{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":53975,"title":"Compute the effective conductivity of more heterogeneous aquifers","description":"Cody Problem 52070 asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single value of conductivity set such that the aquifer produces the same flow under the same total change in head. In that problem, the aquifer had soil units either in series only or in parallel only. \r\nWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided.  \r\nFor example, if in the aquifer below  = 0.1 m/d,  = 0.2 m/d,  = 0.01 m/d, and  = 20 m/d, then the effective conductivity is 0.092 m/d.  \r\nHint: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \r\n   and   \r\nThen conservation of mass leads to \r\n\r\nSolve this equation for the head , compute the flow through the aquifer, and get the effective conductivity from the definition.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 725.117px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 362.558px; transform-origin: 407px 362.558px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.25px 7.79167px; transform-origin: 318.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.017px 7.79167px; transform-origin: 331.017px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.79167px; transform-origin: 25.2667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.933px 7.79167px; transform-origin: 359.933px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.858px 7.79167px; transform-origin: 110.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if in the aquifer below \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.1 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.2 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K3\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7px 7.79167px; transform-origin: 52.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.01 m/d, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K4\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.35px 7.79167px; transform-origin: 88.35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.79167px; transform-origin: 13.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.683px 7.79167px; transform-origin: 342.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"vx = -Kdh/dx\" style=\"width: 72px; height: 35px;\" width=\"72\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 7.79167px; transform-origin: 23.325px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   and   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v_y = -Kdh/dy\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.408px 7.79167px; transform-origin: 112.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen conservation of mass leads to \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVsAAABGCAYAAABi8DccAAAWjElEQVR4Xu2dW+h3TVXH9TYwU/MmRMQMDBXD9FXKhAJTE6RQS9GLBxRLjcA001Ii8oCml5qGwnvhqYMUUmZ54YUHPJQUJAapvIh1ox0VvLT1kf19W888M3uO+/jfG4bf8/z37Dl8Z8131qxZM3Pf+1zPhcCFwIXAhcDiCNx38RyuDC4ELgQuBC4E7nOR7SUEFwIXAhcCKyBwke0KIF9ZXAhcCFwIXGR7ycCFwIXAhcAKCJyRbJ9suD3EwodWwG8vWfyqFeSzFv5pLwW64eV4uNX/ORbeeoNweJDV9UUW3mvhP25QvYurOoJsAfmpFh465fp1+/34RoA/z/L9oIXn74xsf8HK8+gJn/+Z8PlappUYNB5l4bETib57Jj71fqeFn72hhLsnGaS9PjHJ38uKe+LyEVswYtB45CS7P2e/L8j0a2TwCRaevlH/Xx7FjhxGkC0A/5cFSOT+Fn7Fwo9a+DULcwTRUezop3slWrROOuA9U6mfa7+Pt/BHFl4fEUpI9hkWXmrhAdM3JYMH+bzZwk0k3L3I4F6JFjGqxejV9g0E+7RJBr9qv48o6LTMKOn/F+EGYI0g2xB/RtCPTYSyFuFKyCGw3y0QiK2jIPiQ6Z9YYJCIPQj7W6YXCG9OE1aHIj3IvCT+1jgslf8WMqg8qRPa3d6fUoy+N1WEvlWiqR8Nh9XaaQmypfBMPxgJ0XiX7vg07r9O+R1ByNW4X7F/QKLPtPDRSIszYKFV/H1F570E/f+BXFMGyZX2umsFeR9JDjmMmGV9csowJaex8hxN+RmJaTKtpciWDL8wCV7JFLinskxbMF38hIUjLRC90cr7OxZiGgOk+a0JlN+235qFFgT9Hy28ycIRtPyets99u5YMYsJ5l4W1ZnK5ete8n8NIMorS9GMWaha+hEkNSdeU+3BxlyRbNdTcVLkXMBae/tpCLSH15jvie5UdQX5gkKDe8eefsfCpygyFfcu3lVntOvoaMoh2yOzj8xawUx7tmcNIRPy3jXXje2ZvtUR9NAyLyrsk2crmWDMNLir0FAnt73MTUR2xMTVFi5laejQK4DmqaaWm/UviLi2DlEEzq6MObCmMemZXahvJ+DXLMkRGkS1T1ydZwBtBrl/43LHAE9PcSjpKLo6E5AhaLdoP9jzc4+T69SP2b9nDQhOINIpwViAXMtLIeXoIn6XNOLl2Wuv9FjIoMmnV/NbCRvnUYORnV14+kWVcPenr1DtnutPaQ+ki79qYrJZfL9kibHdbAEg02D+zgLsILiIsALHAswTZSnMDqD1rtQgmngfgwIIh5Ik7F54I2Gr55QmFmbg8sgH6dCQcOW1BGP3n1B767my/W8kgOIpI9q7VtmAkjxnff+VeKJfEkgVwDUil3gxnk89769NDtvJrJbHQCC7NjHdLkK3y3nMDakUWwQyJUWYCNYQnW48rf+f5sIU/tsBCmbAtMc+ow5xVu91SBrWSX+p/uhWJtGIkbxnNrrRhgcVoNjqwVhLr+7F6Kq0brd22ku1cAwK29xFdYoFMjbdXD4Q5ogUf71ITDkYiSDrxz1v4Owu3LLBI5u1oJQONPBOOMs2tIaStZVDttGcPhFaMNJDQHgzUj7EAUcon3CsLJQQqz4QjmPxqZLAqbgvZanqKxpYiUk+2JaRQU2gRyJ41Ck0vKeMTLYQuM55sw3poIAE3/IbfbkHnPHg7WmknP6NWsbUMIq+YZ+gDJWRTI9+j4vZg5EkaOfstC373mGZXpbPWo8wCRmEfTaeFbEt2NmnU18g48lAYjao5m2WswgjRUyzQ+OHzD/aHT1tgg4EOEsH+7J//tv+w731uccoTaWr67oXZD0YaSMgTMwFC7XfteI2iVKvXN6XkvKjADUp8axnUoFdiygmrnJIt4iFfX7Sgw1xS8oqs/qmFucWpHozkYaG1g2e7vPzsqmbWKoIuldtBorJYMmHb/IXl9OcWkr7ILWQrTWluaqo41PSH5wrQAIXS7lmU8IMBRUgRUWgOYRNCbhusX1hILd75/L29W9MtyhTT3CWwNVp9DzE0NM8qn2wtg2q/nmmxn6prcMUeGpMvbZlFk2TwLVFeejCS1k65QoXBz65q1gJ6lKRVhKowExQi1lDwjdc5JLSlFr9fl2qfWrL1ApIiqFA7G7mF1udfW3aPpSfR1KDh7a41nSpcWIi1oRdmPxhJo+CbcNGx1l6rfP13owe+QvkcGm1rGaQyIwZ80hGJ8u+U8iBiR4t+sYWcqxVp9WCU67+19lo1/hkGfW1gwXwUauh6R31faOGOLfi1hOWnyDnhiBFGb6+T5te74OO9JWKDhog2CdxMRdSBUgTtTQihKUTfxqanPbvKVN+ltk5qagwsNVuLW+Rhaxn0ZFTbf3x9fXumbPv+wKKX28el22V7MPKKSExeWneVnWHQ11pMin80ENF/7zj1rFZYfCPGbC9+RO0lxFhHlPC12Gtjmh5/C+uhs2HpAKlp3RxJiDBTmr+0onC/ucc29q3fVabtveCdM2tQ1hHT3rk6+91w4dbjFkItySvWdqFWt4QMarBssdf6enkNMbR9Qkzvt4B/doutvaefilBii1+eML0PeIkMUvdRM4LRMlWSXq5/ksbsek0t2ZKgyCRGtpoGlzg7l1QwjDPiYJGURoEg/aaF1OEwpeWVsMY6ibfJhlpDbkFDddeCGgTKlDK3k4xyK+0lyMcLWenqdCmWqXhbyuDcAUI19UrNrrQBgbRuWag9F0NlaMVo7khF33fwwrifhfdYKD27Vn2jxixXg+mScf06y9win/C7o6+1kG3Kv9AvDC11rKIqMmpxTBoFU0OEBgF6bSGBpRpWmk+oreR8Huc2K3iNgkUJnl+0kDoLNyybRtyahbUawV1Ts6VcW8rgCMIIF8fUef2gyEJYqcYYa6sWjDyZxkwIGmhk9kD7fkPFgKD6jXYHrZHV1rh+nWWON71b3G0L5C1k6w8dZoTieclEVID4tk4hSYHhbWU9Cz3eU0LEhWAiQK+oEJy5RpOgg8c9FnTifWqRI3foh5+ekG+Nyw3x/fctbZ4T0LXJdisZBAd1uh77tx94PXFhNugxkfl2asEodwCSBhryYRbzrMr+svQMKyenre99/8zN3jxGt2nAPR0PgdG9Y5+xf//7QiQrgEYQRqhRoOoj4Pz2ahJhQ1Len5r++M/2+28WUivJfoEJX72YRiO8wbplajk3rWwVwrBtcoLYm0/4/doySP6jZ1cMwMyoWOGucaUqxbIGI8XlMKmYe5nklIOQZn1KE4UbNShTzlulAMzEQ1ks8e7w3JOTcU+2t5kSe8h2QF2rkpA2kKvsXKJeo/DxlppeV1Vw4cgjSCJVxFGdaGEIupP3g3WPc76fXflCLUG23ZUemMAIhYni+PWNnuKVtqEvd25h1Nt2D0u2I6Yg3o+VqThnD+gEo5ZV356GXvvbi2z7ER9BFt4cRon86W89ikR/7ZZPYQR+lJJBjyNKe5/SGaIvd86E5weCG0223siNze0HLXD1OU/oitXbkHv7Xob71pVgpkepB5sWi6JgyI0FqYdtpke+qmcEWXiPFGlJXtNtbZ+9yVusPN722bPIvXZdfbvnZsFeobuxZBtqFFpk84I+anFibWEoya93Fd3vdirJLxYnpxW0prvWdyPI1ndGyZs3by3lNrkWRrl8lpxh5fJufe/NR7nZh7fZ3raIeiSbba8Zwav33u4SGr+XcltrbehR3/WSLTilnkfZi3dNL9FYUs/Si6ijsEqlM4Js/aDlO6PvpGce9I9ItsiDP59ibuPOIt4ISwt2mH4v2XoQwqmaf3d07SvVLr1kO9feN2WBrJdsw4Hd+2GG7n2lizdr98Pe/EaQ7dreCNTZ76ybU8g0U75DAw412wf3Iln5/Xct/ncKv+khW28rIrvQXhSaGFrtSWvjR12+WYjfUch2zxj2kq3fohvbzedNDD27/dbGsFQGvYbY2sdIY21vBPL0tvZU2WcPiwrJdoRdrrDvfz8aZPsDhR/0kK3fGZNaCPMuGzn3jliRQx/ewmp1Rys1BR2BbEPtrhucwgR+2eJxf17u6SVbv0U3thAWylDLxgkuEZ0z+eTq2PKehU+0vZJnhGa7tjcC9fKHsafMPN72fsfMJOyoHIy95gPZQoQlTw/Z5jQK8h8h6GvjR7k5U7Pk0fRmidXukWaELTCEbEu0sx6yzc2u1Ia9g/4fbES2ryoQQt/HejTbgqwWiSLtNnVKmxSa6HbkUq1okZJXJtpDtqUeB+F2xD3f3FsJ35CdT6k8R5Jtbb3WjN9DtuGGmtSW81C7X2JwXBMzn1cPfluVOcw3dfKg2jc5Kz4S2coUkPNzCxv31+0PHJWoBzPCCy38iwVti0UIHmIBILXJgfgA93tB3L00em05RkzfbjrZeu209O4xtLm7IrKF9vMBC3Ks19Q4Jq/E/RsXt7bt9xL/DGQLlih+r7HAZaxcY/QwC5AtNnd/jdVtuB+JbFsaas525d2Qcjauo7sseZJYYpX7pmi2dJ7aQStnXwzJdo4YS3c87YVcw3JIYcr5qu61/GG5WFjnmMlvW8iesXAksh11Jc5RGnJkOVsGqpH5nyktmaSOaHPcuh16TIFbl707/xKyRSt6joVfcrlxk+THLfSct9lS+FqtoiWP0d/sAb8WE8xoHHrSY6B9kYWfnBLhFtq/nGSw9KqYnvz9t0t6dYwqYywdprmcgfxD08uSG3pHl2fUweujy7VKeiVki6r8JAtfmkrEbqE3W+CcgddZKLnpc1RlJOhHOh1pD/gdXaNgsOAci29MgvQM++VGjZpLEEfJ4BEPwGbAZ7DieE4e1ideaQG7M/bgtc6rOOpANUR2Ssg2lpG/EFHX+Q4pUCYRrQQefYV2bfzkLH903Lx4+NXf0mtZRsio8u3ZdDCiHL1p+MPF11JedBDUjTTBtJItDb3FlOAsgr42fme1M464k66WtM60drCmeelMuNXKzPfj95CtX4Feyx9VDXaG1cy18DuzkG9lHtHgtYRnR1NH7vhorXWQMylKTXD3kC0ZLnnVSqpCZxT0JTuthPyMB+xs5XKWukyxqRNu/JHsqEsfnn8mzJqabBTZrmXz8dPvpYWjCdDKjzRYLYnfmYXck+2aaweafp9hAJvdYlopz3PRz6QkNcFSSrYI109bkOsNrl9c+PatKdeQ+DC+P9F9Q/x3uxLSSdgpgxvKCyzUuO/ohK6Ww2KaQBrwUS1+2nX0FMubf4fXReuIOVzvkjtWpnJrUaLnRuIBEHQlgTw91YLwkOsX3gkcvMKj2QF4PdLCoy3cf5LZ2MV+rDkgz3dbaPGoORqu9BsuN+WmZx5cv95rgcGYv/uBg/6J1xH4Pc4CuzZDjwXSe4sF2uLlFub68BH77ATTuJ8c2QLSeyxwog+rrwjm/1r4/akIOunHky3CzqEU91jQFef+pK1wj3iLVqeFkdItk+MQq0upBT8RMzeYIsw8fuXbH1TCuzkMzqCBUYf3WWAbNW5Kf2UBNzBwgAQkg55suZ+Km42FX0wDFVm2XoekBeIW+a2Tor7YDFTvsMCWdfD6Qwu4caLsgB0HYYNtSLZgTD8P8VVp/JGDOS8XYXWG2Whza8yRrdyTaIjwSLHw/NeUwHli5bg4rvP+sIVnW2CbGx2C0bVGs6WySjfXyM3ADPhwBH6eWNFMtbmE2QCaHpqHnzGExZbL11FdbUL5+airoO/s/Dk26Hj8wve0D7LIwyysVga18LhnFzDv3hWbCfo7+WInVfnF1dj7UhIlH561FtIHdN/xSaTIFpBpHGkTsamqP/s2tcDjGwvC5jbbV1gYsccbGxCj8twVFeMRK0txFH6ebNAKXmwBDaVk556wrzm4p6x268TyZxDHBnO/BTnlneKVgphWhTcD02RwbnlE5ksucLaUS99oBpiSAX/KXUrr1ICdwhgemKu/ZDh67GBP5Y72bYpsJURzUyxPtnP2QH+84UhNVI24x2ncKPzCM3ZrNFSVYY/4lPQTyU1Kc/RkO2e/VzoxUwJEwrbfFpstdVD77JFI/ECdkhtPtqmDyucOxNbs4BEzDSr8927yK5HJrjgxsg210dhWPq8x5Baqwqlw7XRtroI0JE/LNLALuJmPR+MnYc3h7IukMtR8sxQeLenOmQ+UnjcjzF2QqKluqDiAEUfk9crOXrXbErnxZoSUwuRPjAuVJerOaVcpU5ba8cwXWBbLd4xsvRCnRqMa47jvOKNHN2k3IzXmYvASEUfjp85cYw44uq1W5Z+rs7+va07j9+YIr73liKJUDnRdyuftA7YN7+HxylBqZuPj5OzOMkf4wTs3WIHL5yxg5rvRtloJRIxsczYavvV3KeXsVT7uEquRdBoIfS9XkI/Ez9t+wT2HNXE0AB1Zm5DGlfJj9dpWbjdhTDPLEUUtYUqhaLkzrDavkvh+wE/JjL8qKtcvY7OD3GCl3X17waQEt0XjxMhWdpyUoHtbWc6pW76M2HTQanPxWyqrFVe+fUJLAoO/GYkfAxXhpVMZc51C2gQEtObhLIMhvHdnYqq+6sjkm8PEKwfS4Gij0Pe7tw57GvSFT2og8pcX5gYrcPGzA2YRPHdbSJlgpDXv0Zbd287N389ptili9Eb1nI8nfnqsnuN3C2H4hkW74ClZWc9VUG5Wax4XlyqTNNte/BiowBetKbbIQ51x6vc2cPLG42MvWn6u3VLvpdnGiNQTRalpRZoZ8X/DAnI5emDe06AvzTZFpH6wKllA9bMD4nM8I9dFeVc8taUf8Edj3CpPu/huzmYbI4uShQsqplXKW/Zv3LzCFU1I4v0WYjt7WoHR6FsiPK15lHwnQe/BD7wQaLl5ee8GbGDaveN339GBXmNhzW2rJXi0xNGAFSNbj0XpoBJeZf+sSS5byjb3jcw+lD+3s2903j49aZYxsp3z/54rk8yBpDlnn0YZg3CPPLNapG1iZCvNgQx9x/V2oJgdRo0ByaBdIWxyqfEr9EzlyIOdaXMO+S0V1m4jn3dLOj3ftOCnTkq+rJCDn8feD1Zo77y/5QiD95DQGYgWDGSqYkFGnRZcuaZbM6RSoiW9Eg+Rnjb332rXIP1hS8LVDNQrH+D6EQuxjUq5+pcMcsRBm72INoJmys/W765hCiubKx39bRZiU3/vRhLTSEocqHMNXvKesv+4hVbfyZI8cnFq8fMrw2gOoeYV2tjC9wyEn7WQvXQuV/AdvdcAwtQfU8ldU9laTUX4hZMWA9UI09UcVLoZ4a0b4kkZmD2CG5oo/9e2+/CsjZJiyvSQ8vxRnVt2hJbkf/g4ubMRGAl5Sm6XBWxIbi4u6ZWkdXhgpwrU4KdbWL88kUuIgfBNvT8LZr4eqjN/66m3bI41m0LOgicDefENsDOV1mL3XtzbDtc+ObI9XIWuAl8IRBBgenuPhS01zSM3jEwjpVvFj1zXxcp+ke1i0F4J7wQBTCzYslvPP9hJNTYrhrwsRp1psllFts74ItutW+DKfyQCoakl9OoYmddZ00KL5cH+L6JdYjH7rPgl63WR7Y1r8lNX2O/e49+sjF9T3/ImD7fwLuU1VF6iE8W8yPZEjXlV5d4bn4ECr4XXWxh58NHZIfbbw7UBJLZx4ew4LFK/i2wXgfVKdEME0M6+bWFp964Nq7ho1jLFjDhzetGCHi3xi2yP1mJXeS8ELgQOicBFtodstqvQFwIXAkdD4CLbo7XYVd4LgQuBQyLwf6xczaF0WKndAAAAAElFTkSuQmCC\" alt=\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\" style=\"width: 173.5px; height: 35px;\" width=\"173.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.358px 7.79167px; transform-origin: 100.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSolve this equation for the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.9px 7.79167px; transform-origin: 251.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 246.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 123.233px; text-align: left; transform-origin: 384px 123.233px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 513px;height: 241px\" 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\" data-image-state=\"image-loaded\" width=\"513\" height=\"241\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity2(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 0.1; K2 = 0.2; K3 = 0.01; K4 = 20;\r\no = ones(50,50);\r\nK = [K1*o K2*o; K3*o K4*o];\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.0916;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 5; K2 = 3; K3 = 8; K4 = 6;\r\nK = K3*ones(50,110);\r\nK(1:20,1:50) = K1;\r\nK(21:end,1:30) = K2;\r\nK(1:20,51:end) = K4;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 2.5471;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 0.1; K2 = 1;\r\nK = diag(K2*ones(50,1));\r\nfor j = 1:9\r\n    K = K+diag(K2*ones(1,50-j),j)+diag(K2*ones(1,50-j),-j);\r\nend\r\nK(K==0) = K1;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.2945;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 1; K2 = randi(9)/10;\r\nw1 = 10*randi(9); w2 = 100-w1;\r\nK = K2*ones(100); K(1:w1,:) = K1; \r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = (K1*w1+K2*w2)/(w1+w2);\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-02-02T15:06:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-28T03:19:00.000Z","updated_at":"2026-03-23T06:38:42.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52070,"title":"Compute the effective conductivity of a heterogeneous aquifer","description":"Slow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water  to the gradient in piezometric head  by\r\n\r\nwhere  is the conductivity of the soil and  is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow  (and the specific discharge ) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \r\nSome aquifers, or underground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of  set such that the aquifer produces the same flow under the same total change in head. \r\nFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If  is 2 m/d (meters/day) and  is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \r\nWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \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: 634px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 317px; transform-origin: 407px 317px; vertical-align: baseline; \"\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: 311.833px 7.91667px; transform-origin: 311.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \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: 56.0083px 7.91667px; transform-origin: 56.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the gradient in piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 19px;\" width=\"39.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 7.91667px; transform-origin: 9.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4167px; text-align: left; transform-origin: 384px 17.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.91667px; transform-origin: 104.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the conductivity of the soil 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);\"\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: 244.283px 7.91667px; transform-origin: 244.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.1333px 7.91667px; transform-origin: 87.1333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (and the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 19px;\" width=\"57.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 227.95px 7.91667px; transform-origin: 227.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 7.91667px; transform-origin: 57.175px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome aquifers, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.6px 7.91667px; transform-origin: 325.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\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: 252.433px 7.91667px; transform-origin: 252.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.917px 7.91667px; transform-origin: 376.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.225px 7.91667px; transform-origin: 83.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 m/d (meters/day) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.125px 7.91667px; transform-origin: 251.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.242px 7.91667px; transform-origin: 376.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.458px; text-align: left; transform-origin: 384px 104.458px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 382px;height: 203px\" src=\"data:image/png;base64,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\" alt=\"Aquifers in series and parallel\" data-image-state=\"image-loaded\" width=\"382\" height=\"203\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,1:2) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,3:4) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(1:2,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(3:4,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10*rand;\r\nK  = K1*ones(7);\r\nKeff_correct = K1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,10) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,5) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(10,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(5,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(4:6,:) = K2;\r\nK(7:8,:) = K3;\r\nKeff_correct = 3.875;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(:,4:6) = K2;\r\nK(:,7:8) = K3;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(5:7,:) = K2;\r\nK(8:9,:) = K3;\r\nK(10,:)  = K4;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(:,5:7) = K2;\r\nK(:,8:9) = K3;\r\nK(:,10)  = K4;\r\nKeff_correct = 1.5584;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-17T14:24:44.000Z","updated_at":"2026-03-16T13:48:00.000Z","published_at":"2021-06-17T14:30:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the gradient in piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 the conductivity of the soil 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=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (and the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \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\u003eSome aquifers, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"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 set such that the aquifer produces the same flow under the same total change in head. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 m/d (meters/day) 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=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":53975,"title":"Compute the effective conductivity of more heterogeneous aquifers","description":"Cody Problem 52070 asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single value of conductivity set such that the aquifer produces the same flow under the same total change in head. In that problem, the aquifer had soil units either in series only or in parallel only. \r\nWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided.  \r\nFor example, if in the aquifer below  = 0.1 m/d,  = 0.2 m/d,  = 0.01 m/d, and  = 20 m/d, then the effective conductivity is 0.092 m/d.  \r\nHint: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \r\n   and   \r\nThen conservation of mass leads to \r\n\r\nSolve this equation for the head , compute the flow through the aquifer, and get the effective conductivity from the definition.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 725.117px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 362.558px; transform-origin: 407px 362.558px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.25px 7.79167px; transform-origin: 318.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.017px 7.79167px; transform-origin: 331.017px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.79167px; transform-origin: 25.2667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.933px 7.79167px; transform-origin: 359.933px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.858px 7.79167px; transform-origin: 110.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if in the aquifer below \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.1 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.2 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K3\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7px 7.79167px; transform-origin: 52.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.01 m/d, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K4\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.35px 7.79167px; transform-origin: 88.35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.79167px; transform-origin: 13.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.683px 7.79167px; transform-origin: 342.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"vx = -Kdh/dx\" style=\"width: 72px; height: 35px;\" width=\"72\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 7.79167px; transform-origin: 23.325px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   and   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v_y = -Kdh/dy\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.408px 7.79167px; transform-origin: 112.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen conservation of mass leads to \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\" style=\"width: 173.5px; height: 35px;\" width=\"173.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.358px 7.79167px; transform-origin: 100.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSolve this equation for the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.9px 7.79167px; transform-origin: 251.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 246.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 123.233px; text-align: left; transform-origin: 384px 123.233px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 513px;height: 241px\" 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IAFXXP2N6/QeQDSUtEnjYh7JHfY2EEqwkxuepNIpH8u7e6l4BsOh3DBluf+bUo21QXjHjh1pHzjgrhQgDy6Qp0JY7veRtgJbqZWKr5CWAnm0rG0/cJul3d9XR/8PUSQ/w3xNLfnectcw8k8CwsQxsZ5BuUtbbnxBcrJOKPMyf+Ri6V8H9df/ZkvYXb+pXvfFInMyR/P8lo8M5fM9sljlvcLqGjt2rA6MEvyCezesdsSt2n72s581o+TcloQ333zTjGLcyqitqsqd/5aEVbcS696Q5FZlCasodvSworvJkmv2335Zbo2wCkRLKG+6ch04cMCMknP/+8HFdN0bpWyPqvtR/+jRo3WQtqFXQqr8HtxQG3xyFFBM6GFFd5OLJHnqlV0C6+a51frmLQDRUtCbrnK1rJVbjf3oo/hTVpJxQ7LbYiDcG6Uk2ErrgH2EqbC/7q7bunnz5oTlrObNm2dGQPGhhxXdbff/f1k/9UpIWJXebQDRU9CWgFxVWM877zwzSn/TVXB5qgEDBphRnNsWIGHV9ru6z+WVVgZLlrdyVwzgqVCICiqsKLQ/v7Nf/duE2IoC8m81YRWIroK2BOSqwuo+616Wq0r1SDNZRsuSpzkl+++7YdR9nu+YMfFnVbvLZklYtb8naQfI1e8J8B0VVhSShNWhQy7QVX5ZBksefgEgugraEpCrCqsESLctYMiQIfpOfvv9JcDKx//ujVFuGHW5YdQN18He1GS9quPHjzcjoDjZHlZBhRWFIhdG466J3cwqKwI8WLtSjwFEVygrrEIeleqGYXlUqxzLUhESYO1H+3Ju586daf/bwTAqXxN8EECycOo+fAAoBuvWrNRL39ht3FfjK2BcOrCs/fzsqfFPIIBckrBaOXm8Xm/1wosGqk3bXuJCCUBhK6zZ6OjrJFDK41fdXtMg+bWmpqYOn0IVvHHKvcnKctdvFfL/l81SXEAx+fgI6wciPzauX6Wefy72cJjfv7474QIquN14w2j9OgDFL+8PDigUaQeQqqsIhksUHg8OQNRIgGJedp37sIqOSFHiocc3mCN0ROYoi9X7gQcHZK9oAiv8QmBF1BBY4TsCqz8IrNkr6LJWAAAAQLYIrAAAAPAagRUAAABeI7ACAADAawRWAAAAeI3ACgAAAK8RWAEAAOA1AisAAAC8RmAFAACA1wisAAAA8BqBFQAAAF4jsAIAAMBrBFYAAAB4jcAKAAAArxFYAQAA4LWStuPMGOi0hoYGtXHjRnOkVE1NjaqqqjJHSo0ePVqVl5ebo64pKSlRe/a9b44APwzodybzEl6TOcpbvh/kfYw/i+wQWJETe/fuVf379zdHJ2ppaVGlpaXmqGsIrPARgRW+I7D6g8CaPVoCMiQVw9WrV5sjBJWVlSVUVF3Tp0/PWVgFAADRQ2DNUGNjo5o4caKuIhJck7v11lvNKFFdXZ0ZAQAAZI/AmqE+ffrovXz0TXBNTqqowSqrVFcBACg0eb9G9nz9uRFYMyQ9mC6Ca3LBKuuSJUvMCACA/KutrVV9+/bl071Omj9/vpfZhsCaIVthDSK4JpIqq62qSrWV3lUAQCHIe7AE1ZkzZ55QZELmJO/4mG3yElirq6v1HXDFtC1fvtz87pIjuMbZqmqqnlYAAHLFVlTlPdgNqr179zYjZMP9GfqUbfKyrJUEVrmrPsrkrvlFixapiooKcyZaZJLLzyAf5AKC5YPgG5a1gu+KbVmr1tZWHaSophbOoEGD1Lp16/L2/p6WBNZcq6qqkr8RbMe343+4bcf/MpmfTHTk6/csP89kP2c2NjY2to63Yns/ampqaps+fXrS36tkEV/J/5+v0v08u3P+5KXCKtVVqbJGnfRwVlZWds+VSDeTq95du3blpYeVCit8RIUVvivmBwfIp3qLFy9OaN+TY3kf9pG8j/n6ZzF+/HhdRbXkZygtft19T0peelgPHTpkRtEkf7jyEYX8ZYliWJULFvnHQ/qKAADIN3mvlVUBmpqa1Lhx4/S5qGeRzrI3mbtZxocbqHk0a4akUtrRjVe+XIV0N2l+l0kuk765udmczR0qrPARFVb4rpgrrEFSNDlw4IAqLy83Z/zic4W1vr5eDRw40Lssw7JWGZIAlopvVyHdSaqr9mcl+6jffAcAKDypuPoaVn03bNgwL7MMgTVDydZhlfVGCaqJgg8K4MEBAACgqwisGXIrrLaiKv0yBNU4t7pqUWUFAABdRQ9rhqSH9ayzzqJHNQ3buxqU615WeljhI3pY4bso9bD6zuceVl8RWJETDQ0NauPGjfrJInJnplRVpRJtj3O5vBeBFT4isMJ3BFZ/EFizR2BFXuTzLyOBFT4isMJ3BFZ/EFizRw8rAAAAvEZgBQAAgNcIrAAAAPAagRUAAABeI7ACAADAawRWAAAAeI3ACgAAAK8RWAEAAOA1AisAAAC8RmAFAACA1wisAAAA8BqBFQAAAF4jsAIAAMBrBFYAAAB4jcAKAAAArxFYAQAA4DUCKwAAALxGYAUAAIDXCKwAAADwGoEVAAAAXiOwAgAAwGsEVgAAAHiNwAoAAACvEVgBAADgNQIrEDFNb+xRhw9/rP5+7Jg5A3Teb+q3qYqvD1U3jP+yerzuAXM2PZmDC+ZO0V83a9pE9cc/vG5+BQCSK2k7zoyBnCkpKVH5mlryvffse98cRY8EzXff/YsaOuQCc0aphx9dpYaPusYcpTbqixervXv36nGfPn3Uztfe0mN03YB+Z0ZyXkpQbXjpt3qcyZyS+Xv1lYPa56HIdP6ia2SO8pbvh3y+RxYrKqxAyJzUo4d65+195iimtbXFjFKbPXVMQkgYefU3zAjIjdNOP9OMUptTeW3CPJxw/RTCKoAOEViBkOnMR/nyUe22bdvMkVIXXjRQ3XHP/eYIyI0jhw+bUXLBeTho0CDmIYCMEFiBkJEK67EsQuv2LZtUzd3fNUdKnX32J9XqjfHQAHTFsSMfmZFSPXv1MqMTJZuHT6zdouczAHSEwAqEjFRYe2TwJi+vaz74N/UfM79pzsQ89vONqsdJPQgKyIkePU8zo+QV1lTzcN2metWr1ynmCADSI7ACIZNNhXXsNUPV0aNHzJFSj67coM7/3EWEVeRFsgrrsb8fO2EertqwVf3TOeeaIwDoGIEVCJlMK6xyc8vb++N3bFctvFd9cdgIcwTkXrIK6y0zr0uYhwvvuk8NvuQycwREQ0NDg6qurlY1NTV6L+xYNvl1pEdgBUImkwrrsofuT7i5Re7Cnlo5xxwB+RGssAZvspo+fbqaNOUmcwREx4ABA9oDquyFHcsmv470CKxFpLW1VfXt21ev71ZbW2vOnmjw4MH6NZWVlebMieQvkLxGvh/80lGFVRZyX1rzPXMUWxHgwdqV5gjIH7fCKvPQvcmq/NIvqHm3syIAoqm0tFRfsCUj5+XXkR6BtUht2LDBjBLJxw67du3S43Xr1ul9MnV1dXrPXyL/pKuw/vmd/WrapDHmiBUBUFi2whqch2VlZfpmPyDKlixZYkaJUp1HIgJrEZFwedVVV+mxfAwnFdegZ5991oyUamlpUfX19eYoThb1tgt7T5gwQe/hj1QVVjk/ueJqcxSzcu3TrAiAgrEVVncennxyT/XT1U+zIgAiT96jq6qqzFGMHFMYygyBtciMHTvWjJRavXq1GcW5gVVs2bLFjOLcc6NHjzYj+CJVhTX4BCF53GX/8wYQVlEwUmGdNW1i+zyUsLp+Uz0rAgDGrbfeakYxwWOkRmAtMhUVFWak1DPPPGNGca+88oreyxNmxLJly/TeZb9OngteXl6ux/BHsgrrTx99KOHmFh53ie7w0Yfvq8aGF8yR0ktZffjhB+YIgFtlpXc1OwTWImTDaDCwysf/0gYg5s2bp/dy7LYOyNj2to4bN07v4ZdkFdZ/GZx4YbH16V/qPkKgkHr06KmW/yyxV3XOjEnq8OGPzREAueFZCkL0rmaHwFqE7J2IwR5V+1H/iBEjEiqx7ooCe/bsMSOlrrvuOjOCT5JVWGVdyzsX/cgcxf7s5aNZggIK7eKBgxPuhj5w4K9q1o0TzREAuQlx8+bNVFezRGAtQqNGjTKjxH7UrVu36v2VV16p9xJcRWNjo96LjRtj1RG5+hs2bJgewy/JKqxyPHHSje3VdfH713erJfcuNEdA/tlVAmT5KllOzXr+ue16TVYAMbTbZY/AWoTk6k02sWbNGr0XdjkrG1jt3l3eyr7erjYA/6Rbh/WJtVv0xYa1ckWt2r5lkzkC8stdh/WxlRv1TVeWrMna+PKL5ggAskNgLVL2oQB2iSq7YoB7I9VNN8WfOCOtA/a1wl1tAH5JtUqAkKWDHlj2C3MUI60BzQf/poMukE/uk676nvWP6sePPGGOYuhnBdBZBNYiZaunQqqmr776qh67lVPpn7HVuCeffDKhfcDtcYVf0lVYxZDLLlc3z409q9q6cdJodezvBFbkl1thFbJShaxYYXWln3Xp9+9QA/qdqbdRX7yY4AtEDIG1SEkV1bYFyNqrtn81WDmdMWOG3m/fvr19VQHb2wo/pauwWrPmzE/oIcykn1WC8M4Xn1c3jP9yezCQ7YrLLlS/XL/KvApIza2wWnfXPKA+fe5nzFHn+ln373tTLfvJUnOk1Mm9TjMjAFFBYC1iw4cP13tZn9P2rw4ZMkTvLXuDlrQC2F7WMWPij1SEfzqqsFrSQ3jqafE39nT9rPI9rx97lZp07dWq4aXfmrMxb+9/S83/VqWaPZV5gfSCFVbryfWJDyjJtp918ffm6r1brQUQLQTWIhZclsq9GctKthIA7QB+y6TCKq+RHsKlDzxmzsSk6md9992/6IsWCQTP7fxvtWff+3p7affe9pUH5MKHSivSSVZhFfKkq0U/eNgcxcy6cYJ6771DJ8zFIKn6y9wbcP6F6pqvjzdnlX7kMIDoILAWMQmj7h3jEyZMMKNE7gMCJJywNpzfMq2wimAPoUjWzyqBYudrb+mPb+1jNOW/I6H34cfXt1dqt/36Kb0HkklVYRXjJkxKmIuyVvA3K67RF1epSJ/qLbNjX/ODHy9PmPf0ZAPRQmAtcs3NzaqtrU1vixcvNmcTPfXUU+2vcddkhZ8yqbC67rjn/oTKeqbrs9og0bt3qfp/l/yrHrf9Q/IKGiBSVVit2+5cos4++5PmKDYX5WaqVDas/YW+UUsuvM7/3EXmLIAoIrACIZNNhVVI8Pzp6qfNUUw267PK15/Ss0SPLyA0II10FVYhy6499vPER7fKzVTysX+QPFr4R/fdqcc198efxgcgmgisQMhkW2GVgJu0h3DaRN1DmIzbVyg3x0gPoeh/3gC9B5LpqMIqpFJatfBecxRz+62zzSju4QeW6LaBb1fdqT7xid7mbJz0sLrzFEBxI7ACIZRthVVID6F8tOp64tGHzCiR/RoJq/82IfY1stzZV74W73cGxM23LNDzSvrfZ3+rypxNb2rlHLXwrvtU+aVf0Ns130i80VPm3ZpfrNA3Wk2eNsucjTt6+CPdw2rnKYDiV9ImjYtAjpWUlOie2HyQ7y13sEfda7sb1dGjR/R48CWX6X0m/viH19WHH36gxwP/5ZKEN/377rpF/e6ll/VY+gstCReTpsSfjIYTyZq1zMuuk6pp5eTxer3WHz60IuEiSYLsxDEj9RrDqzdu0y0GyJzMUd7yEVZUWIGQunjgYB04ZcuGfCQrATcYVsWf/vQnHVTdsCruvn2eWrdmpTkC8mfj+lU6rKar6B89etSMAEQFgRUIMQmcnf1YNNnXPfT4hvY1WGWTNVntUkQLvjNLLZjLwu3IH1nG6r57v6vHN38ndsNVKqzDCkQLLQHIC1oCiossPWQfjfmrLb9jiaEkaAnoOmlzGffVEx9mko7cTCj92egYLQEIMyqsQMR05s7q6yZNUyef3FOPt23+L70Hcs32ZGfj1FNPNSMAxYzACkRMZ1sIzjjjdL0/0olQAWRCeqvdlpTgtmrDVv06eRDG628c0OdYuQKIBgIrEDGdqbC+8PwOvSamOP+C/6v3QHc57Yze9LACEUNgBSImWYVVVgC44rIL1a9/tU4/Ycj1eN0D+oYrIetiBtdyBQrFtqV89MEhvQ4rgOggsAIRk6rC+vb+t9Tc2VPU0CEX6Jsz7FZzd+yubfkYdv2meta+RLexPa62wsqTroDoYJUA5AWrBISPVFYfrf2xfq77nj/+3pxV+glG02bNU5cPG67DqoSEzvbBFjNWCYDvWCUAYUZgRV4QWP2VLHASQruOwArfEVgRZrQEABGTLJgSVgEAPiOwAhFD3x8AIGwIrEDEUE0FAIQNgRWIGCqsAICwIbACEZOuwkqYBQD4iMAKREy6UEq7AADARwRWIGKosAIAwobACkQMFVYAQNgQWIGIocIKAAgbAisQMVRYAQBhQ2AFIoYKKwAgbAisQMRQYQUAhA2BFYgYKqwAgLAhsAIRQ4UVABA2BFYgYqiwAgDChsAKRAwVVgBA2BBYgYihwgoACJuStuPMGOi0+vp6tWXLFnOkVE1NjaqqqjJHSo0ePVqVl5ebo64pKSlRe/a9b46QLQmlVFJzb0C/M5mX8JrMUd7yEVYEVuREa2ur6tOnjzk6UVNTkyorKzNHXUNgzR/CbOcRWOE7AivCjJYA5ERpaamaPn26OUokldZchVV0HT2sAICwocKKnJLqZ1BLS4sOtLlChTV/qLB2HhVW+I4KK8KMCityKlhllepqLsMquo4KKwAgbKiwIqeCvay5rq4KKqz5Q4W186iwwndUWBFmVFiRUxJO7eoA+aqu0g/bNVRYAQBhQ4UVOWerrLlcGcB1x5QT+2SB7rbsV0rN+Jo5ADx0508VFVaEFhVW5JxUVfMVVgFfEVYBIH8IrMgLwioA+OVTfc0ACCECKwAAEcCnAAgzAisAAAC8RmAFAACA1wisAAAA8BqBFQAAAF4jsAIAAMBrBFYAAAB4jcAKAAAArxFYAQAA4DUCKwAAALxGYAUAAIDXStqOM2MAAADAO1RYAQAA4DUCKwAAALxGYAUAAIDXCKwAAADwGoEVAAAAXiOwAgAAwGsEVgAAAHiNwIqisnfvXjMC8qO1tVVvmWJOIt+ynZNAGBFYURRqa2tV3759VV1dnTkD5Mfu3btVnz59VHV1ddqQwJxEoWQ6J4EwI7Ai1GwomDlzpmppaTFngfw5rD6h9zU1NUlDwiOPrWZOolukmpNAMSCwIpRSBdXevXubEZAfvdR7ZhRjQ8KIL31Vz8lZ0yYyJ9GtCK4oRiVtx5kx4D3pBxw8eDCVKwDI0KpVq1RFRYU5AsKJCitCpaysTP1uV5OaPHmyOZOoauG9Sq7B2Njyte3YscPMtkRS0Uqmqqoq6fdhY8vVlmpOjhgxQu3cuZOwiqJAYEXonP/PpWrFihXq7bffVtOnTzdnY076n4/MCCiM8ku/oENBc3OzrvwH5yQtASi0YcOGqc07GtXWrVtVeXm5OQuEG4EVoXXOOefoO7CbmuIV11NOOUXvgXyT6pVUtna++Hx7KCgtLW2fk9dff70+d+jQIb0H8s3OSdlGDRtkzgLFgR5WFA3pb33zzTd1dQHIl2zmmbz2wIEDVLmQV/zbhyggsAIAAMBrtAQAAADAawRWAAAAeI3ACgAAAK8RWAEAAOA1AisAAAC8RmAFAACA1wisAAAA8BqBFShyDQ0NauTIkXqTBcYBn7jzU8YAkAyBFShyu3btUtu2bdObPA0H8Ik8xtbOT5mrAJAMgRUA0G1aW1vNSKnS0lIzAoBEBFagyBEC4LNTTjnFjBLDKwC4CKxAkSMEwGcff/yxGQFAagRWAEC34RMAAJkgsAIAug09rAAyQWAFihwhAGFB+wqAVAisQJEjBCAsuLgCkAqBFShy7l3YgG/ckMrFFYBUCKxAkeMubPiMkAogEwRWoMjxMSt8xvwEkAkCK1DkqGDBZ+78JLwCSIXACgDwAhdXAFIhsAIAvECFFUAqBFagyBEC4DN3flJhBZAKgRUocoQA+Iz5CSATBFYAQLfhEwAAmShpO86MARSh2tpaNXPmTD0uKytT5513njp48KA+PuussxLGW7du1WOgUNLNz549e6ojR47osczPtWvXEnCBiCKwAkVu9erVauLEieYoPf45QKHV19erK664whyl19TUpEMtgOghsAJFTnoEpYp16NAh1bt3b/XBBx+oM844o31vz4uqqiq9Bwqpuro6YW663Hm6ePFicxZA1BBYAQAA4DVuugIAAIDXCKwAAADwGoEVAAAAXiOwAgAAwGsEVgAAAHiNwAoAAACvEVgBAADgNQIrAAAAvEZgBQAAgNcIrAAAAPAagRUAAABeI7ACAADAawRWAAAAeI3ACgAAAK8RWAEAAOA1AisAAAC8RmAFAACA1wisAAAA8BqBFQAAAF4jsAIAAMBjSv0veC+r3U695SMAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\" width=\"513\" height=\"241\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity2(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 0.1; K2 = 0.2; K3 = 0.01; K4 = 20;\r\no = ones(50,50);\r\nK = [K1*o K2*o; K3*o K4*o];\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.0916;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 5; K2 = 3; K3 = 8; K4 = 6;\r\nK = K3*ones(50,110);\r\nK(1:20,1:50) = K1;\r\nK(21:end,1:30) = K2;\r\nK(1:20,51:end) = K4;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 2.5471;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 0.1; K2 = 1;\r\nK = diag(K2*ones(50,1));\r\nfor j = 1:9\r\n    K = K+diag(K2*ones(1,50-j),j)+diag(K2*ones(1,50-j),-j);\r\nend\r\nK(K==0) = K1;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.2945;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 1; K2 = randi(9)/10;\r\nw1 = 10*randi(9); w2 = 100-w1;\r\nK = K2*ones(100); K(1:w1,:) = K1; \r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = (K1*w1+K2*w2)/(w1+w2);\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-02-02T15:06:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-28T03:19:00.000Z","updated_at":"2026-03-23T06:38:42.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52070,"title":"Compute the effective conductivity of a heterogeneous aquifer","description":"Slow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water  to the gradient in piezometric head  by\r\n\r\nwhere  is the conductivity of the soil and  is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow  (and the specific discharge ) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \r\nSome aquifers, or underground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of  set such that the aquifer produces the same flow under the same total change in head. \r\nFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If  is 2 m/d (meters/day) and  is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \r\nWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \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: 634px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 317px; transform-origin: 407px 317px; vertical-align: baseline; \"\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: 311.833px 7.91667px; transform-origin: 311.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \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: 56.0083px 7.91667px; transform-origin: 56.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the gradient in piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 19px;\" width=\"39.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 7.91667px; transform-origin: 9.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4167px; text-align: left; transform-origin: 384px 17.4167px; 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,iVBORw0KGgoAAAANSUhEUgAAAKoAAABGCAYAAABc8A97AAAGTklEQVR4nO2dz5HiPBDFXw7c9ujrHkjAERABEXxkwHkvkwJVmwEhkAMpEAMpfHuwu/QsJOuPDRjzflU+zIgBj/zU6m61BCCEEEIIIYQQQohsmnffgBAhtgBaAEcAJwB7r70BsOvbLwA2L707IeAEegfwf3+xEE2c1nZ79Q0KwZgYr5F2E+rpZXckRIAbOiEeA20tnFB3r7wpIZgGTohtoP2nb7tD/ql4IweMC/Hat19eeVNC+JwRF+IGztqG3AIhnsIGLtV06H9nQjwEXr+j9i39vulff/R+L8QkNnBpqDM6X/QEN637QjROcG6BccAwnXWHFgnEDDRwgvST+Sy2EJYNOPc/m7htEUDZADELDZz1C03tY/lRzgbs0UX/Z2r/oXZZVFHNBuMRuy9Enz2G/qu/KmXvHbPGi2YDN/oudB2gUccc0VmnS+DiAKXFY19e0FnA1HR7xLgPyUIMpaUsG3DrL/ZhORtwfvzTyRzxpCxDA+d43/oPafG4lvzzjA//YMwHNEGFEu7AcL09pw/ZWsaWPe15xZZNOWDyLe5upG0qdu+x+6pmj7QQt9B6cQgWYMyCmOW7Iz9oMWsaW21K5Uf5eYUE80z/1Ppk1pUwG5U5CWF+raLEoVhi6SET6TXSHiP1sFNC5vbQs3rWahVb6lifFMOjKueG+Sa0HDfsjxseBWX9W+MDjllDtpYsZLaMLHQfHmCWSZjDqm4wdIVmMWjsiOcmfLkKJ+bAfxM80FmMDTqh3BFOKeUQE+qG3psNxh5Dl2zMTeMB1qAT/hXTn+cRnVB55p0U03BurmQN2Bfqt0//bD1MkDt0fXtDPLDKwSJ2Dnba/n0PGApxj2HqKZXItwFms8Bl4r0CTlM77/4mZRRY8SUOr+9/fLNQOSo3y8RT/dSptMXQmNizMtFym7+9JFXWxwHgWKaihDOc9WeDVh35+x1cEsGzg14SLe4RzjeWXksqnvBdJwtO5syIcOHIHkPRWdowFsDZ38Te14pa5nDfTJh2L36QWfUZ7FeVRmX+SMy9AV/gtdeShMqzUu3AXwtXPP7fbPGrnhtX24Qi1TH4gZRE/Q3c4sGUa0nwg/BFu6QB9WysEsufXdmoVbmItaPf909ro9lXscV0VyNn8cOmNhbrt6TuNuhEGuonnrmLI38/ai8RG0ehpZb4Hfj/a80Vi1g5qrVgwff9vyHQNDGGBjlnRIoj/9r0kv8Qlm5NgW4gTXU1YsFibN2effHZ17kXhs0qB4T7LjSYs6kd9Tyt1TyAtUX93IfsO9tU+EkDupYLxrUwOfLnjswRKlvhG+ryg2uK+tlXD2U+Don2XH6/4crF+iCln0nPrmR5iy3ElMTwmqL+nPoI9s9qlhD/Yp6BXXr9l3l/N+TNrJMif14+Havs5ury0sqfNcPpvVRZn/Vx6Sz0C8CfN1w52OyYI7zSGtwHuCPPeJye/PrUpUf4r6LEx+fXrSVdtYXTRY4mOFNU3QeWZzTfk9MKd3Qugqxoh+2lZ2tqM00L99As0xDyyc/eaz8NNl42m8T00QZen/qbJOYY//QfIHE+kkp1+ULNee2nEfpfxoQau6r0ZS5ASULWai210W+5NFjR8/GLU+4Y7o6M7XqcUgwsnsMW3bRqu10/YeUwCZ+6kbrYdzUxf8PS4Kexxcq2CVnxhF+H2KIbjTEBX6Ho/xNIpc1Wh315wSc7/98GV3QpIBaLxZZuV+GfivViccQzjucRYhZC+/SFeDu2h992Ifj79JktOvHagW7sFtjhwHYInhCzsIOrXLI04QluqfLmvd5O1Asd28RFR5bZkW8rJmP1A76guF54bA+clR5aed4ZLuV4gPLjYgZMpKHCdRbqmNj4LH8721WI2Ugdz5P6jimDSztrd2oIEYRPx4tZwLHvmGK4llaHMYtZ4f1Xoa04vFUoZ9nURP+Np7mIJ2LCiq028XSeWjb1NyUKMQupL4NgtyC1bGr75DhNpXoAMQsczaeOzDEh26G8Ple4b7UJrWAtZYev+EDGvtxjj2Gy3so2QwfynjC0yH5w5p9ULUQxfD6AHZ1jB+ayf2q1xJa456J3f4GA86n8dZNCVNPicSfnCZ3weBq/weVY/TOfxhYIJFIxK7Ei9phPaoXvMZpEuxBCCCGEEEIIIYQQQgghRBn/AIVPgzHP7TJeAAAAAElFTkSuQmCC\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.91667px; transform-origin: 104.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the conductivity of the soil 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);\"\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: 244.283px 7.91667px; transform-origin: 244.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.1333px 7.91667px; transform-origin: 87.1333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (and the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 19px;\" width=\"57.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 227.95px 7.91667px; transform-origin: 227.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 7.91667px; transform-origin: 57.175px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome aquifers, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.6px 7.91667px; transform-origin: 325.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\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: 252.433px 7.91667px; transform-origin: 252.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.917px 7.91667px; transform-origin: 376.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.225px 7.91667px; transform-origin: 83.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 m/d (meters/day) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.125px 7.91667px; transform-origin: 251.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.242px 7.91667px; transform-origin: 376.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.458px; text-align: left; transform-origin: 384px 104.458px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 382px;height: 203px\" src=\"data:image/png;base64,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\" alt=\"Aquifers in series and parallel\" data-image-state=\"image-loaded\" width=\"382\" height=\"203\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,1:2) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,3:4) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(1:2,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(3:4,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10*rand;\r\nK  = K1*ones(7);\r\nKeff_correct = K1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,10) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,5) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(10,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(5,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(4:6,:) = K2;\r\nK(7:8,:) = K3;\r\nKeff_correct = 3.875;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(:,4:6) = K2;\r\nK(:,7:8) = K3;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(5:7,:) = K2;\r\nK(8:9,:) = K3;\r\nK(10,:)  = K4;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(:,5:7) = K2;\r\nK(:,8:9) = K3;\r\nK(:,10)  = K4;\r\nKeff_correct = 1.5584;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-17T14:24:44.000Z","updated_at":"2026-03-16T13:48:00.000Z","published_at":"2021-06-17T14:30:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the gradient in piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw: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 the conductivity of the soil 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=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (and the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \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\u003eSome aquifers, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"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 set such that the aquifer produces the same flow under the same total change in head. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 m/d (meters/day) 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=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. 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