Odl5b3f2nLlzz71TrTTIVW0QHZVSiL0TZUT+XUTGsaJTYAC48eG8v+bIJcgHgWngsF5CFkG8ach3cF+oh5AWkD4BTYb8CvehegjZBumsEvKKcXvRQjpB+GDy4kCRt2L8llVMmmRlgr4DE8AL0GbI+fusKCFTINoFRgHaVVxD/iVgqyghjMCJcsg6xsuG3ItzkmwNSeeAEeDRkGsLe3GOSwgT9BZYBdZU+KWy8i8vznEJYdXsAYYB2xlfSlhm58QJ0at25WJm58QJuQP7M0CSsMurc6KESDLGdVevzgkTIv3kIiYajNCKSWKOMzsnTIis1HXW8OocW4j0E5bsqNyQfOnH4Dqhc/hdOS70YnwMBKqxFsItOQe6gCTV0nZVVKmXjj2P77IcyLwjjNk6fi4Rwod7gDQyPtsA+BGppjKH744BrLb6/bA5JJ4E7JOc1KBa/XEVNBX51ENxXlgiU8gn0CcLzVOIHBXsYsft4HnmHui2tyb1ch0TJOnZh3Sz5DTZrkBO5RURSUi7IYrT6MoZoNa/8hLClX+YqDWbu7iSbSMggs/zFMLV7xsRPFR1ADxS0Im/zrh5CkmVd6UQO1xlRMqIuCz0Dccbaik6k+SxAAAAAElFTkSuQmCC\" alt=\"Ao\" 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: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the orifice, 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);\"\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: 111.708px 8px; transform-origin: 111.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAmCAYAAADN0BvRAAABE0lEQVRIS2NkoBAwUqifYRgbEA4Mm0IgNoeG0UkgnQvEp9HDDFsYZAAV5QPxRCB+D8RJQOwG1egOpHchG4LNgGdABbZAfBdJ4U6oISDNIEPgAN0AkE3BQJyO5lSQl1YA8Q0g1iTkAmxJA2QwyBUEXYBNM0gMFC7TgbgKiNvJccFKoCY9ILYG4nekGqAM1HAHGngoMQAyiJikfAKobiO602GuIGTATKhC9FjBGY3I3gMFnCMQZ6L7m5gwAGlOAGIvNM1C0NgApQswwOYFWKJZBZR/iGwbkB0DxKA8AooVrAaYAkX3ATEPmkYY9zmQoYPsKkKBiMMchPCoAcQlZbwBORqIo4GIqzwgmAOJKZGINmQYpEQA0UUlJ+mjkqgAAAAASUVORK5CYII=\" alt=\"^2\" style=\"width: 8px; height: 19px;\" width=\"8\" 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. 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data-image-state=\"image-loaded\" width=\"308\" height=\"223\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = drainingTank(h0,h,Cd,Do,D)\r\n g = 9.81; % Acceleration of gravity (m/s2)\r\n t = sqrt((h0-h)/g);\r\nend","test_suite":"%% Rounded orifice\r\nh0 = 3; % Initial depth (m)\r\nCd = 0.98; % Discharge coefficient\r\nDo = 0.1; % Orifice diameter (m)\r\nD = 1; % Tank diameter (m)\r\nh = 2; % Depth in question (m)\r\nt_correct = 14.6440; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Sharp-edged orifice\r\nh0 = 5; % Initial depth (m)\r\nCd = 0.6; % Discharge coefficient\r\nDo = 0.2; % Orifice diameter (m)\r\nD = 2.5; % Tank diameter (m)\r\nh = 4:-1:1; % Depth in question (m)\r\nt_correct = [27.7579 59.2645 96.6372 145.3422]; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))\r\n\r\n%% External mouthpiece\r\nh0 = 3; % Initial depth (m)\r\nCd = 0.8; % Discharge coefficient\r\nDo = 0.1; % Orifice diameter (m)\r\nD = 1; % Tank diameter (m)\r\nh = 2; % Depth in question (m)\r\nt_correct = 17.9389; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Convergent mouthpiece\r\nh0 = 1; % Initial depth (m)\r\nCd = 1; % Discharge coefficient\r\nDo = 0.05; % Orifice diameter (m)\r\nD = 0.3; % Tank diameter (m)\r\nh = 0.1; % Depth in question (m)\r\nt_correct = 11.1146; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Re-entrant mouthpiece\r\nh0 = 4.5; % Initial depth (m)\r\nCd = 0.75; % Discharge coefficient\r\nDo = 0.2; % Orifice diameter (m)\r\nD = 5; % Tank diameter (m)\r\nh = [1.2 0.8 0.4]; % Depth in question (m)\r\nt_correct = [386.0058 461.6427 560.2147]; % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-01T12:15:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-28T00:41:34.000Z","updated_at":"2025-03-25T15:09:17.000Z","published_at":"2023-03-28T01:19:52.000Z","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 to compute the time to drain a cylindrical tank of 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 from an initial 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=\\\"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 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\\\"/\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. The outflow occurs through a small circular orifice of 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=\\\"Do\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the bottom of the tank, and the 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=\\\"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 can be computed 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=\\\"Q = Cd Ao sqrt(2 g h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = C_d A_o \\\\sqrt{2 g h}\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=\\\"Cd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a discharge 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=\\\"Ao\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the orifice, 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=\\\"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, which should be taken as 9.81 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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\",\"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,iVBORw0KGgoAAAANSUhEUgAAALwAAAAnCAYAAAC16CIrAAAHw0lEQVR4Xu2cR6stRRDH3/sAZlfiQgwLcaFgXKigYN4IKiqKPFCM4MaccGGOOyMKIoKKiiAo6kJBRRADioILA2/h0uwH0PrJ1KNuvw7VPTPnhumG4px7puO//l1dXd1zt2/rqSOwIAS2L2isfagdgW2d8J0Ei0KgE35R6u6D7YTvHFgUAp3wG0/dZ0uXrhc5Y+jae/J5i8g3G6+rxR7dLDkuEDlmyPmUfN4l8luxZDzDVfLzM41l/y/WCT8GvenLXiRV3iDymMjfIpeJXDg0c5J8fjJ9k7PV+KTUvK/IiyJ7DuOC+H+IHNZAerDROps73QnfDN0sBX+UWk8X+dnU/spA+lflE6VvhnSkdPIhkUsMsfeT75+JHCJytUitpQaHn0TuGAPAkgmPAvYKyFXCkjKHD5m+b7BSufpPlIdnRRSKi/O2yBcix5Y6uEGe48p8J/JO0J/75O/bRe6vJC64/ypylMgo126JhAe8y0VuFbnNaWkg450ilH1tmCjXyCc+6fOVk6aWk7T9schmsvCpMTIRsPy1Fh7f/SaRQ2vBC/MvjfAADtH3GYDwAI8b8bIIm0e7RLNsfy2CT4pvat2QsXqx5bV9T1+nbHeOuvDBMRS1lvrzwdA8PLZTSyH8wQIUVv1bkZMH0MGuRCIlNXljSlKLNae7AUlwZc4UaY1ujOXJVOXZo7wvcm1FhegO3x3ff7RRWQrhLb7qIngI/65kIjyYIrQqw1NXhY53ZdX6N1uEJjZWVqp7RcJNeQkXDW1Osn/phE9HC6x1z22ysFpYHzsp1PKXlKnP909YbybcmyK1EQ1vu6vKpxGaHdJgbWgVfNk/EaUZnTrh02TSiAIgX5wBXMOG5NNlF8t8QIV2YhEf2ie1huFYyUj/iJQiG/T3LzPpPNEord8TrcIHv1skjNqUIFKjkzIItjx59xh+SE4qD+F18LUzszSY9XrudWnUnaGfuU2Wtea5iVEzXpZ/9hq1p5I2AoXfi8+PS8b30EpCkBNErhBh080YmRzsGfSUlz6zKb90ICv13yPCxtOmc4bnsTFSHxOuZZXSg6bc+YMeSBExY9IeJMJvjPm5sN0Y4TUefLRkPk6EiAaVpTYaLDnecJFahRgw3t88FitXl5fwvw9jpy4v4Wvjy7F+oqwdIjYiRD4lW0oPPGeSQnJ7FYGQ3tNDQ/xOpAOLfr6IPfan75zqPitCDJ30ksGAfcRbIg+KfCpyoAiE1IhXzArznAkTrlLo4AiR0iRABzrZhi6t+VBdhsEHXRl2C0qkLDzgPTEAQAspy6UnakQQPOlfT6ZCnrHxaC/hbV+9hB/bNz1kwsDsDHC4Uv7mjk3KLcBtgHzhplAPbagO8nHcr8liQdiVyWQjIRoS1bKnyBfrHml/YxzBJdOzCiyvJg77mFilzSt1M+Fsf0Nq5MKc0ZUl59JoZTSS8qHIg2K88VEs0Nj0QUV7sbZqCR+SJKzT1jeG8BiPD0XUYobtsEQfLxILTSoxUyuM7kcgtTVOJSzsZEmNTQ2DbdtOlJgOPDixN8LC50KY6nbGPJDoKpIjvEYfQpB0AIDxg0g468cSeu7yJSVr+6rI0mUna+U8ipxjfKqr2vClBwvFoUT4KcfuvUpgAwtMuMcTBmEX5inC25Cc+n2hoiaNj87BgkSdHiVTdD1cmhYYrBWuPcH0YLEehNeYfWlvqEZXV0WMU/a6SIrwNvIQA1EnRG533qK8VZTxKJl+tERpSie3c4zPjmerEL7mKgFcfEOEkLAm3L/zRHYLx6YIT4OEqigYm2U8J9Wefm2mKI3dw3g3rethACzha8Oinsm/agvfcpVAw7FcTLNpN33ECG+XyNhmQIlQ6y+GbkKrtRvrK3qUTN/sxitnuXUlmPsSWQove70hFz6mPLol6cbXg8WqCV/jKmPdrRUHixtF7DnBmjs4McJbRdsZYg8dWpfuzRSlsf5hjkgarx87EVsNAOV008r33CUrIh8PGJJsRMIzlkdESjF6xgqfwvOKrLGKEd4u5fpcNxGAWbIiYxS3irIeJWs/dC+TitTYCE2t/zzlWO2eK7XSxE4tPVis0sLXXCVQwr8gX2L3bNQtX+PmxQivFgv/nauckF13wbU+4pRKnaouj5JtWwpcbFVTdyYVyZqqz6V67OtzmtceXnFoRQrj+B4sVkl4wowYVe+rjODP2GNXp1kpOLRa865CSHgbjrQgA96jIqPvI5c0N/Pz8AQZN+Q6kdw9cz2yBzid8Na9m+I6wRTDjkUrtN7Ufz6wK0Pq8Ia3rUixgy87YXIHY97x6UGT92akGhw7Pqub4qYV0Ihj0vBOkdh7id7Ob7R8KPfUSKf+lN++EuFVvRzx9UIXGyMSJ74AXbqJuEocUPZpIueK7C2CgfpIJCSQvhDDfSmbyI/vzJhieIEVp8HkwRqH5XnOfymovRVJHzxXCUIs0ckvItzr4bKd1c3rw/jXlPHcllylwnpby0WAPQap5m2oarQ64ash6wVmQEBD4S2h7qrudMJXwdUzz4SA9yrB6OY74UdD2CuYAAE2n1+KtL7d5e5CJ7wbqp5xJgRarhI0d6UTvhm6XnAiBHgji9cMa+9lNTXfCd8EWy80IQLE8se+tunuTie8G6qecSsg0Am/FbTYx+BGoBPeDVXPuBUQ+A9BRwdGsx0lHAAAAABJRU5ErkJggg==\" 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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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54735,"title":"Solve an ODE: concentrations predicted by the cells-in-series model","description":"One approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume . Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) is and the first-order decay coefficient (dimensions of time) is , the concentration in the th cell is given by\r\n\r\nWrite a function to compute the maximum concentration in the th cell and the time it occurs assuming that the concentration in the first cell (i.e., ) is at time and no contaminant enters the first cell from upstream.","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: 183.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.95px; transform-origin: 407px 91.95px; vertical-align: baseline; \"\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume \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: 237.25px 8px; transform-origin: 237.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) is \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: 173.742px 8px; transform-origin: 173.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the first-order decay coefficient (dimensions of time\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAmCAYAAADTGStiAAAAwUlEQVRYR2NkGCDAOED2MoxaTK2QFwYaFALEa4D4LTZDaRHUEUCLpgGxIBCL0MviVqBFR4F4K9SXdLMYFqr/Ry1GT2C0SFwgO4ZWUIOygxyRGfojUN1MLGrJ8jEoSxgTafE9oLosallMpJ14lZHl41GLSQ0BG6CGw1BNBkD6Ij0qCS+gJTpoFh0D8o/QqwAhGEq0KrlGLcYIgdGgJpgoqKVgNKipFZIEzRkNaoJBRC0Fo0FNrZAkaM5oUBMMImopAACNICMnaBvayAAAAABJRU5ErkJggg==\" alt=\"^{-1}\" style=\"width: 15px; height: 19px;\" width=\"15\" 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: 11.275px 8px; transform-origin: 11.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is \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: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C_n\" 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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in 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);\"\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: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth cell is given by\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=\"V dC_n/dt = Q C_{n-1} - Q C_n - kVC_n\" style=\"width: 170px; height: 38px;\" width=\"170\" height=\"38\"\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: 193.958px 8px; transform-origin: 193.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum concentration in 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);\"\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: 145.85px 8px; transform-origin: 145.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth cell and the time it occurs assuming that the concentration in the first cell (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 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: 11.275px 8px; transform-origin: 11.275px 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=\"C_in\" style=\"width: 21px; height: 20px;\" width=\"21\" 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: 24.8833px 8px; transform-origin: 24.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAkCAYAAADSO4eRAAACr0lEQVRoQ+2YuW4UQRCG8RMgME8A5FgyyAnEXCGBsUgsgWxDjEBAzC05NPAENikSCBIcGAIwBORAhByZQ+IB4P+lqqVmt7q7bGtn5aFHKvXsdG9319d1zYztqVePwFhl8Y9AhWGsocKoMPzgUC3jP7OM46LvBtqvuYTRVcs4CKWvQs5D7gmAObSfIdchnzwoXYRxBIquQn5AzhnFx3H/DnIIchbyoh9I12BYhReg7JM+hekya/LsANrvtj8Kg+a215k854Kj6LuGRe9DfkKOJmIEXYXW8VTcqLfPCAw1uxu7AAZdYx/kA+RY4jSW8PyyZx0lGDSrZ7IAaWaj8ShMwax5BvfP5fcjtFcS+5nH88fSN4N2RcelYDAaX4TclIFf0M7KfTFFjQiKugiX9+KFbsvGjQY0DwZB0JR4nZSWPvhe7k8FldX8HhzuDvuNp24adEbzhKfleRRGw51ybmIJuqmooOWfnVCQ/w4EucycL83hRWHwkPfrnDkY1uwG0lBAUW5up9drTPAgOImFMVGwKD2oMIx1TMj09AoSdY3gvocyzMI4gRXeJFZhLbIpfSEY9g8sX6OnMxQtg5MOzU1smspRDu6zlWHbySaNmJSKGbexfabVhhltUaW2swmr5GXZYzSA3sH4W6UAmixZtwCk7WzCkoD1EK9cFrIW1MiSqTpDJ80RLnFpO5twPxo3uP/DiQ1qPcIxU5Dey5oHw5obU9Q3WSRV65egtNlvayMv1tnEMHDQHgx9kVFypH0JEq0E21TeW0vjnecq6iJuueDBUFNj8ORb4ENI/3eBUStcWl8PlAFyUVxBX9AI4oJ1j1wApZvMQn5B7u4ii+gHRJc5DZmUjo9o30IGvnDlYJSod7a/9D2js4p7ilUYhkqFUWH43l8to1pGtYxiZqxuYhD9BQ0YjCXJTsMdAAAAAElFTkSuQmCC\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\" width=\"33.5\" 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: 171.133px 8px; transform-origin: 171.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and no contaminant enters the first cell from upstream.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Cm,tm] = CISmax(Cin,Q,V,k,n)\r\n% Cm = maximum concentration in the nth cell\r\n% tm = time at which the maximum concentration occurs in the nth cell\r\n% Cin = initial concentration in cell 1\r\n% Q = river discharge [L^3/T]\r\n% V = volume of a cell [L^3]\r\n% k = decay rate [1/T]\r\n% n = index of the cell\r\n\r\n Cm = Cin*exp(-n);\r\n tm = log(Cin/Cm);\r\nend","test_suite":"%%\r\nCin = 100; % mg/L\r\nV = 100; % m^3\r\nQ = 10; % m^3/s\r\nk = 0.01; % 1/s\r\nn = 4;\r\nCm_correct = 16.8325926; % mg/L\r\ntm_correct = 27.2727273; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 50; % mg/L\r\nV = 1125; % m^3\r\nQ = 25; % m^3/s\r\nk = 0.001; % 1/s\r\nn = [8 23];\r\nCm_correct = [5.4745741 1.6086642]; % mg/L\r\ntm_correct = [301.4354067 947.3684211]; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(all(abs(tm-tm_correct)\u003c1e-6) \u0026\u0026 all(abs(Cm-Cm_correct)\u003c1e-6))\r\n\r\n%%\r\nCin = 100*rand(); % mg/L\r\nV = 1000*rand(); % m^3\r\nQ = 70*rand(); % m^3/s\r\nk = 0.03; % 1/s\r\nn = 1;\r\nCm_correct = Cin; % mg/L\r\ntm_correct = 0; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 42; % mg/L\r\nV = 2560; % m^3\r\nQ = 180; % m^3/s\r\nk = 0.004; % 1/s\r\nn = 6;\r\nCm_correct = 5.5885481; % mg/L\r\ntm_correct = 67.2834315; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 8; % mg/L\r\nV = 3100; % m^3\r\nQ = 124; % m^3/s\r\nk = 0.006; % 1/s\r\nn = 9;\r\nCm_correct = 0.3650487; % mg/L\r\ntm_correct = 173.9130435; % s\r\n[Cm,tm] = CISmax(Cin,Q,V,k,n);\r\nassert(abs(tm-tm_correct)\u003c1e-6 \u0026\u0026 abs(Cm-Cm_correct)\u003c1e-6)\r\n\r\n%%\r\nCin = 100*rand(); % mg/L\r\nV = 531; % m^3\r\nQ = 6; % m^3/s\r\nk = 0; % 1/s\r\nn = [7 14];\r\nr_correct = 0.6844581; \r\nCm = CISmax(Cin,Q,V,k,n);\r\nassert(abs(Cm(2)/Cm(1)-r_correct)\u003c1e-6)\r\n\r\n%%\r\nfiletext = fileread('CISmax.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-11T04:58:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-11T04:52:21.000Z","updated_at":"2022-06-11T04:58:19.000Z","published_at":"2022-06-11T04:58:19.000Z","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\u003eOne approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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. Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) 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=\\\"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 and the first-order decay coefficient (dimensions 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=\\\"^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e^{-1}\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=\\\"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 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_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in 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=\\\"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\u003eth cell is given 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=\\\"V dC_n/dt = Q C_{n-1} - Q C_n - kVC_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\\\\frac{dC_n}{dt} = Q C_{n-1} – Q C_n – k V C_n\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 to compute the maximum concentration in 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=\\\"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\u003eth cell and the time it occurs assuming that the concentration in the first cell (i.e., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\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=\\\"C_in\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_{in}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at 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 = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and no contaminant enters the first cell from upstream.\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\"}]}"}],"term":"tag:\"ordinary differential equations\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"ordinary 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