{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","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":"2026-04-16T00:00:00.000Z","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":59147,"title":"Determine aquifer properties: steady pump test in a leaky confined aquifer","description":"Problem statement\r\nWrite a function to determine the hydraulic conductivity  of a leaky confined aquifer and the hydraulic conductivity  of the leaky confining layer given the pumping rate  and radius  of the well, the drawdowns  measured at distances  from the well, and the thicknesses  and  of the leaky confined aquifer and the leaking confining layer, respectively. \r\nBackground\r\nCody Problem 59002 dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in other pumping tests, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\r\nAn analytical solution for the drawdown can be determined by solving the equation\r\n\r\nwith the boundary conditions that the drawdown far from the well is zero (i.e., ) and the flow at the well is . Using Darcy’s law and the convention that flow to the well is positive, one finds\r\n\r\nThe governing equation is related to the one in Cody Problem 51783, and it is the polar coordinates version of the equation in Cody Problem 59002. \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: 819.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 409.55px; transform-origin: 407px 409.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.408px 8px; transform-origin: 171.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine 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: 179.325px 8px; transform-origin: 179.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a leaky confined aquifer and the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"18\" alt=\"K'\" style=\"width: 19px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the leaky confining layer given the pumping rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAAC30lEQVRYR+1XTUhVQRTWvW1qZZsWtTDUbBNJ7VwoiCIkVNCysFq2MDJciIiCLsSVP9i+BImoTRkuhMJq0SaojaAgtUoI2tf3wRw4d+7MvWce78kD78DHfe/dmTnf+c6Zc+a1tjTpaG1SXi0VsdTIVIqdeMVuQYEbwCWgQ6nxDp9fAiupCvnzU3OMhBaBdmADeAaQDEc/sOSI/sDzOnBUK0ErsdMwsAzcBP4C94AXAaOcdwC0ASR3sZHEaOyDU4J2bkdICYdVfBhzX57iOVcLOYtiu9j4qtt8Dc/7JYYY0rduzi88zzaCmPaeRroMeaOJkdMFYC+VXJFivoGyEIrtWtdluBcR0yG0qsXNHwA8KDKsDpmI+V4vYNVjYzh0+LnkjCH8ua1jirEUsDTISMmT71gkRTdFaZNiPzGLRZQjpViytPxWFlh8B4xKlxLzN7eUCNm0LvnFzUKh9PPrIeZZe58O4yesG/Ty6wq+zwD7QA/ALsH9c63LQsx6qsrKhLzXB4mFuBvI1ccQMT+UVmK6vLDBs+Hrwbw9BZxTClHBz0AuXWKnUie/JZQT2HzWsQiFkCSfA6HG/s+ty3CJEZvH5HG3IOS9VkK85m80PAT4LUj2Cx0kUToTmRgxhvMbICUjViSZN5sArzl0IJjI+F2MFxHLFPGilkQlXjlyLJQjwBcn1XkXOhZhvnsEhO5noqyFWIZ02bWHyj0BhgF9heZl8SPAazSVKrup1p2YeCw5Yj2hXEdVJddYFhj2olAmKUYD0jfZXiZVOIV06MlTOAXIQahb8ovHb7wQCgnm1WvgK7CllKEqdwFW/FFA/1GhaiwlvZ4nUi4yByyWY/R4HTgE/riN5HpdpBTf0fgdRVbmS23UNqXU5Jp9rPLzXv8+EDYS7gPY5zoBlgkO1q8dYBuInc5YS7qGNZd9R8pOZZk6qe9Jbhpg85bBf1K5/wTHTczsSEXMLJWbWClWKZaqQOr8/+6UrClQAbvIAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5667px 8px; transform-origin: 36.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rw\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.35px 8px; transform-origin: 86.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the well, the drawdowns \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.2917px 8px; transform-origin: 74.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e measured at distances \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the well, and the thicknesses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"18\" alt=\"b'\" style=\"width: 15px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.767px 8px; transform-origin: 229.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the leaky confined aquifer and the leaking confining layer, respectively. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59002\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59002\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: 310.817px 8px; transform-origin: 310.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eother pumping tests\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: 215.092px 8px; transform-origin: 215.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 254.808px 8px; transform-origin: 254.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn analytical solution for the drawdown can be determined by solving the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136.5\" height=\"36.5\" alt=\"d2s/dr2 + (1/r)ds/dr - K's/Kbb' = 0\" style=\"width: 136.5px; height: 36.5px;\"\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: 239.6px 8px; transform-origin: 239.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith the boundary conditions that the drawdown far from the well is zero (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"60.5\" height=\"18.5\" alt=\"s(inf) = 0\" style=\"width: 60.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and the flow at the well is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law and the convention that flow to the well is positive, one finds\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"141.5\" height=\"35\" alt=\"Q0 = -2pi rw b K (ds/dr)|_{r=rw}\" style=\"width: 141.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.267px 8px; transform-origin: 146.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe governing equation is related to the one in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51783\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51783\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: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and it is the polar coordinates version of the equation in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59002\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59002\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 370.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 185.35px; text-align: left; transform-origin: 384px 185.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"504\" height=\"365\" style=\"vertical-align: baseline;width: 504px;height: 365px\" 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\" alt=\"Steady pump test in a leaky confined aquifer\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp)\r\n% K = hydraulic conductivity of aquifer; Kp = hydraulic conductivity of confining layer\r\n% Other variables are defined in the test suite\r\n \r\n   K = Q0*log(r(1)/r(2))/(2*pi*b*(s(2)-s(1));\r\n   Kp = K*bp/b;\r\n   \r\nend","test_suite":"%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.4 0.25];             %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 93.54;\r\nKp_correct = 1.82e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.4 0.25];             %  Observed drawdown (m)\r\nQ0 = 2000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 187.07;\r\nKp_correct = 3.64e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.6 0.4];              %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 71.32;\r\nKp_correct = 7.00e-3;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.6 0.4];              %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 3;                     %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 71.32;\r\nKp_correct = 1.40e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [100 240];              %  Distances from the well (m)\r\ns = [4.0 2.8];              %  Observed drawdown (m)\r\nQ0 = 3500;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 35;                     %  Thickness of the confined aquifer (m)\r\nbp = 2.3;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 11.43;\r\nKp_correct = 3.74e-4;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [100 240];              %  Distances from the well (m)\r\ns = [10 8];                 %  Observed drawdown (m)\r\nQ0 = 3500;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 35;                     %  Thickness of the confined aquifer (m)\r\nbp = 2.3;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 6.959;\r\nKp_correct = 1.126e-5;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('steadyPumpTestLeakyConfined.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-04T15:23:23.000Z","updated_at":"2026-02-12T15:06:18.000Z","published_at":"2023-11-04T15:23:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine 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 leaky confined aquifer and 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\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the leaky confining layer given the pumping rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the well, the drawdowns \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e measured at distances \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the well, and the thicknesses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the leaky confined aquifer and the leaking confining layer, respectively. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59002\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59002\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother pumping tests\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\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\u003eAn analytical solution for the drawdown can be determined by solving the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d2s/dr2 + (1/r)ds/dr - K's/Kbb' = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2s}{dr^2}+\\\\frac{1}{r}\\\\frac{ds}{dr}-\\\\frac{K\\\\prime s}{\\nKbb\\\\prime} = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith the boundary conditions that the drawdown far from the well is zero (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=\\\"s(inf) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and the flow at the well is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law and the convention that flow to the well is positive, one finds\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=\\\"Q0 = -2pi rw b K (ds/dr)|_{r=rw}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0 = -2\\\\pi r_wbK\\\\frac{ds}{dr}|_{r=r_w}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe governing equation is related to the one in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51783\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51783\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and it is the polar coordinates version of the equation in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59002\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59002\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"365\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","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: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\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: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZkAAABQCAYAAADLNQgGAAAZDklEQVR4Xu2d++t3S1XHj3+AVOZPBnHoAgpGkWkhFSiYURCB2gUlDiSVBUJ3byWhZVeKA3ZDoR/UivKHpHtQkCFmF4yKglPxUBIEVlZ/QK3XOZ93zzrjzN5r9n3vz9qwOM/5fvaeWbNmzazrrHnGI/kkBZICSYGkQFJgJQo8Y6V2s9mkQFIgKZAUSAo8kkImmSApkBRICiQFVqNACpnVSJsNJwWSAkmBpEAKmeSBpEBSICmQFFiNAilkViNtNpwU2I0Cn249v83gNw1+ezcssuOzUOBbDdHPNHjzGginkFmDqtlmUmA/CiBgftfgzwy+fT80sucTUWBVnkkhcyJOSFSTAiMU0GbBay9MaiUFHAU+3/79TIN/NfinCmXgnScMfmVp5SSFTPJhUuA6FMB64flKg3+/zrByJDMo8A327c8afJpr40fs3++uCBsE0R8tLWhSyMyYvfw0KXAgCrCRsKG8xOCvDoRXorIfBb7Kun7c4BU3nuD/33MTOD9n/625U+GhXzb4NoNfWAL1FDJLUDHbSArsSwECtz9v8I03LXRfbOq9oyX/mMGrDdLKmj5DP2yf/pfBjweawLJ9baF0IGh+y+A/DT63MRf08SaDLzP4k0A/g6+kkJlLwfw+KbAvBeTi+H1DAy30iM9VBYziHEM0Lzfpz7KXn9P4ILqhf599/6jBWGIH79WE0f/e+n92Q8gQn/lTg2cNCKIwn6WQCZPqUC+ymZByWD74WaNaIhrN84sG0JAWMZEPRa1rI4O2+tlLbAYrkYmN+P0GX2FQCziv1O0mzTK2zzD4IYMvcj1iJSAA/s6gdF0iZJ5bfIPrinXX4+bEPfrAIGLRlMRAyPyjwecMUOlL7bcPGvyqwSzlJYXMJry4SicwKwzgmbulmZQIsDg+WiyK19j/55mKVaZqtUblJvv+iZvNaojdGla227tum+ja/e3VvuIY6v8LAgIDKwP34dRNXNlgX2NtRC0g8NPaJ/g/di6GTLOvN5jlNkshsxdbLtOvfKdqLcoMaL9eOB11k1qGStdsRZvMf9jwhjTSPUfPRvotB8ZvKdr4dfh71ijZfWPPEnEPhNvbDb7YIOrBYE7eYNCKx3i8UWSxeMasnsGxppAZY4Vj//4Phh6uEj1fbf8Ys0akQfmRRTSvY1Pi/rDDXfI6g6MG+yUEcRuhEV/58UpbNCtLbk7iHq0HqwNrdSj2gpLxowYRt5nmpMdrMZvPUsicl/WlZeD/VQ78GIPLVEYzkXDi+yFGPy+Frov5IhrmyuSRxnx13mLj/rijZURh0zetNGKak6uRtToUE8EiwqUVsWYR9pyD6Ym7zua1FDIrr7QVm5cfGJ8uTMYz5mfVYT3+ixbMM9UnvOLQsukRCki7PLKbEyv7z0c2yCtMtI/HRN1K+qZlhfp465ilqgD9mBcjmpFWmxPFZsZwqc5nCpnzsjkTT1zl9QbkvY8JDGmWHNYj20eWzCTGOS/ZTo+5XB5Yr9FEj60HLYt5zLKu4aW04DKYzbifZ9Aqi7L1GNWfBD7/P2SZePz0TTl/jPGVBu8wkHcC4fHfBv9j0Mo+I1tsSMFEqH2tQWkRIczIKB2L5+hsTVSIPm0uUsjsxZrz+8UXi6B5nwGphjxojrWaVVr0aL6/bgCz6EHYXC21dD51j9uCMsqiG9oeIxGO0UQUNrFvMiDN2W+uii/60igE1o90oJN1KJyjChtWHlAmCLCeP9XgRa5NxsvD2m0JGTwTCIpawoGSA0p3GgLtvY1vajyj+O+YxfRJ36aQ2WMJzu9TJjJM/REDCY2WpiE3GQJIGwBYTNJM5qOfLcyggILM3Yt9Rp+9nypzKqrAoASxgcr/T39y46oUCkIVF++RDp2WRwEilmXEytNhyTH3t+aFqtsvNyj3c+0TKJ+ltYIge6NBND6jOe12r6eQ6V0+x3hfGWJaxGJKsCsZXe9Kq5R/lXePrA0fg9LHwkIb1NGTNVqbXoSa+paNkZIoBKpxCx/R2vYKWzR1Wd+0EgQkGKBVVJGQ+83v51gq7zTAMmo9PRahF6gRYfr/faaQibD98d7xlgnYeZPdM0Dt4JV/N8rEx6PAfWI0WZvcmFxzhIxPsUfQvNVgLC2/HF6k3MsYSTitPxar0DhpK5qEwTe4rlrZYP7MTXR/LhXJsbFN/V0us6hb8Ml+ooOYilR+tzwFlP7oTWnP7BIcSoHEXyyGnmLeLz+CbHEqBeQq61rkUzub8d0cIeM1+W7XzA1nvx6mDiOSiuw9CJH4UyR1WXMctYwY31ZCRhZT17zMETJsWGR7+BpaZCp82AD/qjIlCDSPaQRTGeEev1Omh7dCakKmdqLYa4k9THyPdD7amH28Ihrr2GsMc4QMOPfGJMpxwvsvmDl4DkAOuehKhS2yl9bWrkfTn7mJWkZeyEQE4xyy+ArO4fNPEcKURPhm+wOlImB0AscE4h7cXtLf9U0r22nOQO/9W90b4stCeOEBc37IgIyzMnA4xby/d3ofZfw6W3GGZI05QkYVgNlfjqwI+fMxUTxrsRPPX9rE+VuPwFCctXc/7+VtLwQjltuT7fcg5dMIYfTHDGqF2XzeeDQ7onew9/x+Lf3RCxmC+aSC8pR+317z/p7pfLSxT3JV7DSIMjGlBw2fmMJ3XUHmno5mvuvXXGSfi7jKNMe9iR0IdbLFwtbFjLErLhO2tKJCxgsO/HHfYTDkApMmM+Uw1ozxX/5Tf97F1yryGpDKzJSaRvlOpEDe5Ql6ogF2L+4dxyYtP6zt3nAl8+p7bwqszn4dNTnFZ5ZFhIzc10MWiua4K+Zh9Gqdu1mDBaQEhHGMCJlSwETuFpjKZGsQ5UptttIffbCU8daY3methBnkSsQ78VgmuSl2HK/iR2Ft13CVAiXLpYzLKCU3sv9sMXQfI8OzM1QJWetz6MiAb0/KOcr6WGxIvNFD6zn0kQUXtrbGhEx5cC9aUloEO6qpO4fIe37buqDKM2hr8qdUit1zrNn3Qwp4JeIsawp+GyruyOZIfPefDT5m8AEDfzeKPy9DbT4UoynpzGvyUemm/knrrEwWYA+lTAxHB4b2Tx/jIR71PQYkUI0dltR3PTGcOTTp5sUhIVNmT/SarTrFO2dA+e1DCkiQtJIppPnV5skLIVrsncszz4O/AZQN7Q8MvKuXRVq7ZZR3qaZALSn/8Pda6XoWHw9xSjZQNhRuHlU7cw4T+s1sTDE8ylxJQW0JRT8mcC5d617Brf1+pHGq1hgKHrzxwOBTDIiNcpA0UgqnPB80Vn1Z48fTRCWPWjmpNWjk5ULIHTrEsD4TKbPE1piueJu+KiuMXLsPQrXMyrsn2Px++sbs6jHiQ45jd8w3VY6ExYpQIQlCGZEUFfUH/Hy8itF414M/ZV/Snd++zgBNm7bZKEnjZ+GrnpWoM8edIVdnNIvpCDOiQp6t0iXQjt84kf54MR/gz/dvM4D3a78fYYzCAVxfZvDlN3z19z+0f3CEI6JgQA9uyuSJjleusq3PTUmhDcXcW0Km1HxDjS0w6/Rbao5TmiWFt+dK0il9bPVNiyalRo1GHtXShfuV6OTnQy4Ez7c6nIpmieB5hYEvONgK5LbiYJqXV1k7umUUIYAwe4sBLqAXu40D/KauIyl8ZxIyjFeB/Kibfas1dZV+sH5eahC5iXPJMatqSEhxagmZ0pTd6vBXGcCeSpipi3lqf/ndcSjA5o/lXSuk6C2WWvKD4lZYi1yJgKB4wmDo5kHPszW3iP+ddqdk9QmvM1qgCEg0+sjNjcfhouNjguVDXTf4tFWdea1RSOkJJRC1hIx3lW15+GspS4bFvjXh15rQbLePAnIt1VwIPkuLDb8svOj9zfDQJwxQsNAUWyn7Xoi0lBufoTnFtSH3REhz7CPX6m/LgvxO6+kq3oXViTbSgWj6U/beHldbd1nWLSHjD+1lPGZvlsr+eyigswZo/cRHykd+b/5ey8jpteIjQsZbUFOskSWEzBIKXCvpYWx+FG8YuhNlrI38/SEFUFr+eCcBAxZSmkLu24iQyXLwyd5noYCPJcK3D0YQrwVlfVkTrHgyhIYCtxEh4y2okIvB4e2/nZMVuIQruhd3T36dcxk7yH0WXtsLT5SgvzHwiStb49KV7ZhCZuvpyf7WpIDfSOecG+g5uBoRMoxZ1kjvRu3bD6WMNgi8hCWz9+a2Ju9k23EKLCJk5HKg2y3dZUssBHC+atZUnA3u802/IU+JfUA1xWXge2WNDW3uvUKmN66ylJC5T47IUa9BgUWEjA9UjpVMKAcx5xDmEiY9+GR22Rqsdfw2feA+4uYl1bkMnJLJBXDS+qO3IQ+tgYiQ8W68XpdXCpnj8929YbiIkCk3+6iZzqJ9u8HUvPilLJlodhnBs+feG4dcYLwE9EkFrj3K4VcacivLkDMcnPR/s2uExfOGW9tkk0Uq7UaEjAL/vQobqJ1FyORaOufC+jxD+986UV9EyNCnt2ZwHQylcfI+HXOfzFQB0znORV7PhbEIGTdvZEjI+AVQO3QJsqon5c+syArybjafBMB3tThPRMjMqUqeQmZz9rqrDncVMlDa3+3Qum9b1gtxnFcb5C2Y2/Po0SrUbk+Bhz36k/36q88008V6pdsKFxm8W56e9pt8Tdnyv9eEmqoPhNI9K4Q7i5DZc86z720psJglI7QlRDiUxoMbgsKBLGYCoyy8vQ4FbUva4/YmK7K8pOy4GK+LGbz5XoOXV7opL9xTjazX2bu1oLxPIaY5hIUvv16e+KdPndH5Qvs3dc1o9903IdY78hQyvRTL99emwOJCRggTL3mOAfWYeEhn/HuDSPG3tQd9z+2rEOFvGBHQzu/hGXKX+fHjAvsSAyri8s3fGpSnzlkw/vHxvFaMkLZUgr10l1E/jmKJ9LlEBeYUMvfA0eca42pC5lxkuB9sVYTwZ2zIP3gnw44KmS3IEYnJzMEjhcwc6uW3a1AghcwaVD1wm8TC3mKwRw2jA5NlM9TWFjIMpKu0+mYjP2dHWLe4NMdK8DOv8trURuqt2dIa9u9PdZMembo6rByqa3mWC5COTPA9cVO8LGMx+83ClkKm9yDnflQ5Zs9yLXPXT6QiBO9/l8Gb3HBapYb8zZbErYcqdx+TOnGsFimQGe8u39yTAmnF7En9p/reQsh03d+xP0kOi4HPlo0ImXJ++f/WtSc68tFKmz8sUSYglkJmAtHO+AmaE4z9rDMifyGcvX+aumRrFIDsur/jQrRdcijldc5RIeO/a6Wh+6rE93CMo+t+o3SXTWNjGO/DBnveWYMV84sGvZdBgTv+5DVjOAhATtO3HhVaHKrw4H3e02Zp3a/AnVRlrg8uHy7pWtIX36U5rjvsU7aug7a4G3XVQ1TI+Lu1SnelzqcpTT2yFoln8PhKE2cjatfVEylk+qdX7pEp94L091b/QlZM7y2L0rp7KwFPwZtNGA3Pn1VpafplrbzX23d7ljKfMt41v9G8hQKtayJywrZ1OJebUn/H4IO3MUSFjL9by5fXQnC9ywD32WuC/Kq4zdTirUcgvz83Fio3lkKmf9pkKm6xUbewm2LF+OKRW+FelnipJSj4E/q164v7Z+h6X/igcq7ZvvnFcniBAW6s53UKGX/ZnL86Wy60nlp0fi082/A4a2UUH4MMCepk2D6G9f7ZvbRKJvkDBj1WTFmDaysh4wOtrdP0uCOoHLGnZdjHBdu/nWdlptFcQkLB+t4NsrxXiHjbOw1wj0WqfIM1CsJ333ic/2ffwM3NM5ZGPW3U637VrfCkkIlPiE9/1Fd7aCRsyvj8I/5f4clmr9gB7quthEzL1QBeU9wNWJFvNbhHV5poeWZXS3y1zX9T65USQIo/9goZeS3ABqHCLakk2rzRQBUfhjBVzJHqD0qDxlpn/fL0rOH5FFmmBQnecC2+FDJxwhM3eKEBOfaq4xbySca7GH1zihWj+A3WgmIkWwgZv6C9q4FBomG+x4DU3LHrjUUUxW1aKaSjxDv5C10ZPScf6xLoo4x9wgD+19MjZMqadWojciV3ib93u229ZyxBS9+GEiHCnocUMrEpUDwDBuF0vYLZW2uVTPBfGEQzU9CkKGCqwOSWqbDe1SCtxxejjAo6n8Gz5S2tMc7Y7q1uDXI71A7Xk0otldeO9AiZ8nAlCpGUy/AGe6OM5q5Utg5HuABCsqjDl++lkAlQ1V7xWlHkIqtIq1oI0dP6WiA9mrxuecRlwNMrZMZKa2ictXRj72rgplJSvpWNE3E3IFxeafAOA6xHHrka6A9/9lmDpxH+KN/x2nCu2zYFvUJYFkPtETI+4xFX2fsMlJmGsMAzEC0OTKIO6zaqWE3hjy2+8clD4VBBMuv41Hh3E0zlNZywX9J147V5/hy1hhAQ9C+BMYY5wvBVBv6yuaiQYUN7/LYwxvrh9zIIWroa0PwopY82+JhBufhrfUjAqVy++nlg/6C68ZrnfCJj3vqd7tTRrRE8QH/KVPw1w6UW7+gRMhIMfo36MzNRgeGv3j77tfBKfOryKKSQGV4ZysqCoeSi8ozam2GmA3xo52jzZKlEJqzXitH7ZYphRMhIiCJAsbLQwBgni47nRQZYFvyuhyu3veDwWren8BShfCVXw9x9WNl6ve6auf2e5Xt4BWWGumG159Hb7/ymO3/4d5nl5TV2fpf3oPx7JIXXK6WR949Ma/Ffl7BMITM8pbrzvSzd4rOmwmajdYXQkounJy0V050nYsVIMP6EvV9mwIwJGXD6JQP5ssVUPliJNcIzlEJdXt2Na0FP2Jd7+0ButykC6sgLdgpu2rB6lZspfZ3xG29p9OBfbv5DRxVK3iYZaOjxNc2irvEe3Ld611vSPS77R1LItKdIZm5NantTek62SKRciPCITqzSlctrhBnpmJBBU/uYAYJQ/eJ/lpDVJjfmKihdDZSYUTmPiOWmWbmSq2GJzWDyQl+i8xO0AX8OlTN61H7H0uHxV3KXJYD8+a7SalQyjeKEY0qTiptGz9Uclcxa+z3r98mxpJBpTymMRnptzfTWPfF8HY2p1HrypvRQdVe+jVgxih+1rIwxIeNxlJvKLw4tvqExe8FAe4yLQP0TBlqYUXP7Sq6GpTYPacZZ9r+fotGYjPdU1IRIWcmizGITZt69pjXD3/asedhPtae+iKz9atspZOok9/XJ2CDL56X2B6Uxz/WPS+uvaTrasCO+XGlY1Gj6ywYnSTiijRAc5WkF0aWByVLzWvSQi7Dlaij/3lqYHnVtqN6amrpIrvKdeDNdZv0zGhEy/h16qPF6eTC7pTR5nkfZeqYBFn3Ny9A/mu2+0NqflIKdQqY+UWz8bMT+IJd/c26GWaut0pphk0V4RJiyXBxRFqy5vjS+Wr2msdiIdzWUgtO70SLCeUgAR8d3xfdElzFXzRXHPmdMESHjz3cNuYb8e62UZq0F2nmtwfsNIsrVnDGu8a2E5SSXXwqZT54SEXTIepiTYVb26LUi7wKRFRON+QyVzVefsmR8/SSV3fd41dxqCsCPuWlkAdFeuQmWBQeHzhrUXA1rLKAztukzACMKyBnHuAbOY0KG36kLKLcuwuMlBqV7yx8QFp4oX6wN/65PRGDNPWYQSd9fY+xz2pRSE40LP62vFDJPJ702fFxOLSuGL8pzID0ZZrXJlo/XWw49VkyUgSIxGb8QJST8hu//hsvQn0eIuBqiZw1KVwNnhM7qz47OT897sxZ+T0cXetcrYmWwfyhpwLuUx5IL/LvwK2vkzIeHpdBMsmLgnRQyT19BMoEjMZCh4o+969ILLfy75O1/3CBqxUT7GxMyShxAk/M+f+8eJID5EQPcbGWxSh8QbbkaSkHUorVcDcIDoUOhwTMWFYzOT897sxd/T2f57t1SYLYyk0LmIe9IW4+m6Hm3UDRbaohTfT49pcBJLljaFTIkZMozBt7V5YWHxlCLzfhSMkMxF/9ei96iL+38tcFjK9Dj7DuH5mxpZeTsdEn8l6GAFJkxF/lgbylkniKP98VGqqyW2jgbJaf3o7WMapNSpv6usXEMCRkflC9N4/Kkc+2ypvIOdWjiS9pozIwTd6SKDfJ3+vsBA1+LzFuKrbaWWUrnbUXzMpaMcd4RJuZ7UUCHuul/VrJCCpmnsrcoxFg+H7I/lEG6seB67ZseJvHZKGMniXva1bvyJ9eC/YztZQb/YlC7rwXB+mKDWsozlk7r8TQZeo/v/bskCTy/0d+UsV/1G1mZc85rXZU2Oa7pFFDoYLaym0Jm+iSs8aUspExNXYO6120T9yOWYU9l4OtSI0c2lwL+nGD0WpFmnylk5k7H8t9nBtXyNL16izqIS0LG0nG8q9Mux/d0CshNRqbrIt6UFDLJYkmBa1BgUe3zGiTJUUyggMppDRXA7Wo2hUwXufLlpMChKaBsoIzPHHqaDoscGa7wUO0A6mSkU8hMJl1+mBQ4JAUkaDKud8jpOSxSOiO3qIBhtClkDjvniVhSYDIFVtswJmOUHx6ZAqvySwqZI0994pYUmE4BkgF45pzdmt57fnkmCsArlL7x59QWwz+FzGKkzIaSAkmBpEBSoKRACpnkiaRAUiApkBRYjQL/Bz3CXatp2ptEAAAAAElFTkSuQmCC\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \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: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, 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);\"\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: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; 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: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \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: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, 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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; 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 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 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 mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\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=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 is the discharge or volumetric flow rate, 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=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\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\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\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=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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cVclhqVyVyaTjWZhA6ElwhZl8jSOj8B7pIq/3FjNZmPlFIGgkZ2F7ru2DkuKAuG6eS0C8Y5aQDriUe2QEz9pnGOumGscMHUUbbFXashPyQMnJRAwwEo5P6IkpyTqA3nAVdhbfj4ghfu8E4hZnAxZEAg0zdLG4Vvur162MgIgEP9ejnYlhgmB0Dpk7uDw3dwevCwkEGcXBVKHlRM/lQgEF2BIS8LLtRr74yrRSwTC6oIw4AiyVXPnyCpAGGZa2qmXfncJhKuCDbujJzUTAiYEQhtSQMSNy3hgSbymy96Z8DpcshR15nwa6Mk+VGHoDpRTXWDhvG1C7yXyF2Gto6thI+YIgpau5OwjQJj1JVRhHme7SK5EEEq/O4FwAnG4yfaAFTIhEBSD8za/JwUofZ/6AXE7VJVgBwHbFUh0Yo/Wp2qiwWuv8Q6uqU4RAsaDegt3HDwqoeZ0xJIg8wiyVsHxcjO4Z0+RBwyghyXQgDJFmmmo2eo7YkkMLPPShrcx6VaJQGiD1R4/EHPZQJTqZYGhlQrDoixrp4Ex+CsS3i1h5F6UteuxZv6Ye14uYQ6VlgmB0CJuLET3SKg5e78mqJ73JQI8HZBb3BgHJPGXJECCAMNBtHfp5lASTKaPz2s6z4q1fUiGviKRoBOE7QturHwq02G4qORIEeoMx2FnkMphwvrwhB1gAynTl3SBkD4tgQ658LteILREE+/3kE1rAoGFDBd/oc+jT+CBvxu47of7bcvHikDw+oDnpHAWiy8Wi+clzK2aJpbA/A8lwIC9JU8t7TziOtRTPxD26xKw0bN8TAgEDchgTwALf4vOalnJOdMq2WHgymQsPrwvJFaWLdhhYMf3UQm5EylsZ9QBZeYtiiV8eUKBvhPQ6bY4sPVtkKhTzRFQxONuOWVHQglO1TGnEpjB76WjrrpvYRJJPTnjz5Yi5cYD8MQChMu0Yg/KADVX7Ogux1FtWSwJRG7scixY7u6sCARJMQiP9ltS6jOoEySFlCiiTUmc5ujDsTal9O/BhrkC7QRJISSGIHdw+gbj/nsa0qjtX2vEG60f2hB2apa3YZsQiDXA3FKeaFg0Dr0womzowPdLCMkUF1PEwe69tLtdqp40hJ1DxA58ILnAc7eE3G5+qfpa5UPbhtzxZSxmcJFrOXB1+VGGn5Ogb7NEeWI331KShPfpVbTmGLMVXkulY0kglioz88GkjMdCcqBVRZTkUDIBokavl8wb0qA/kkBJQ62PFGuMQF7Qh2vHDDDD8WcQBqrP2ddjflusyzt3elb1g6rWcs1xAmHU8nqgphYTrVMfvarYqNhXksGAw5Xsc5wSoFgaRAJi/KNIqThJpWwkUO97Z8JUN54eyPg+RQS1v5bXS7wW0fAcfW6uNPdMICwx0f0iNi9ReoY8Yw7g9O9L+XehxOPWynmCdQyJgnZu16MGs2yHkbQs60ciUottqdxOIEoIVf6u3TjH3BzXGORVZjVrNEtdGXY6d0igKJST0VIT0axATYlzQY7VCVKdDy1EmLTdQOpmPJZ1i+TVuq1ol7KkYzvrOlikVyKW2ig0doeR9ni7lPoCu+QPSqiRjGk1TewkGcu/pH8ii3ZjGnPUD/MwgoU9hO5fVf2j5ATHErw9paUHWuhpkAsJdoV7EOFjB/A9Bh0M4k+Iy2g4SCnNkQgET2/AwRYMvlhXtPlDEmJqrDn6tTZkDgksyOsjEmDs2nOHxxzlnTtNLRE885wVEohwktc4hQSi9O4cbUiJXsxhXSw/bkpS7vM5L1u515+jzrk056hfK8a58jWPM6vBSEtS6PluknCzhCUtfC07gh5o4VXmtEiHbi6mk7Ysh2VaaJ9RNUNIGLDI4TnSSQRMUNjlot2hqqBKANIXa+v8XPumCOzeyKtVH26e2Kwy3lg6JRLQQiCWUANgwcS8UzNH6LKnNiV7JhBz1Y+qHYv2bB5nowQCHfonJMBCFpMuREs8zoUdUs5Zz8bG5gvF0WJAio95fhn1POv15mhruEaFGuMWCdqye6tt2VouEMTbJVidYmjNH/G1oZsmsFRrgOCczS+LXjjnMAzuaac13gkJRCgd3RKB4GmlGilZjft87SF5bxKIuevXQtRy/Zb9p1pVOEogUBhtFPI6+YwjfWRFe7SY1YZGYHWflQDdNyYuiLEtj3itMQl5nttGINRjQ21ClcVedb+jiDcbd41muNH39SKKIoa7zhyB0MQU71bpuAdwoGi9dNkcstB9PrWT1n1gb+Ng7vrRHmp0PW82Vh7NEI3PThtKGyhu2tOOQVv6om6o09HOHw/MCf7qAghoAouJEqoyeG88M3nV4/JINjc93Yl2Ong3XEhzBEIvYtU7zJ4CTu+wLCWionfnocpYZ68Ni/ck2V6ifrVYl5qTBKIaXwsCEXO8Q/HVEh21BErL7yFL57spS/iWtD2uI1BCICSwjJ/yA1FK70i/84bgGpH4keod1iVUccHREu1zUgRCL2JIL3dXjhV2XIxKa4z2ZZJTD2ufO0uU3wqHJepHclUj7cnVi5v+6jFWatwSiJzwQp0UK1TNZEoZLfS77qSoEwYnn7PvfBZqglNnEzqGwqJJm6K9jSXrhuSCdFYbJI2n7ifY3NA9dIxAYDMHzDiXVS8Ogw1YSyD0kXmU83OJfO9TY2FPUu0l6kf1zoghpd68VBORUQJBNqwnNxTkmamxR9Mf7MPNr2vxIFgujAXp3W1vhjvNlfcXVkdAE1h6Efz0VKo92hNZAkoRvI/DC1RBDN4uAWQC7q0hpcJDwon+ogkoFuf3SVjK2VgtgdAnjrCOwF17+FyXL6BKxmMh1S65M6/pt7VG5EvUjwRihBxqG5PaY7fXRhf4mOMdflfNYmpaa4E4+pZKDkR05i9OAxTfjTC8BargWewcgZDAYveifUKcefetd92j89bOu8kNxef18zwRhwiQTLxXwlrH6WsIhDYKzREDbf8wskgSuPA0S09/qBmLS9XPgkA0n8AAaKMDkRMeDGW+JAFXtWKgv0rCUky3p/Fj7+hOqjtz+P3ZjtBZ4evp5BEILewppg2/LxmlHRVnTfD3tjlZqk1yRpRLlYH51BCI2rs59HXw2uajt04WEoiaC+Es6geJ/lsk5PJrOfGSwoyqlqYTLiMEQhtKwlUpns9I2OLNjDUdTeuqQhD1zvDsuugaLD1OOwIpAouUQtucOe43aS/x8m9wHLokMI79lggEVU45cbgub8owUksL9jb3WtSP5CAnoWE+I8SaY6vJQHWEQOzVUDI17dHKG7+HBpM5y+flp1HP8YgIaAIbTpS8ARW67lj/PCIesTqRSNWIj8+Cia7nlghEzcmAGu+MlGTs0QbIon6UQEAllZLqk6z1rudautdkoNqbITotJ7wR1rOVQR7qxGKs2XXRW2mtY5ZDG1vFTvzoyeiM3ijR6iTyWEzgG8OfqwhsiUBQ9ZaTFpUWWD0vN+2MN9Ixlqof1iYQjV7JJKUczQbKvQRCnytuYiwbadiwGLqhUyCW/NCHaYLV4U4QPC+TABuRvap3NtpshylWDYENz/KXxPi8nwYgvWQKvEl1z8BRUujHqm9sxdJtnLXtzr4D1/UwJL9NAu454n066K96LgNZgLFmeF8MxOJPS0jdFJkjCLq/l1QXSIfPnfJPzc2ftViMxLOoH9cRjb8uE49fljDK1YPCgNKcckMavQQCC65+noh0nhHgl35Xe//LNYSOl2NrZHRgzbgJE0eQzmr8tnRb7jE/PfHn+pWOlxPp8tpg2PLguNmjEponh40CSTXGyIS50aoNF6t2fkplhMUKuGJT+KCEByTAEyokXrgQ6y4JH5k+68sEIT1Dv8X9R5pEoL9i7stJi6h713ZnWBSxq4bBZK6dGQ/E5gMSPiwBhAXz71ae3vrxmC6Pr6bWakrlejfy2v9Dcxq9BGIrjWNRDm28hvQwEDBYwtsr0aDonDxnjbjo9O+OxMUuCeEVUwHxv4X1sEV9PY1tIYBdyscl0L4BxCB2iklf480aaCdCulbcUXBCwOePSTiCBIK7Ogt/ANvqCX2l4Q4VO2/6rGFK9CVSc5RTk853TQnE7NzYt/SGiPFC1S916zn1A/NFlpBUfEXCe6bx8Db5+1QGFubL9PEZ6aUkHn0Ij701Uj+Sg5zND9rjpRJqbjyN1YSb3S5vy2cnEKEkRQOsT5Tk4uGd8PQJWSftQ0KR31iX9LePggAGL5yVxR7tqCYXD++GTm24S+eZ+aP1P44vV2NcXGYI8pB7SkcOaaSrNz1IL2bdz+80KUD/hKQ1tnBDCvHKwgKH/CHduGmqRM5gUNczXPyQDp5QlbL2fNFbP0ocU9JDErQR6TYJYZeNydkJxFwdi8wR0ox7JezNJ8ZcuHi6yyDABQG53S0ht4tbpkS2uXDn6acxbHDlIhISMqpE9DpBCZBWLYDQaZWGLhU9Ez8sX84hAWMZLRxM2aBplwrrllItQM3zrARKjFpzJgHpNkp2AtEKeX38Lscc9cl7TEcgiwAX2ZRKbs/wHc2Ie822SC0iJAqhaJvf02YBEgkYWj6WqQTE+E9mSMZI/XnaI6X6G0l7zXfZLimbKIxvbE57T16gbpQmdZMvJxC2XYTWwLBQpnHKHs8v26LiqS2FACadO9ROjzuYI4r6Ofm5MeVY76IaIHSel9rZc2FD/E9JSKkuwlJBKgubhjdLCO3LemqA9udpC4r6j9QX2C6xOoE0fUhCzFavFkuScMS/tbdNnEDUwl0XDx0ZbJwdm74jqi8nqcvGYzkCUQQ4SdOgiovsEQmEyQTo/eiFXagmELChwc4Wht/oO6+VoO0bcOoCRqxQXbQY72Hhg6HnKImgWoRqk5haZe9NSzsm2NHhNMw7JcC2Axg+JOH+3kV/AmZY+oB0nEDYdjMQBpy8eL0E+H3ARVzvl7CVc8m2tfXUtoZASBjQH/G0TPJbq1OuPEfzhrsG9lqFgbnqjRJwhBM2C6+RABE6Pmu/DyAQXVb78h4W/1EJREgY0O/fIaF7J70G8IU89fX1n5S4VBGhvUaNREm+YTQ7dLeTEwjbnoMd4Bck0KJ4z3eD2CLjqS2BACZWOP+BGgOnO2qvHF6ibHPlUTI0myvfI6XLy6UgPYVPHyzwmMtunz6HCxaIW87mYW5sUN4XS/i6qYy63HPnvVT6kDSAwNWeSGkpl5lk0glEC+we1xFwBLaGAI3oenfEW6uPl8cRmBMBjheTE0xOIOZsKk/bEXAElkAg5ptgiXw9D0dgbwhAYodjoSbqHicQe2t+L68j4AjEEIDOGKob9/jq/cMRiCMQcww2hJUTiCH4/GVHwBHYCAK0zMex6ZHjbRupjhfDETBFgIanpnfiOIEwbSNPzBFwBFZEgPcOwInblu5DWBESz9oR+P+jnzjJYT4unEB473IEHIEjITDbZHkkkLwup0GAkrncterdYDiB6IbOX3QEHIGNIkASASnEHPcvbLTaXixH4AoCvO4chpOzSOScQHiPcwQcgSMiQN8G7sTtiK3rdapBAET6tjlJtBOImmbwOI6AI+AIOAKOgCNwBYH/A5T+Hss0cN9yAAAAAElFTkSuQmCC\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":59147,"title":"Determine aquifer properties: steady pump test in a leaky confined aquifer","description":"Problem statement\r\nWrite a function to determine the hydraulic conductivity  of a leaky confined aquifer and the hydraulic conductivity  of the leaky confining layer given the pumping rate  and radius  of the well, the drawdowns  measured at distances  from the well, and the thicknesses  and  of the leaky confined aquifer and the leaking confining layer, respectively. \r\nBackground\r\nCody Problem 59002 dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in other pumping tests, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\r\nAn analytical solution for the drawdown can be determined by solving the equation\r\n\r\nwith the boundary conditions that the drawdown far from the well is zero (i.e., ) and the flow at the well is . Using Darcy’s law and the convention that flow to the well is positive, one finds\r\n\r\nThe governing equation is related to the one in Cody Problem 51783, and it is the polar coordinates version of the equation in Cody Problem 59002. \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: 819.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 409.55px; transform-origin: 407px 409.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.408px 8px; transform-origin: 171.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine 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: 179.325px 8px; transform-origin: 179.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a leaky confined aquifer and the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"18\" alt=\"K'\" style=\"width: 19px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the leaky confining layer given the pumping rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5667px 8px; transform-origin: 36.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rw\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.35px 8px; transform-origin: 86.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the well, the drawdowns \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.2917px 8px; transform-origin: 74.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e measured at distances \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the well, and the thicknesses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"18\" alt=\"b'\" style=\"width: 15px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.767px 8px; transform-origin: 229.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the leaky confined aquifer and the leaking confining layer, respectively. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59002\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59002\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: 310.817px 8px; transform-origin: 310.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eother pumping tests\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: 215.092px 8px; transform-origin: 215.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 254.808px 8px; transform-origin: 254.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn analytical solution for the drawdown can be determined by solving the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136.5\" height=\"36.5\" alt=\"d2s/dr2 + (1/r)ds/dr - K's/Kbb' = 0\" style=\"width: 136.5px; height: 36.5px;\"\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: 239.6px 8px; transform-origin: 239.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith the boundary conditions that the drawdown far from the well is zero (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"60.5\" height=\"18.5\" alt=\"s(inf) = 0\" style=\"width: 60.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and the flow at the well is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law and the convention that flow to the well is positive, one finds\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"141.5\" height=\"35\" alt=\"Q0 = -2pi rw b K (ds/dr)|_{r=rw}\" style=\"width: 141.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.267px 8px; transform-origin: 146.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe governing equation is related to the one in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51783\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51783\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: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and it is the polar coordinates version of the equation in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59002\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59002\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 370.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 185.35px; text-align: left; transform-origin: 384px 185.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"504\" height=\"365\" style=\"vertical-align: baseline;width: 504px;height: 365px\" 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\" alt=\"Steady pump test in a leaky confined aquifer\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp)\r\n% K = hydraulic conductivity of aquifer; Kp = hydraulic conductivity of confining layer\r\n% Other variables are defined in the test suite\r\n \r\n   K = Q0*log(r(1)/r(2))/(2*pi*b*(s(2)-s(1));\r\n   Kp = K*bp/b;\r\n   \r\nend","test_suite":"%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.4 0.25];             %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 93.54;\r\nKp_correct = 1.82e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.4 0.25];             %  Observed drawdown (m)\r\nQ0 = 2000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 187.07;\r\nKp_correct = 3.64e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.6 0.4];              %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.6;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 1.5;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 71.32;\r\nKp_correct = 7.00e-3;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [30 75];                %  Distances from the well (m)\r\ns = [0.6 0.4];              %  Observed drawdown (m)\r\nQ0 = 1000;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 10;                     %  Thickness of the confined aquifer (m)\r\nbp = 3;                     %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 71.32;\r\nKp_correct = 1.40e-2;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [100 240];              %  Distances from the well (m)\r\ns = [4.0 2.8];              %  Observed drawdown (m)\r\nQ0 = 3500;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 35;                     %  Thickness of the confined aquifer (m)\r\nbp = 2.3;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 11.43;\r\nKp_correct = 3.74e-4;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nr = [100 240];              %  Distances from the well (m)\r\ns = [10 8];                 %  Observed drawdown (m)\r\nQ0 = 3500;                  %  Pumping rate (m3/d)\r\nrw = 0.3;                   %  Radius of the well (m)\r\nb = 35;                     %  Thickness of the confined aquifer (m)\r\nbp = 2.3;                   %  Thickness of the leaky confining layer (m)\r\n[K,Kp] = steadyPumpTestLeakyConfined(r,s,Q0,rw,b,bp);\r\nK_correct = 6.959;\r\nKp_correct = 1.126e-5;\r\nassert(abs(K-K_correct)/K_correct\u003c1e-4)\r\nassert(abs(Kp-Kp_correct)/Kp_correct\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('steadyPumpTestLeakyConfined.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-04T15:23:23.000Z","updated_at":"2026-02-12T15:06:18.000Z","published_at":"2023-11-04T15:23:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine 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 leaky confined aquifer and 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\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the leaky confining layer given the pumping rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the well, the drawdowns \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e measured at distances \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the well, and the thicknesses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the leaky confined aquifer and the leaking confining layer, respectively. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59002\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59002\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother pumping tests\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.\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\u003eAn analytical solution for the drawdown can be determined by solving the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d2s/dr2 + (1/r)ds/dr - K's/Kbb' = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2s}{dr^2}+\\\\frac{1}{r}\\\\frac{ds}{dr}-\\\\frac{K\\\\prime s}{\\nKbb\\\\prime} = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith the boundary conditions that the drawdown far from the well is zero (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=\\\"s(inf) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and the flow at the well is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law and the convention that flow to the well is positive, one finds\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=\\\"Q0 = -2pi rw b K (ds/dr)|_{r=rw}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0 = -2\\\\pi r_wbK\\\\frac{ds}{dr}|_{r=r_w}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe governing equation is related to the one in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51783\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51783\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and it is the polar coordinates version of the equation in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59002\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59002\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"365\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","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: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\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: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \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: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, 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);\"\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: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; 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: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \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: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, 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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; 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 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 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 mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\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=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 is the discharge or volumetric flow rate, 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=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\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\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\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=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAACcUlEQVRYR+1Wuy5FQRTlD7wqUQgKjZCQaCg0no0O8QEeESUJpUdCUHp8gKBQEioJGo+CSoM/8PoC1pLZss0983DdI4ozyco5Z86ePWvW7L1niov+SSv+JzyKMiL2TmSK/FSRGgyoDAT0ufnf5rG7w78nn5/Q1pBIPTAJdFmOhvDNCW4VkR68zyi7Y7zPA0LWySVERAZytWfKS7vD+Qj6N40die7GlodYIoNwuGOcPuBZlzCB2LzgX4dSKopLLBGubMB4XMRz1vIuSnArhgFvPCQxiyXyjMGlxkEfnofmvRzPOWAMSCIYpQaNYog0wu5GeawwK2b/PlALuGKmoESm4G3JeKT03YBsBeOlE3iMntFhGKPIEcZK6lJ+KsB42QMYoAVpMUTe1UzMCMbKtVHmx0HpYh0i0ouBBwlE2DUKbBVEDjgJEVmAjVRKbsUJIAWL8dEKFESVEJErTNRiVi0K3Js4YfevUlar6SPCc4arltaEF54rersYMySaatboss4JyxQpnUkb6B//baz4FFmHc1ZMNnsy+xAUtfLm4yOiy3rSSaqJ5n3GCHMXEbuss4jZcWDHkD6DQsrwjKoyMfdp6yKi7xWuY5/jtSq+IseJtw27VzxZmaeBZZ8iHHQBUAU2X73QdYa2TOc1wK4tQliUZVlYBb4uTrYizJR+oMTSlttyqgbSrgFotuz4aduyT+4zEmscf2lsP12EClrCPHl1SZY5T+u/IkL2so1ylfi2orSJ6OzQsZdzkUqbCLdkApB7i6iSU5fSJiK3O8kWZg9vdDmndtpERAlm2BtQDazobJFASZtIdIplRGypMkUyRULp8wGAmHwpAQoZLAAAAABJRU5ErkJggg==\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAoCAYAAADg+OpoAAAB50lEQVRYR+1WyS4FURB97wvE8AWGNQliw9b4AUgsXkJi+ADCXkx7w8IaWwlhZcGKWNhjJVbGL+Ccl6pO99Xdr9XVbyF9k5Pq4Xade+pW1e1yqU6jXCeeUkFkjnQRuiJ0QQSyJsMEvmgA9qyxy0LUCecXwHKeRP1wfgw0Am3A418raoXDaWBFHD/AVuT62UIYFzqSbIvTIbHvsNdyPWxRlbZHDNulOB2DPbUQ6DdpRIuYtCETW2Bf8yK6geMe4BwwhSu8sCRFzZj0IhOXYDd91PDbJKJRvDsR5wOwV3kRrcIxU5vZ1uRLkqboHi9ZoEcA24/3SKojFijHHGDub7WSgQoOZFIX7BNwBvT6yIpTxK4wD1BVn5DMwN45RCzoEWBQwrwAWwHaAe7rFBAUeRwRV8/Ww0R4A7ZSwqfdg3PXgX2AxwkXyWcdQLXQ44gYOq7sA1iLURIWNoubXcBNmi+ZFHT8LOdR2LF7fYgH40C41rTYNfSJitIcu++48ohD3GsyRVT6KNL92YFzJoIO3ePIQelDpN1jEgwMIYfu2Y/+6EOk3V1XriGLLXIrkW44U5hqaD8BHiluvVWlWol09e7+JCaSlUi7R+Yj3kqk3T3zL5iFiNnWLTG6hWXbqfm/ZyH6TUEHc/8f0Tfny1wpwHGjIQAAAABJRU5ErkJggg==\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAoCAYAAADg+OpoAAACQElEQVRYR+1WuS6FQRS+HkDE8gSWmgTRUNofAIlCZ+k0JJRCUIulkOjQaQhaOhQqheUJLPEEfJ+cI3N/M/+cOzdExCRf5r93zsx39pmKwg+Nih/iKfwTJXv6V7quFuYsAO1i1j3mNeDcYqbVonocdioHdmDuBnYBkvH3U4zMSnSBg9qAFuAaGAc2gRegJkbCdQvRsGh/grnPObQT3zcWa6xEdxBsACaALYv2PpmYRdT6TDaq25K4YkTrOHWylFiEtPARNUO4UjbsiNsuMU87h5hjo3t8RMeyyLphpnEwjRkrjitgvlT/5blOU5hnDgJHpR7uyucRaXwoXwdEizJPkTwiTWvGR9tOslEhIsbnUU5dSolJVqMQkVs/I9i0l2yKbAwRzWB9RWTYFR6+i4gp3itp3VguCfeHLHrGWjWwD7Cplj18RLx7WKAcZTVSVzsfkV4LlMtrpEyYfqAHYByngDGAruYdNQp8FrmPaBECc4DlUtPspOwysA1UiUf4XxPwUeihXsdEsMRH21RW9k3c9pmxPiIV6oJw7OHB+hoCXFkt9qL3RJZoAJsOjW6j0lQq+0DRGBdZSSL6WTXXRmrpBhqfDUkE8VZBa7Co0EnEmmHQOG5FQ0sT1aRxldKYzeKcVWXWZGCXZorSGqam6Z0GOX2CqebqMm/t0SJtmAfOt6uM71sDzhTmfs6vAJ9kfPd9GbHHSYhQtc/GJ6hgKpEmjfmKTyXS29d8haQQMdtaxUd8EbHtRO+rFKJYonjX/x7RO1S6din/Er4mAAAAAElFTkSuQmCC\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"fzero\"","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:\"fzero\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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