{"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,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACqElEQVRYR+1XPS9mQRTmB4hga4WPmsJGIhQaK6tUWKH3VZEgaNmw/S4SSpZKIrFZlYJoKKh9FGp24xfwPDJHzjt33pm5Ljck702evPe9c865zzznzJm55WXv7Cp/Z3zKSoRCGSkplFWhdgRo8wS5x9iqGZ/y2K1j7C5EhuMxKauB3QQwqwJe4b4LuLZe8g3/f5tn//G7CPyIISI2MYRoS6UOVeB6BxkO/wJGABLuBc7TkIlViHZDwIoJvo/fbseLhAzHB4CoFNlxYhX6C8cvxnnaSgNT+hPoA+yxtAJF1RCDPqjIHbg/Mv+b8LsGMIWDwJ/UDCyHGIW+wmfP+LFQG006JI2sl9aXpuglKVuAk6ywbdyPqRQt4340qyraP0ahEzi0GCcS4HKvBmYA6UGvxilEiAV763hbsT6UmViIkN3o/pkC5ou/A3OZGaQsauktdGO6NgFpkCxwptLu1pk4hhS6VIr0434L0D2JRU4VYy69Lx7DQVpHga+PEHvMmbKW7cJ+3gwb3xbBOuQkqgBRlWFlxRZ0dB8hvV2wiBsUOZ3KUzz/7JGIZHYAWZGc0IEhmOjsPkJMD7cDXnYB1+EZiXDWvHoAV5emHZWwCctkE5PxEdLbheuFPP8sGULFujUJVQB2SuX0EE3IPm58QlB792ZtXCiVhlVaPBl8GpL4idZRTCG9XfhqRNulaQOibmJBuAiR/a6aOV/U6ZBdHztEEZ6FWKihgxnbCWsr0VhtQuwptUX0vsFzFjovnx3Hta0djgU9CehV+2wTaoyhWkg7LucnnjidJ8o8CUmDHAcZZ5fm7PIiRDIbwLyDDNMvpZALIVGGR137/MR6qgSeP5XyUEh3fFfNFXxSvTUhFrF8rbjIJFbjWxNKuwpzqaFUpEoKheQqKfThFHoEELuCKSbInJgAAAAASUVORK5CYII=\" 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":"2026-04-05T08:16:36.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57497,"title":"Locate image wells","description":"A mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \r\nIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\r\nWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. \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: 664.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.35px; transform-origin: 407px 332.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.933px 8px; transform-origin: 369.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370.7px 8px; transform-origin: 370.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.892px 8px; transform-origin: 365.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 406.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 203.35px; text-align: left; transform-origin: 384px 203.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 610px;height: 401px\" 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\" data-image-state=\"image-loaded\" width=\"610\" height=\"401\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [xI,yI] = locateImages(x,y,xb,yb)\r\n%  x = x-coordinates of the real wells\r\n%  y = y-coordinates of the real wells\r\n%  xb = x-coordinates of two points on the boundary\r\n%  yb = y-coordinates of two points on the boundary\r\n%  xI = x-coordinates of the image wells\r\n%  yI = y-coordinates of the image wells\r\n\r\n   [xI,yI] = reflectAbout(x,y,xb,yb);\r\nend","test_suite":"%% Vertical boundary, one well\r\nx = 100; \r\ny = 0;\r\nxb = [0 0]; \r\nyb = [0 200];\r\nxI_correct = -100;\r\nyI_correct = 0;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Vertical boundary, multiple wells\r\nx = 100*rand(1,2); \r\ny = randi(100,1,2);\r\nxb = [0 0]; \r\nyb = [0 200];\r\nxI_correct = -x;\r\nyI_correct = y;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Horizontal boundary, one well\r\nx = 100; \r\ny = 50;\r\nxb = [0 200]; \r\nyb = [8 8];\r\nxI_correct = 100;\r\nyI_correct = -34;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Vertical boundary, multiple wells\r\nx = 100*rand(1,2); \r\ny = randi(100,1,2);\r\nxb = [-8*pi 8*pi]; \r\nyb = [0 0];\r\nxI_correct = x;\r\nyI_correct = -y;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% C E 473/573 problem\r\nx = 0; \r\ny = 0;\r\nxb = [-550 1050]; \r\nyb = [900 -50];\r\nxI_correct = 503.4657;\r\nyI_correct = 847.9422;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #1\r\nx = [150 210 280]; \r\ny = [50 70 95];\r\nxb = [0 200]; \r\nyb = [0 300];\r\nxI_correct = [-11.5385 -16.1538 -20];\r\nyI_correct = [157.6923 220.7692 295];\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #2\r\nx = -[50 65 83 104]; \r\ny = [20 35 49 65];\r\nxb = [-107 -69]; \r\nyb = [57 22];\r\nxI_correct = [-65.4477 -81.6280 -97.0577 -114.7269];\r\nyI_correct = [3.2282 16.9468 33.7374 53.3537];\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #3\r\nr = 100*rand(1,2);\r\nx = -[50 65 83 104]+r(1); \r\ny = [20 35 49 65]+r(2);\r\nxb = [-107 -69]+r(1); \r\nyb = [57 22]+r(2);\r\nxI_correct = [-65.4477 -81.6280 -97.0577 -114.7269]+r(1);\r\nyI_correct = [3.2282 16.9468 33.7374 53.3537]+r(2);\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%%\r\nfiletext = fileread('locateImages.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-03T15:19:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-03T15:19:08.000Z","updated_at":"2026-02-12T14:18:55.000Z","published_at":"2023-01-03T15:19:28.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \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\u003eIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. 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oNV80Dy2WefVfep5R002jJtP/zwQ70FwEakGiDN5TneJwtQZoQst+zL53K8zyBczgX79u2rKgemabXz7jgXruP0tIwKaMoFewyqOEhA15xNq+n3v/99dZ/zZwKe9IqW6ovc5/sNm+gmjy/n3/TSjFp+IFmStcwcVuRnlNeXmUDLIGAz8IjyPNJDWios+q9virU+79z6ld/roOBl1OdgquoysbnQrOsctBhTv9Rypn+lfE1uK3/I9WfvVepIx/m+bRu2CFXZt3Lgqvfc0dZrKe9ts/YWYNkM6rEYV/o1+s9T497SdzBtq/W0jOp9KHLezWNGnSuaP6f//Wz2tOS9yjkvzyVfk+9Z9ud+0PPIvvL1w275+pVgoP6K3+Q6ovm4fK/83Dw21yTN5zDs+mI1zdee26Dfa/M6oNzy3IbZ6PMu79mo93PQ52Ca5irT0hzRGSfCz0JbZdRi5Y+rus8Ixajpg1cOXPXWeDJCkdGx3AaNVkxC6m3L8yolb83SsD/96U/11r2m/VrKewuwrDJiX/on1yrH8Z07d677WJoMzKhR9Emb1exhqZooZU55r5I9yLS9ee+TYVm5AK9m/4r+55FzWSkdy3VAHpvvlfvcVi7cq8/l+yY70X99kNe3cq109xoiGZv83Dy2ZGxKlqd/vZRx9VdKDFoos3kdEPk/17wm6jep5z3q9yrTQts2JXKptzsvB5McqCJp0VF1vM3H5gCVPpbyB5/7H3/8sdoucuDPopMJasYttSpfU0zzrSwHmUhtbl5/DkI54PYHGG28lvzMshhYDopXrlyptgGWQc4xOWbmwm89x8CUEmWtjEm4fPny0GbyjcqxPufalG/lPNp/oZzAK49JSdKw803eq/RhpLF9WE9p3o98r/ycBBODlOfyr3/9q/fYY4/1tmzZUv3M/OzyudKzUuRz+R3lIv/atWv13ns1rxdyUX/+/Plqu1+eYx6bHpvvv/++2pfys1z0b/T9L+f3TEjw5ptvDgxIynudx6TMLa9tHOt53vlZ+br+9zPG+Z3DVCRomRc/NdKdg9KZTSXtmfsiKdHy9SsHxXrvHaWkKqnTcSQ9Xb5Pnku2R5UI5HNJ7ybNvR7N156f2dzuN+3XEs1U9aDnALCIcixuHoNzWwla6s+Or5yjJnXL8+JezbKynLNGKb+PQaVZQDfMbXnYf//733rrfslKlLTnp59+Wt3Hyonmbio4oxoZRRgkWYdSJpVb/+OSEs0MH8lkJIuTkYtkb0aVYyUzUlahXU9KNa+9lCCUEZloLkA5yDReSzSnp1xtBhaARZAR5mSYm8fgKFnnceXryzlqUlIOzb3GmbAnch4sv49MHw1009xNeVzqM1PLO0guyssJJWne/gvqUvcamXmlKBfp+ZpcxK8EdNUtwUYCjaRWiwQQKS8radGkqVMPO0qZez1We+wwb7zxRr11R4KYQenhab+WSGq4eOaZZ+otgMWU42aOqYOOj2X693FlYG3S0ufRPC5z71onKeVrnvuKXDM0V5VX7gTdNXdBy+7du+utOwebfiUQyYV7M0ApUr9ZAp+MrCQTEeVElECgWZucGtl8r48++qjec79SIzpKmc4x32vcOtR+/QfT5sKTTdN+LVHmks/3k2kBFl3OHeknLOePpuYihKsp55xpSCaI32RQrlwH5HyfaodUHOQcnLVvsp2BvPSHRioOnM+gu+YuaGk28WVO834pB8sqt8nENMvJmnLBncekeTEjZ0392YzIAlM5mA0r60p2YpRm6rk5orMezefb/9z7TeO1REbzSqbrtddeq+4BFl0udjMQlDLjDNisRzPrPmllMInf5Joh5/tUGhQ5H5dzWH6PKR3PYJ8sC3Tb3AUtzd6OrB7bL6MkuY3KZuR75DEZORsW2DStNl3jatmJUmucg2OyHeuVQCMBR2S0b5zn3m+jryWao3kO8sAySaZk8+bNVVltLnaj9EqOY5pBiwV/B8v5PufeUiqdjFlu2c7vMf2c6zmfAu2au6AlSrYiIyODalQnbbV65VHZiQQaqTWOc+fOVffrVQKWaI4arcVGXkvxt7/9rbrPiVoqHVgmx48f773//vvVdi52c/G7lr6+aQYWJaPPaBnUXG+ZNjA7cxm0ZHSrpOY/+eST6n6aMid8sjvDRmJGZSdKliVBxkbncW+Ww603w7GR1xIpDSsnxkE9QwCLKrM1piS2OViz1gvg5syLAIxvLoOWOHHiRHU/qRreEgSVrEiRi/Sk80eljkdlJzIKl96TU6dO1XvWJ5MOlGBhtV6Wab2WKOVt+RkbDcKSJTt48GDVEJkJFjSRAl2VY3DON8mubMRap0dei3LsB1hEcxu0pLkuGZdkMoY1la9FmXEr3ysX0kUyJPlcfwDQNCo7kabNrK670XrZf/zjH1UfS24lYBtmWq8lMsKY932jpW6ZljozuaTkLQ2Rmb0lwdg0pgIF2KjM1jiJ7PJGzwWjTDMgApi5X6msXDzfXVV45eL+7iq6ZV+/hx9++J7HNG8rgUX9qNno+mtprlI86JbnD9AVK8HKxFZKz/cadNybxO2tt96qfwrA4tmUf1YOdtCaZH+akwr0S8/NtWvX6o8AZicZ62QwkhGeRPN2vt+0yrgyta/JUYBFNbflYcyv//73v/XWYOkDAuiCTICSGSsnNdtUysNW60tcjwz2CFiARSbTQuseeeSRu303w/hvCcxamu937txZreUxSdPItmSwxzS+wCKTaaF1WZV/NZnpDGCWJtV83y/ZllElsmuVGc0ELMCiE7TQuj/84Q/11nCpIc9MYhmRBGhbVr6P9a6JtZp837Ki/kak1GwS32deZObJTJNffj+LLIN3ZUkAQHkYM5KDcKY5Xk1KKDLFc6a4BmjDpJvvR8n6VOvtcUmGZZkClmZZXTJV0woou6SUUyfj5zzIspNpYSayfk1OtuUElPusI5O67DSUFjlYv/7669Vok5IxoA1Z/ysr37dRcpUL7xz3nnzyyXrP6nKMzExhyxSwRCZFiJwvliFgiUwCEZNaSBvmmUwLnZTRxwQr/Q37CWxOnTo11QXagOU1reb71WRg5o033qh+frIIt2/frj9zR4KaF154offSSy/1XnzxxXrvcilZh5wHzpw5U+9dbM3skskWWHaCFjotfS2pYW7KATyp8mUZaQPaU4IHx5duaZbRLdvFe/5PplQxmbWUBMKyUh5Gp+UAnRPUrl276j13SsZy8sqBPKOSAJOQ5u5kcQUs3VN6IDNotWzZhlIi9re//a26h2UlaKHzcoJKD0xKJkqaPDLytHXrVrOMARuWY8jx48d7Z8+erfe049VXX3X8GkPp6SgX8MukLBqaAbtknGBZCVqYGxn9TJ15f/NpyscSzDiYA+vVZvN9kczON998o0dvFcmol/7G5557rrpvStCX80AGsP7+97/Xe++X9zuPmda5Is+zlDSvFojmOYz7XJo9TOPMugkLKz0tMG9u3br167Zt29KPdc9t165dv16/fr1+FMDqcsx4+OGH64/asXIRXv3MHMsY7fTp03eP8ZcvX673/ibvYd7LfD73eW/75XdcvseRI0fqvZP11ltv3f0ZFy5cqPfeL8+vPO7AgQP13tHK68t5D5aVTAtzKaOh165du69kLKNQSsaAtZjWyvejJLOTUqdl689Yj2Sjimeeeabe+k3ew/L7S0YmM0/227dvX3Wf88W0Zh5LqV/x2Wef1Vv3y3mrGGex5SgZppRFw7IStDDXSslYpsBsSno+i8MpGQNGmUXzfcqI0qOxLNP2btQXX3xRb90JUAbJ76+s8ZWgoFkmlkGsMoX0uXPnqvtpyHNrPodhA2elPycB1Lj/7x577LF6685K+bCMBC0shJz8M8tYOWFERtwyy1hW3zfLGNAvF5WzaL6fRWZnETSz6oNcvHix3upV2Zb8fnMr0+bnfDDtNW4yXXbRzKg0lb6UtUwq0Fx89D//+U+9BctF0MLCKCVjuRhQMgasZlbN96ZVXpuSJUn2fJT8HstELfmaBA0lMMg5oY1Asfl7HbSKfX7/RRYKHdcTTzxRb/V6P//8c70Fy0XQwsI5evTo0FnGlIwBUUq02l6sb8eOHa1ndhbF008/XW8Nl99nyUok21KyGidOnGhtlrZSrpyf3T9QVgKZPMe1ZH2aA3GpIoBlJGhhYeXkdf36dSVjwH3SmD3N/oZhsuZGm5mdRfL999/XW6P1Z1RyDshgVluaGZRmZiUBTAmich4C1kbQwkLLBYJZxoCmXEhu3rx56v0NTTnOONZszLjvXyknK9Lv2OZ7n/9X5XzTLBFr9rg0Zxobh+wKCFpYEqkzzolLyRgst8y8NIvm+wySDGvMZjw5hq8mwUl+v1HKxIZNgxyZZWzTpk0TPwekVyoyRXGZ7evDDz+s7pP56c+2rfY8vv3223rr3qZ8WCaCFpZG6plTMmaWMVheOQbMovn+0UcfbbVEaZE0g4/VJDgpj7t69Wpv165d1XYCxkHH98cff7y6n3Qmo5lJyeyWCabKGiuZPa7fas+jmT0qj4VlI2hh6eRixSxjsHxm0XxfRv7LKDtrl8kLilFrlCRbUbJZ+R3nWN/MqJUFJpu+++676r55LpiE/OwyOJbn1MyyDepnWe15NPt5ZFpYVoIWllZGPZWMwfLIRWvb66OUle/TX8f6NC/SR61RcujQoeo+F/7luJ7goTkNcgalmoZlLRIcpVwrt7LOy1qVjEp+bilZS+Zn0Cxmq2VPvvnmm+o+70Vbs6BB1whaWGqlZMwsY7DYSvN9m+ujlMzOqVOn6j2sRzPgG7ZGycGDB++WVvXPCpdjfMlgJABpZtJLhqPf559/Xm/1ejdu3Ki31qaZUSnPrUyH3G/Y8yjK1zezTrBsBC2wwixjsLhKidYsVr5vc32QRdUMND/77LN66zcJDkv5VTIZg2aFawYyzZXox+kPWW85Vn7v/aVgw4LmUc+jOXD2/PPP11uwfAQt0GCWMVg8ac5uu/m+9F5ovp+MZkP9IDlmJ6Ny5cqVes+9Esjk87klg14My3A0B6nWOj1x05tvvllv3XmOw4zKtJw8ebLesr4LS+5XYKCV4OXXbdu2/Zo/k+Zt5eT56/Xr1+tHAV2Wv9WHH364/oh5tRKs3D0Gnz59ut67cfn/ke+Z79+U/zPZf+TIkXrP+qwESXef9+XLl+u99xv2PKI8l5yPYJnJtMAQZhmD+Terle+ZrD179tRbvd5XX31Vb23coAxHMuvpIUlZWKYr3ojSz5TvNWox02GZlsyIVvpZBk2VDMtE0AKrMMsYzKdZrHyf/oM0hTNZ6Q8px+BhJWLrMaiXpAQaG51prhlwrFbWNayn5ZNPPqnuM3Cm1JBlJ2iBMZhlDOZLWfk+s3e1KZmdP/zhD/VHTFKzP2RSg0X9GY4EujmuJ0DaaLD70Ucf1Vur98UMy7SU/79lhX1YZoIWWAOzjMF8yCBDLvTanLmrrHzf5rTKy6QMHmXgaNQik2vRn+FINuPXX3+tfs5GlYxQnu9qk0AMyrTkXPLcc89VkxA0AzZYVpvS2FJvA2uQE0pmdelfeCzBTGro2yxJAX6TrOfOnTt7P/74Y71n+nI8SLno119/3eosZWxMSrj27t1bBRizDDa78jygywQtsEEZ8Xv55Zeri5WmjK5dvHjRBQy0LH9z6Udoc+CglP9stHEbgMGUh8EGDZtlLEFMRl6VjEF7ZtV8n94DAQvA9Mi0wIRlxLV/5e1Md5kyMml/mJ5SopXZ/trsZclEHFll3exOANMjaIEpyMhr5tTvLxlLQ2UCGiVjMHmZanjLli0jVx6fhvy9Z5IOAKZH0AJTlFKVTLta5uovclGV2WDaHA2GRTaL5nsA2qOnBaaoLEx55MiRes8dZWHKzBgDbNwsVr7P369+NYB2CFpgypJNSYPuoIUpM8Xl9u3bJ7bmACyjWTXf5+8XgHYoD4OWKRmDyUnAn8GAtpvvM9iQvjXN9wDtELTAjJhlDDYuf0dZhX4SK5iP6+OPP64GGWRIAdojaIEZMssYrF96Sl5//fVWg4f0sGQ9pmR2/H0CtEdPC8xQpkkdtDDll19+aWFKWMU777xTZSbbdOzYsWpiDQELQLtkWqAjEpzkgqi/ZCzBTGZFarPJGLouwcqVK1eqW1vKtMpt988AIGiBzhlWMpZm44sXLxrhZenNauX7TKIRmu8B2idogY4yyxhdkv+PCRbaXm1+kKx8n0kr2my+B2C2BC3QcWYZY9ZK83nk/156sGZVrmjle4DlpBEfOm7QwpS3b9/uHThwoLd7927TrjJ1n3/+eb115/9eFlXcyP+9BEHrbaDPyvcJmtqUgYNSGgbAbMi0wBxRMsasJEDJrFmZ2a4p+06dOrWm/3sle5jszVoyJgl0bty40Tt//ny9Z/o03wN0g6AF5oxZxpilsjZKMi5F/u+dOHFirAb1BD9poo8EPMkkjiNfl2xjJqhoczKK/CylmACzJ2iBOWVhSmZpUNZvnH6XlJWVbE2+dtzsxaxWvv/rX/9araUEwGwJWmDODSsZy8VdRr6VtDAtyfqdPHnyvv6UYYFzAu2tW7dW2wluxp06ONmdQ4cOtdp8XyYfsPI9QDcIWmBBmGWMWUnpVgLnCxcu1Hvu6O93ycV/yspKMDBuQL19+/beu+++22rp49tvv9374Ycfxi5fA2C6BC2wQDKSndmVmv0GkZHvS5cuybowVcmIvPPOO/eULJZ+l0gvTFy+fHnsACRBd9sr35e+G6dHgO4QtMACMssYszTs/18kgB43AEmJ1ixWvo/8bH8nAN0haIEFlYuujGz3l+zMenFAlkdKrPr7XbLm0LPPPlt/NFpWvt+yZUsnVuEHYLYsLgkLKqPEWc9i0MKUG10cEMaRySCSJclCqJEel3EDlpQ6ZlHLNgOWBPrJEgHQPTItsCQy4p2maLOMMQ/StN92RjCTWfzyyy+tLl4JwHgELbBEMpI8aGFKs4zRJfm/aOV7AJoELbCEzDJGV5WV79sOHjKt8v79+/XPAHSUnhZYQukryMVhym8yJW2RlcrzcRqok5WBtmXWsWQD2wxYsvJ91mQRsAB0l0wLLDmzjNEVWecl/xfbnCAi//+tfA/QfYIWoJKSscOHD9+zMGCkZCw9MC7omLZZrHyv+R5gPigPAyopGbt27Vo1m1h/yVgW+EtztJIxpiX/v55++unWM3uPPvpolVEEoNtkWoD7mGWMNuX/26xWvgdgPghagKHMMkYbstBpbm0vJOn/L8D8UB4GDGWWMaYtzfc3b95sPWDJ/1//dwHmh0wLMJZc4JlljEnK/6lkWGbRfB9nzpyp7gHoPkELsCZmGWNSPvjgg6rM8MqVK/We6bPyPcB8ErQA65KG/FOnTvV++umnes8dmX3s6NGjLggZKWWHab7P/582/69kWuUE3fk/CsD80NMCrEt6EDJafeTIkXrPHelz2bp1a9WrAMNk5fsEuG0GLFn5PgQsAPNHpgXYsGGzjB04cKB34sQJJWPcY1Yr3yezc/Xq1WqCCQDmi0wLsGHDZhlL034uFJN9geKdd95pfUHH9M/s379fwAIwp2RagIkyyxijpBcqjfdtNt8DMP8ELcBUKBmjXwLaZOLabr4HYP4pDwOmopSMpdl6UMlYRtxZLinPmkXzvUkhAOafoAWYqjLLWDIsTelzSbbFBeVymMXK95FSRQDmn6AFmLqMrJ8/f753+fLlqrelSOnY3r17ewcPHmx1JinalbKwWTTfZ+X7PXv26KMCWAB6WoDWDVuYMqPwKR9iseT3fePGjSpwbYuV7wEWi6AFmAmzjC2HZNC2bdvWevCQle/TQ9N2ORoA06E8DJiJUjJ2/fp1JWMLLCvfHzt2rNWAJWuyhIAFYHHItACdMKxkLOViLj7nk5XvAZgUQQvQGUrGFktmh/v0009bDR7yfyj/f44ePVrvAWARCFqAzikj9BamnF+zaL4HYHEJWoDOMsvYfEq2YxYr36cMTUALsJg04gOdleBk0MKUCWYsTNldmbUr5XxtN9+//PLL9UcALBqZFmAuZN2Nffv2KRnruPJ7anvmt0ceeUTzPcACk2kB5kIuRnMhnLKwlB4VabrObFHJvjBbKQtLwJLm+zZl5ftkdwQsAItLpgWYO2YZ66ZZNN9b+R5gOQhagLlllrHuSBYsGa+2m++z8v3hw4dNcQyw4JSHAXMrGZVRJWNvv/12vYdpy8r3+T20GbB8/PHH1b2ABWDxybQAC2FUyVjbCxwumwQPmemt7eb73bt3986ePSujBrAEBC3AQjHLWPvyngoMAZgm5WHAQmnOMtZklrHpSAnejh07BCwATJVMC7CwzDI2XbNa+T5lYe+//75ACWCJyLQACysX0pl+9/Lly1WgUqR0bO/evb2DBw9WF96sz6xWvr9586aABWDJyLQASyMXvMm89EspWRrJGV+ZbrrN5vsEmCnxs/I9wPIRtABLxSxjG5f3cOvWra2/X1n5/pdffml18UoAukHQAiwlC1Ou3yxWvp/V4pUAdIOgBVhquQAftAilkrHBZhU8JIh88803LSQJsKQELcDSG1UyZpaxe2Xygi1btrQa0KUX6cMPP+xdu3at3gPAshG0ANRGlYy1PUtWF81q5fsElcnsKNkDWF6CFoA+ZhkbzMr3AMyKoAVgALOM3St9P8lAtdl8/+9//7v34IMPyrAAIGgBGMUsY3cCuDTf37p1q9USuax8n5sJEQCwIj7ACGnCTw9HSsOakoHJhXxmH1t0Wfn+2LFjrQYs6Z/JyvcCFgBCpgVgTMs4y1gyTe+8807rM3c98sgjVr4H4C5BC8AaLcssYwnSZrXyfZw5c6a6BwBBC8A6LfosY7Na+X7btm2t988A0G2CFoANWNRZxmYVPGzfvr13+PBhK98DcA+N+AAbkAv6ZCIuX75cBSpFSsdSWpUV5BPYzJvjx4+33nyf9+m5554TsABwH5kWgAlKSVXWNOmXXpd5uRif1cr3ADCMoAVgwoaVjKXc6t133+38LGNWvgega5SHAUxYs2Ts4Ycfrvf2el9//XVv79691exYXS0ZS5bohRdeaDVgycr3Vr0HYBSZFoApG1Yy1rVZxmbZfJ8FLC0kCcAwMi0AU5aL8Z9++qm3a9eues8dCWRywZ51X7rgyJEjrTffZ9roELAAMIpMC0CLurowZZrv//rXv85k5ftz5851vs8HgNkStADMQLIsKRvrN4tZxtJf89RTT/WuXr3a+sr3v/zyS6uLVwIwnwQtADOSYCG9HF9++WW95462ZxlLAPXDDz/0zpw5U++ZvjTf79y508r3AIxF0AIwY8NKxtJjcurUqale1Fv5HoB5IGgB6IhZzDK2e/fu6tZ2I3yyTDIsAIzL7GEAHZHAIRmPtmYZS/N9godZzNwlYAFgLWRaADqojVnGMnNX2833meJ4z549FpMEYE1kWgA6KE346Tfpz4JcuHChWmW/rG8yrnyvpmRvEjy0vfL9yZMnq+cPAGsh0wLQcZOYZSzlZU8//XSVpclCl7Novk/vTF6H5nsA1krQAjAnNjLLWMqx8nXJcmRNlgQPbfaypH8mP68/4wMA4xC0AMyZ9cwylv6VZFiKZFo+/PDD1srD8vO//vprvSwArIugBWAOJWORDMu4JWObNm2qt+6V7zHtRSWz8n20uXglAItF0AIwx8YpGUtPzKDm9yeffLL36aefTi3bUkrBZtE/A8BiMXsYwBwbNsvY2bNn784y1iwLK1JKlq+bVsCSmcLSO5Pg6cSJEwIWADZEpgVgQQybZSwZlZKJycKVCWim3VuSmcJu3rzZ+/nnn6uPjx071mrjPwCLRaYFYEEkm3HlypXe5cuXq0ClaAYsly5dmnrAkpnCEjhl4coff/yx99prr1UTB+TnJgMDAGslaAFYMKVkLCVgTQkkUrK11oUp1yo9NgmaSuN9nkd6WjZv3tzbunVr7+DBg3f7XQBgHMrDABZYMht//vOfB84yNo0pjzNTWLI5Maj5PlmYBDWhZAyAccm0ACyorOeyb9++uyVjzRnEsmZKsh4JMtILMwnJnqRf5sEHHxzafP/KK6/cVzKWGdAAYBRBC8CCSRCwffv2Kih49NFHq30pGUuwMGiWsUmVjL388stVWVh+5tGjR+u9gzVLxvbu3VuVjE0qeAJg8QhaABZIApUEAcmkRH+2owQLacovMiVySrYS6Ky3UT5lX/mZmS0sZWfjSJYlWaALFy70Pv/88yoTlOwQAPQTtAAsgAQNjzzyyH0X/cmi9CvBwqRKxvLY0nyfKZfX2idTSsaSBTLLGACDCFoA5lzKwQ4cODBwEclRJlUydvLkyeo+WZaswr9eJQuU75NeHAAoBC0Acy7BR3/JVzEo09JvIyVj+VyyO2m8TwC00ZXv//nPf1Y/+9NPP633AIApjwEWSkqrkqkoWZfTp0+v2hTflKzNoUOH7svaHDlypMqi9AclZeX7Sa27khK3PXv29M6fP1/vAQCZFoCFkXKuzMbVLPlq9qyMYy0lY9nO+i87duyo92xM+lkSLCXQAoAmmRaABZEsxdWrV+82wpfsR7Iv65GvT4alf2HKNNynfGvnzp1VIPPcc8/dXf1+vfKz8r3WmhkCYDkIWgAWQGb8yvoo6U+ZtGElY5EA5vr16xvuZUnvTFy7dq26B4Am5WEAcy7N8JcuXZpKwBLDSsbi9u3b1TorG1HWeBl3fRcAlo9MC8CcS5bijTfeqNY7mbZhJWPbtm2rgo61rtESKWvL+i4bLTEDYHHJtADMsdIY30bAEmVhyjT4T2JhytJ8v5H1XQBYfIIWgDmV4OD48eO9ixcv1nvakUAjmZFhs4wlmEnJ12rKGi9pvt9oTwwAi015GMCcmmbz/SgJSLKWSgk0VptlbFjJ2KTXeAFgcQlaAOZQshSZcjjZjq5Yy8KUCXwOHDhQzTy2nj4YAJaL8jCAOXT48OHWF2FcrVdl1MKUKRlrLkz5+uuvV8GMgAWAcci0AMyZXPxnpq421zRJwJLFH5uLV44yapaxLEaZQCYZGb0sAIxD0AIwR0rwkNm61rvS/Xqk+T5rspw/f77eM55hJWO7du2q1pYRtAAwDkELwByZRfN9+mcynfFGMiMJejJTWFNKxlLi1tZ0zQDML0ELwJyYVfN9ZvnKbdCK+GsxjYUpAVgOGvEB5sQsmu8zy1dK0jYasERZmPLChQsDF6ZMNma1Zn8AlpOgBWAOpPk+pVltl1Jllq933323/mgy8hoGzTKW8rH06zRnGQOAUB4G0HGzar5PluWzzz5bc/P9WqRk7OWXX65eW1NKxrLSf5uvF4DuErQAdNysVr5vUwKkZHXGWZgSgOUjaAHosC6ufD9NZhkDYBA9LQAdNovm+6yt0h84tCXZpFu3blXruBTJvhw4cKC3ffv2KogDYPkIWgA6ahbN9+mfyWKQL774Yr2nfWYZA6Cf8jCADppV830Cgh9++KF35syZes/sDSsZO3HiRO/o0aP1HgAWmaAFoINm0Xyfmbwya1fKs7rW+G6WMYDlJmgB6JhZNd8fPHiwt2XLloksJDktZhkDWE56WgA6Zt++fb1z587VH7UjwcA//vGPTgcsMWxhyrNnz1bldHkdACwemRaADknz/aVLl6pG9DY98sgjvatXr/aeffbZek/3pWQsGZYvv/yy3nNHSsY+/PDDuXotAIwmaAHoiNJT0nbzfSRDMa/roAwrGUs25s0331QyBrAABC0AHbEMK99Pk1nGABaXoAWgA2bVfJ+fu0hlVGYZA1hMGvEBOiDN922vfJ+yqvzcRVqoMUHJtWvXBi5MmUb9ZLMsTAkwf2RaAGZM8/30DCsZS4A4rz08AMtI0AIwQ7Nc+f727du98+fP13sW17BZxnbt2tV7//33zTIGMAcELQAzlAUdn3zyyVab79PHsnXr1mq2rWWaWSsZrePHj5tlDGAOCVoAZmRWzfe7d++ubl1fSHJalIwBzB+N+AAzMquV71OStqwBSySrdf369WpGsSLZlwMHDlTBXIJJALpF0AIwAylV2rx5c+/FF1+s97QjF+Tvvvtu/dHySh/LoFnG0veS0rlkY8wyBtAdysMAWlZWvr9165Y+ig5IcHLy5EklYwAdJmgBaJmV77tp2MKUZhkDmD3lYQAtSnlW1mRpO2DRq7G6sjBlsitKxgC6RdAC0KJZNN///e9/7928eVOmYExHjx6tZnTrn6wg5WNZUyeTGQDQLkELQEtm1Xz/+uuv9z799NP6I8ZlljGA7tDTAtCCsvJ92833yQ7cuHFjKVa+n6ZkVxL8WZgSYDYELQAtyMr3W7ZsaXV9FLOUTZZZxgBmR9ACMGUpI5rFyvezCJSWgVnGANqnpwVgyma18v1///tfAcsUmGUMoH0yLQBTlOb7THF85cqVek97khHIBTbTlSBFyRjAdAlaAKZET8nySAng4cOHlYwBTInyMGAhpByna+tnZMrc1157rdWAJYFS1mWhXQlKUjJ24cIFJWMAUyBoARZCpqPN+hnbt2/vxPoZCRy++OKL1le+P3LkiPVDZijlYMmsWZgSYLKUhwELYdOmTfXWHbNePyPB0xtvvNFqT0MuiPO6k21h9swyBjA5Mi3AQrh8+fI9K5dvdGT71VdfXXeZVX52gqW2m7CTbUrzN90wzixjAIxHpgVYKJmt6/jx4/esXJ5g5uLFi2PPpJXvkQAgUuqzlhm4ZrXyfS6Ab9++beX7DjPLGMD6CVqAhZPAIUFHmqKb0l9y9OjRkcFEmfErQU/uM1K+FlnQ8cknn2y1lyXPOYFSnvOsyuEYz6hZxs6ePWuKaoAhBC3AwsoFYhZ2TAaiSECR0e5hI9spC8vFY1y/fn1NfQf5ebNY+X737t3VzUKS82NQRjBm3YsF0FV6WoCFlYAjWYhm1iMBTGYZS0akv2E9QUcJWHLxuNZG6QRIbfeUlHI0Act8ScYvJYSZ7a2p9GKZthrgXjItwFLIxf3+/furJuimBDTlgj+lOQlq0mew1mxJLjZv3Lihp4Q1G1YyttZeLIBFJmgBlkpGsNPv0l8yluxLaZLOTGQvvvhitT2O0geTi04XmKyXkjGA4QQtwFIaNJNTpCH6ypUr9UfjSR/Mo48+2mrzfSkLa7t/hulr9lUVq/ViASw6QQuwtJIhSU9Bs2RsrTNwlcxNf3/MtGm+X2xmGQO4l0Z8YGnlwi9ZlUyNnIvB3K+1BOedd94ZmLGZpgRKN2/eFLAssEwCMWxhymTYkilMtg1gWci0AKxTgpUEPWstJ9uIXKhmNfVPP/10zbObMZ/yOz927Nh9JWMJZs6dO7em/iuAeSVoAViH0lPS9sr3CZTMUraczDIGLDNBC8A6ZJ2XLVu2tFqilb6ZBEpWvl9uZhkDlpGgBWCNMuKdhSTbbr5PoPT8889XCxOCWcaAZSJoAVijlOGkQbrtXoKUpBlFp8ksY8CyMHsYwBpkFHvz5s0zaX4WsNDPLGPAspBpARhTWfm+7eb79DDs2bPHqDkjmWUMWGSCFoAxpYcgo9ezaL5PoCRoYRxmGQMWkfIwgDFkQccvvvii9QUds2L/e++950KTsQ0rGUsQo2QMmFcyLQBj2L59e+/dd99ttcQmgdLrr7/e+ixlLBazjAGLQKYFYBW5uEsPS5sBS0bCDx06VI2Ww0acOXOmd/369ao8rLh9+3bvwIEDvd27d8u6AHNBpgVghFzQlZ6SNpvvU8KTC0sr3zNJFqYE5pWgBWCEjETnZuV7FkUC8ZQdXrhwod5zR0rGZrH+EMA4lIcBDJGekps3b7befB+5oBSwMA35f5UM3qCSsb1791ZBuj4qoGtkWgAGyGh0Lt7abr6HtqVn69SpU/eVjGXWuqNHjwqegU6QaQEYoGQ62m6+1xRN25JJTM9WptduSl/V1q1bex9//HG9B2B2ZFoA+syqpyQj3rl4zGxPMAtZmHLfvn1VqVjTrl27epcuXZJ1AWZG0ALQ5+DBg70tW7a02suSDEsWAtR8TxeYZQzoGkELQMOsFnScRaAEo5hlDOgSQQtAg5Xv4V4pGTt8+HDv66+/rvfckZKxrLT/u9/9rt4DMD0a8QFqs1j5PhKwfPrpp/VH0C3PPvts79q1a9VsYilhLL788suq9yt/NyaQAKZNpgVgxax6SnLBd+PGDSvfMxfyd3Ls2LEqw9KUkrH8X37llVfqPQCTJWgBWDGLle9zAZgpZbPIn8Zm5olZxoC2CVqApaenBNbHLGNAWwQtwFJLtsPK97B++RsyyxgwbRrxgaWWkeKnn3669QurTHGciz2Yd8mmpCcrZY7btm2r9/aq0rG9e/dWgwKymMBGCVqApZULqVOnTlWjwW16++23q3ulMywSs4wB06Q8DFhas1z5/tatW9a3YGHl/7lZxoBJErQAS2lWzfezmKUMZsUsY8CkCFqApZQsRxZ0TElLWxIoHTp0qPfjjz/We2A5jJplLOVkAKvR0wIsnZSn7Nixo9WApcywdO7cuXoPLI+jR49WJZEHDhyo99yRv8UMICSgBxhFpgVYKqWnZBYr31+5cqW6wTJLydjhw4d7X3/9db3njgQ0J06c0OsFDCTTAiyV/fv3V7OFtV1Ln6xOavhh2TVnGWvKOi9lljGAfjItwNKw8j10SymbtDAlsBqZFmAp5OLonXfeqZrv2yRAguGaC1MmUCnKwpSZltzfEBCCFmApZCQ3F0htNt/Hzp07ex9//HH9ETBI/i4TnPQvTFlKxsqCrMDyUh4GLLxcDOXCZxbN9zdu3KhGkoHxKBkDBhG0AAsvizmmAT/TrralzFJm5XtYn2ELU5plDJaT8jBgoaU0KwFEmwFLJEhKqYsLK1if1UrGzDIGy0WmBVhoCRraLimx8j1MlpIxQKYFWFhp3s3K921e0JSLKyvfw+SUWcYuX75sljFYUjItwEIqPSVtN9+nDv/kyZOa72GKUhp26tSp6u+76a233rpv0UpgMQhagIU0i+Z7oD1KxmC5CFqAhWPle1geZhmD5aCnBVgoZfS17ZXvM0uZBfCgfWYZg+UgaAEWygcffFA137e98n1q6dv+mcBv8jeYdZGSYWnKYEKyLcnAAvNLeRiwMGa18n0uilKaovkeuqGUiCoZg8UhaAEWRqY93bJlSzXi2pYyS5mV76F7zDIGi0PQAiyE9JTkQqTt5vvMUpZbm4ESMD6zjMFiELQACyFZjjTft9lXYuV7mB9mGYP5phEfmHtl5fs2A5aM3iZgsfI9zAezjMF8k2kB5lqCh1xwpKekzeb7yAWQ0VmYP0rGYP7ItABzLaveHzt2rPWAJQQsMJ9yvMhsf5cvX64ClSKlY3v37q0m9UhgA3SHoAWYW+kpyYVF203wafoH5l8yKsmYJrvSlAxMSsiUjEF3KA8D5lKCla1bt2q+ByZiVMlY28cZ4H4yLcBcmtXK9++88859o7LA/BtVMpYBkpSMtT2lOvAbmRZg7uTCYdu2ba0336dU5MqVK9UNWGz5e8/MhP0y+5h1maB9ghZg7lj5HmjDqJIxs4xBuwQtwFyZ1cr3CZRyoZJRVmC5pJctwcughSkTvMxi9kJYNoIWYK7MauX7TIPqcAnLLb10CV76KRmD6dOID8yN1Je/8MILrTffZ3Q1zbnAcjt69Gjvp59+qjIsTTk2ZUDl3//+d70HmDSZFmAuzKr5HmCQUSVjJ06c0PsGEybTAsyFI0eOzGzle4B+ZWHK/j63NO0/9dRTFqaECRO0AJ2X5vtZrHyf5nur3wOj5Lg0qmQsGRlg45SHAZ2WYCWjllevXrXyPdBpZhmD6ZFpATrt5MmTvf3797fefJ8LDyvfA2tRSsb6jx0pGcs6T0rGYP1kWoDOmlXzfco6/vWvf1n5Hli3UQtTtj1tOywCQQvQWbt3765uVr4H5pVZxmAylIcBnTSr5vuUouVnupAAJsEsYzAZMi1AJz3yyCOtN99nYbidO3dqvgemYlTJWPpgEuAAgwlagJnLKGQzs5GekpRSnD9/vt7TnlxUmOEHmKZhJWNZj+rUqVOOQTCAoAWYue3bt/eefvrpaqQx6x1Y+R5YBh988EEVvPRLKVnbpbHQdYIWYOaSZcmIYxrgU+Nd+krakkzP559/3jt69Gi9B6Adye7mmPfll1/We+7I4M2HH35oljGoacQHZu7nn3+u7pNl+frrr3uXLl2q+kvaklHNb7/9tv5oeW3atKm6HTx4sN6zOEa9tkV+3XRfMsqZXv3y5ctVb0uRY+HWrVur/5cJbGDZybQAM5cLxkFS333mzJn6o+mY9Mr3ydqMes7PP/98Z5tty++hjfe9baNe2yK/buZPevoGzSiW8lnZYJaZoAWYqYwgpiysX1sLsKWf5o033ui98sor9Z6NefXVV3tnz56tPxquixcg5eI960fMYhKEaRr12hb5dTOfRpWMvfvuu2YZYykpDwNmqn/2nEi5VjIW0w5YMpqZ0oxJBSzxyy+/1Fu93q5du6qLjNzn1iz9SPNtRlS76IEHHqi3Fs+o17bIr5v5MqpkbO/evdXgiJIxlo2gBZip7777rt66c5GfWcPaaMLPCT9BwzhZkbVoXvjmouPatWvVfW4JxJqvLUFTm70742oGXotm1Gtb5NfNfBq2MGWOW8lQW5iSZSJoAWaqNOFnsbVc2Le1Ev20Vr5f7cK3fyrT9NR0jUwLdEuOGRnQycBOUwZeUuLaxeMITJqgBZipZ555ppo1bJIlWuP4/e9/f9/o5SSMc+HbLHu7ceNGvTVYLkYympr1HNaSlUkmKV+bi5rcsj3u168141B+1moXTuUxo8paMqo8znPNY9bzvsi0MK8ywDKqZMwsYyy8NOIDMBkHDhzI5CbVbZiVi467j3nrrbfqvffK/vKY/tuFCxfqR90v33vXrl0Dvy63PL9bt27Vj75XecyRI0fqPeNZCf7ufm1+/iDjvOZ4+OGHq8fkNQyy3velPGbQaxv1OeiqYX8Lp0+frh/RrvyNX79+vf6INuRYnvf9p59+qvcsNpkWYO59/PHHVWNqyiSat4w8ZiS+OfqYkfxpGifT8tVXX9Vbvd4TTzxRb92R55rnXmrVUw6ycnFSzWxVRlezndfbL1+bEdcy41C+tkwEUL42ZXg7d+6stodZa8ahmSX76KOP6q17NV9znsMgyZgk6xYp32vayPvSJNPCokimOH8v+VtoyiQf+VtZLfM5Sfm7zLEn68rQnpdffrl63/M7Xwp18AIwVzKy1BzhX+2WUcmMSmV7mpLJKD9zkGQDyueTVeiX0f7y+f6sRV5z8/v3j2qW15f3ZdDIW/NrB2VEyufWk3FYCY6qrx30mmIlsLj7/XMb9PyaI8f92aCNvC9RPifTwiLK30T/31j5Pz3ob23SSoY0f4e0p5wDhx13F42gBZg7uaAddIIe5zbtk2rz4joX4Tmp5D77m885J5n+C/NcXJTPD7uAbj5mra+l+bV5Tv3W+32jGUCOChrKbVAJy666rC0BUNMk3pf1fg7mybCBnOwvctzJ31H+znLL9qBBjHE1B2I28n1Yu+Zxb1ZlgW0StABzpXmCXO9tmgf3XPgO+pnllmCleQHR1LzgyMlomHJxv57RtfL9B138j/rcahKolK/vD4jyfmd/graSkekPEJon3/73ZxLvS/n6Sb9u6JoEJeVvoXkrAUr//nJb7///8je9LKP9XVPe/9wvOj0twNxIP8rKxW790fql/nda9d7NnpaVi/fq1qw5X7normYMGzTLz8rFRr11Z9HNPMcyk1bZzu2xxx6rHpPvtVYrgUN1P+nejsyIVr73F198Ud0X33zzTXX/wgsv3O1V6e9r+fzzz+utO2tTNE3yfdHTwqIbNcvYqHWp8rnSMzauHMfyfaO/D412vPHGG9V9fg/T7tmcuTp4Aei0jLBnJC+HrUndRo3ar1cz09Kv+blBo5plxGwtt0HyupLdyGjrsO85jYxDcxS3+d6W31tKR5oZmWYZWXlvBo3WDho1Xu3Wr+yfxuuGLkvms/wfX+221tH6kkXNbVBZKNOXY235HQwq+10kMi3AXMjI/MrBuf5oMo4dO1ZvTc6o2cPOnz9/d+Qzo5qj1hdZuXioMjS5Nbeb+94bsM5MMg4rF/5VNimziJVR0PJ1xTQyDi+99FK99VsmJSOx5fe2Y8eOKiOT5xeZ9a0oj3/ttdeq+6abN2/WW+t/XwqZFpZN/h7GPXaW48W4Ll26VN3nb7q5/hTteeihh6pjX/ztb3+r7hdWHbwAdFZzJGnSt/5m+I0alWmJZBvK5/tH9ldOPNX+9H6sRzOLsXLxPrApNt970M+O8rUbyTiU75H3IUo/Sp5PUd6j8jqbz3vQcx6VhRlX+f4yLSyr/A2W/+vDbmv9G8vj83Xl771f82cOO9Y2M0E51ndR8xiVY9oo5ZiX26TPL8PMw3s4CTItQOc1+x0mrTnaPwmrrdOSfo1kAyLZlmZvS1bpj/RtrMf//M//1Fu93rVr1+7rDWmaVsZh5eKlui+Zk7Lif/pZij/84Q/VfV5nXn/5HWS0dtBzLu/puKPFo8i0sKwOHz5cbw333HPP1VurS/9E+Zts9s40vfvuu/XWnTVF+iXbXPpojhw5UmUNuqiZIT516lR1P0zJduTx6S9qQzPLNc3z5awJWoDO++yzz+qtySvlDZMyzoVvs2G12ZDeXGhyPcFUaXgfdgHRNCq4Wi3wGuX555+vt+5ckJTX11yAcs+ePfXWnddfGveHNfKW0odI+dtGTOt1Q9cdPXr0nr+lQZ566ql6a3X//Oc/6617L5qbMghRBjJSetZ/XNu3b191nwv81YKBWSvHpwRqw45DOeaVQadplB8P8+CDD9Zbd57DohK0AJ33/fff11uT98MPP9RbkzHOhW8uHoqTJ0/WW3f2l9G8zDo2aIaxpv7PP/3009V9TpqDZpHJavHlhDqtjEPztTVHdpsXNRlNLdmmBI3NvptBEvCU9+XQoUNrfl+aZFpYZplVLAMF5e8v8rdVbmfOnKn3rq55cdy8aO53+vTpu3+/6bUrf5/JsJTjUR7T1SxL8fbbb9dbvd4nn3xSb92rGZQ1B2qm7fHHH6+31p+pnweCFqDzSgZhGiZ9gB/nwjcn5zL6mJ/fPPnn5B3ZnxN9TpQZ1ctjcv/BBx/0Dh482Nu0aVO13bRly5Z6606pRU6gCV5yv3379numO51mxqFcEJVgpLzWpjJqmckCilEn+fK+ZJQzo8HlfSnvTS6Ahr0vTTItLLv8naV89Ndfq7X6ej/++GN1u3r1av2ItXvmmWfqrfvleHfixIlqO3+/yUAkcClBQAYr2rzAX6+UepUs9rAMfcks5xjYVmlYNLPr0xzkm7mqswWgw1Yu3u82GU7jNklp5h7n+66c3O4+Lg34Tc1GzlG3TDfab+VkOfCxueW5pWE227nvVx436HNr0f/8BzWuNhtbc+t/DwbZyPtSPjfN1w3LpBxLchun4Tx/4+XxzePUSiBTP6L7cmwpzzvH8Ka1NOtPQ/nZeW8XlUwL0HlrqbNeq1K2MClpZM0o28oJvd4zWEYW85iMMva/vpSGZUHFlRNf9fkyipbvm4/L55ulWEVGUJOVyOPy2vI1ybpkBDClH2mCz+eavSdFnk8eP+hza1Fq58tt0PNMuVh5/bm9//779WeGK6879/maPNcY530Z9dom9bqB4ZqZ3pKFzbGq62VhTTlWFM3XE83SsEHHoGkr57JJlzx3yaZELvU2QCel7Kek3SctAcHCryIMMGHpkSsX7hksGKccavfu3feUhKZcbJ6Clmiej5rP/5FHHqk+zgBKeofaltLYWORzmkwL0HnTHAFvjpwBMJ5HH3203ur1/vOf/9Rbw6X/rBmwxLAZA9Ojtlp/2qyUKdujBC/pq0vAEslsN+U1TPu1NCcf2bx5c721eAQtQOdNM7CYhwZQgC4bZ0KTzPwXKcUsF/YJYvqnQY6SvRi3fLcEBs3btIKEnDPK8yoN+c01soadU6b5Wprv/2OPPVZvLR5BC9B5OYFNI3DJyXPY+gIADNc8dq42DXlKyUom4uLFi/esyZJpkDciF/SZOj7dDuWW/rZ83+Y0xZP02muvVfcJulKKVYKXjZ6n1vtampmuRZ4FUdACzIU0bE5aTp4ArF1zmuP0tAyT0qnS+5IL8PS+ZCCqHNMTzCSoWa80vff3cGQSk/R2pHxrUECV4CBBwGoZjGGazzdZoxKQ/fGPf6zu12s9r6VfemoWlaAFmAs5yU2yGT8ngjbn0QdYJM1My6igpbnqfY67RS7Qy8yICWqa61U1JbBolkoNe1y/9Hb8/PPP9Uf3On78eNU3s94sT84dydRH6dPJ63vxxRer7WGm8Vqi+X1GrZkz7wQtwNxIrXBG6jYqKfxJfB+AZVYu3G/evFnd9+tf9b5fc0HLEtxE6f/IsTqlV6VUKlmNrVu3Vk39q8mixMOmyy+ZkY04fPhwvXXHsEkFpv1aotnTssglz4IWYK5kpG4jGZd8/fnz5+uPAFivcqGei+ZBWYPSh5EL9kEN6slYlKb8fI/SlF+CigRFzemDs9ZUgoCPPvqo3jNYAoF8jzy/0tQ/SAm61qO/f+VPf/pTvXWvab+WlIyVc2J5LxeVoAWYOzn5pRyhjGCNIyeMy5cvy7AATEgzEBk0C1jJKowaKMrFe3lcf2Dzxhtv1Fu/2bNnz6r9HSUQGLTIY/N5vvvuu/XW2iWAKEFPzkWrZTim8Vri888/r7d6vZdeeqneWkyCFmAuldlSrl+/Xo0uldropuzL5/KYrBS/Wr0xAONLpqQce//2t79V99O22uxYaZJPIJDboMxEGbhKpmQj54RkQMrK/seOHavu12qjryXKJAcJnBb9HCdoAeZSGijPnTtXjW5lpC4zrpTRunLLvnxukWt8AWbpzTffrO5TwjRuY/lGNBe17JdG91zEJzAZVI6WQCNlaLnA3+iMlM2yrkE/axwbeS1FmQhgWE/NIhG0AHMnzZ2ZTUXmBGC2UrZUSnUHlYhN2r/+9a+qLKs/85CL/AxmJYPSnKWsqcwWlgGvYZmLcWRALNmPyHNZ70yUG3ktkccVzbVvFpWgBZg7mYGlpMQBmK1SHjWpErESBPUf5xMsZCat/ov8ZHhykZ9StVH9M1kUMr2NGx3wavaR9M8i1m9aryWai1puJAibF5t+TQ0FAACsU0qvHn/88YmU45ZMQ7IQTz/99N2L9927d1flUJmIpWQ3cvGf6YDz2PQutiEZpfzcWG1yl2m+lgQ43333XW/Hjh1LEbTItAAAsCHJXkyqf7BkJzJFcJrVy2KMuchP70yzHKuUT6UpvrlwY7mVaZcnKT0mCVZWC1himq8l73fe92UIWEKmBZgbBw8erJonl+UAvRYZzfv222+r2WbWW189axllzMQJTzzxxNDpPQFYToIWYC6k+T71u22l/+dJ5vgvo3lpDl3vTDazllKHrBAdzZIJAFAeBnReLsozM8rFixfrPTSdPHmyuk/gMq8BS6TUoaz5kIwLABSCFqDz0sSYWV+MvA9WZuzJ6srzLr/nSGYNAApBC9BpmZEm00uOmqt+maWXJc2c8cc//rG6n2fNqUjzuweAELQAnfbOO+9seOXiRfbVV19V9ykNW4TFNpslYs0VpwFYboIWoLNKidA892lMU3p9yqrMpaxqEZTXkteW1wgAghagszLtbea2Z7DmqsyDArtc8KfEKrdRF/+ZtSuPKYulbUS+R75XvudqynPr/7nNjFEJygBYboIWoLOyHos1WYbL4mRFKalq+sc//tHbu3dvddu/f3+9914JGjLNcB6TVZ436siRI9X3yvccFQTlc+W59fcrNReo++abb+otAJaZoAXonEmN+i+6rGVSDArukrE4cOBAtZ0AJ037/dIzFAl6xlndeTUJWopR0xY3s0QvvfRSvfWbsu7MF198Ud0DsNwsLgl0SsqYMkqffha9LKNt2rSpuk/AMSzIy/v51FNPVTOMJRBIoFMCnLfffvtu39Dly5cn1sg/zvPavn177+uvv66e048//ljv/U35fDhNASDTAnRKehg2b94sYFmDRx99tN66XwKUMvtaApdjx45V2wkmSsCS7MgkZx4r2Zbbt28P7G3Jzy4BybAJBJ5++ul6687jAVhughagM3JxmoUkz549W+9hmOaFfPMCf5AEgNu2bau2894mkCiBRTIdp06dqrYn5U9/+lO91RvYJ9PcNyw4feCBB+qtXu/nn3+utwBYVoIWoDOOHz9eXUxb+X51zQv55gX+MBcvXqy3elX5XWniTxZm0pMdNNdaKav1N126dKm6z2OaTfdNKWkrvvvuu3oLgGUlaAE6Ic33ac4e1bzNb5oX8qPKw4oEgv2zdO3atWtqZXhlAoCUpOV3W4xTGhZmjQOgSdACdIKV79fmmWeeqbfu9I6Moz8QeOyxx+qtyXvzzTfrrV7vk08+qbfuLQ3LOjzDfPvtt/UWAAhagA5Ij8Vzzz2n+X6dvv/++3pruMwilvK7KNMJZ9KDZhZkkhIglT6aUg4WpVwsWZ5R2ZQffvih3ur1duzYUW8BsKwELcDMpa9BWdjaNPt+xlmAMRMcpFQrSnlWHDp0qN6avDfeeKO6z89NhiWlYSUrNGyxy6L5msrzBmB5CVoA5lRpdl/toj7ZlGRVIiV4zf6WfG3Wa5mGPXv21Fu93meffXZPYDqqNCxKpiVZIRMzACBoAWYmF9O7d++uP2KtmmVTKf8apmRTEuSUYCGr35fyrazXMmg9lfx+sshjboM+v5qUf5WplRM0lcCpNOmPUjIyKRsEAEELMDMpWfrzn/9cf8RalUxLDGvGTxalZGL6Jzr48MMP661eb9++ffXWb7766quqlCy3QeutjOOll16qt357jn/84x+r+2GaAVhz6mMAlpegBZiJDz74oFr5fpIrsS+b559/vt4avIhjsiNl1ftkN/rf6/QSNVevL48tHnzwwXqr13viiSfqrbXJz2wGVyn3Wu13nqmvizTsA4CgBWhdGrIzk5WV7zcmF/9lJrAvvviium9KeVdKwHLhP2w66ayGn8/n1r/y/K1bt+qte/tT1qo5/fGotVmK9L8UZpQDIDb9uqLeBmjFq6++Wt2bMWzj8l6W4C9BxqSa1lOiVQKiZGM28rtKiVrJ4ly/fn3oKvjFpk2bqvsEUleuXKm2AVhuMi1AqzL6n3U7BCyT0ewZaZZVbVTK9yKlXRv9XZW1WfK9VgtYys+NUroGAIIWoFVWvp+slIiVWcCajfUblbKx2OjvKkFqmQhgnNKwNP9HsjxKwwAoBC1Aqy5evOhidMLKIo6Z5WvU1MfjSilXAo1Mi7xa0/xq3n///Xpr9bVZokyLfOzYseoeAEJPC8ACSC9LZgBLZmSc4GCUTJSQpvzVSrlW0+yLGac/JTOgZZazfM2PP/5Y7wUAQQvQkvQq5II0Cw6yPFIe9vjjj1f9LH73AKyXoAWYuly47t27t+dwAwCsh54WYKpSIpTm+8uXL9d7AADWRtACTFXKwlIWtNGGbgBgeSkPA6YmDd2ZjjezWk1q0UMAYPkIWoCpOXjwYNWA/d5779V7AADWTtACTEWa7w8dOmTqWgBgw/S0AFNz7ty5egsAYP1kWgAAgE6TaQEmKlMcAwBMkqAFmKjXX3+995e//KX+CABg45SHARPz73//u7dz507N9wDARMm0ABOzb98+zfcAwMQJWoCJyMr3jz76qJXvAYCJUx4GbJiV7wGAaRK0ABv26quvVlkWK98DANMgaAE2pGRZbt261XvooYfqvQAAkyNoAQAAOk0jPgAA0GmCFmBdUhb29ttv1x8BAEyPoAVYl+PHj/d++OGH+iMAgOnR0wKsmZXvAYA2ybQAa5aV70+fPl1/BAAwXYIWYE3+8pe/VGuyvPLKK/UeAIDpUh4GjM3K9wDALAhagLFl5fs4c+ZMdQ8A0AblYcDYnnvuOQELANA6mRYAAKDTZFqAVaWXBQBgVgQtwEj/93//VzXfC1wAgFkRtAAjvf76673XXnvNbGEAwMzoaQGGsvI9ANAFMi3AUFa+BwC6QNACDPTBBx9Y+R4A6ATlYcB9ysr3V69e7T377LP1XgCA2ZBpAe7zz3/+s7d//34BCwDQCTItAABAp8m0AAAAnSZoAe5K831uAABdojwMqGTl+6eeekrzPQDQOYIWoHLw4MHeAw880Dtz5ky9BwCgGwQtgJXvAYBO09MCWPkeAOg0QQssub/85S9WvgcAOk15GCyxsvL9119/3fvd735X7wUA6BZBCyy5v//9770XX3yx/ggAoHsELQAAQKfpaQEAADpN0AIAAHSaoAUAAOg0QQsAANBpghYAAKDTBC0AAECnCVoAAIBOE7QAAACdJmgBAAA6TdACAAB0mqAFAADoNEELAADQaYIWAACg0wQtAABApwlaAACAThO0AAAAnSZoAQAAOk3QAgAAdJqgBQAA6DRBCwAA0GmCFgAAoNMELQAAQKcJWgAAgE4TtAAAAJ0maAEAADpN0AIAAHRYr/f/A/N0QMjxIqZYAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":53975,"title":"Compute the effective conductivity of more heterogeneous aquifers","description":"Cody Problem 52070 asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single value of conductivity set such that the aquifer produces the same flow under the same total change in head. In that problem, the aquifer had soil units either in series only or in parallel only. \r\nWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided.  \r\nFor example, if in the aquifer below  = 0.1 m/d,  = 0.2 m/d,  = 0.01 m/d, and  = 20 m/d, then the effective conductivity is 0.092 m/d.  \r\nHint: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \r\n   and   \r\nThen conservation of mass leads to \r\n\r\nSolve this equation for the head , compute the flow through the aquifer, and get the effective conductivity from the definition.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 725.117px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 362.558px; transform-origin: 407px 362.558px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.25px 7.79167px; transform-origin: 318.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.017px 7.79167px; transform-origin: 331.017px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.79167px; transform-origin: 25.2667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.933px 7.79167px; transform-origin: 359.933px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.858px 7.79167px; transform-origin: 110.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if in the aquifer below \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.1 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.1917px 7.79167px; transform-origin: 35.1917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.2 m/d, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K3\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7px 7.79167px; transform-origin: 52.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0.01 m/d, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K4\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.35px 7.79167px; transform-origin: 88.35px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.79167px; transform-origin: 13.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.683px 7.79167px; transform-origin: 342.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"vx = -Kdh/dx\" style=\"width: 72px; height: 35px;\" width=\"72\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 7.79167px; transform-origin: 23.325px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   and   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v_y = -Kdh/dy\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.408px 7.79167px; transform-origin: 112.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen conservation of mass leads to \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4583px; text-align: left; transform-origin: 384px 17.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\" style=\"width: 173.5px; height: 35px;\" width=\"173.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100.358px 7.79167px; transform-origin: 100.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSolve this equation for the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.9px 7.79167px; transform-origin: 251.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 246.467px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 123.233px; text-align: left; transform-origin: 384px 123.233px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 513px;height: 241px\" 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\" data-image-state=\"image-loaded\" width=\"513\" height=\"241\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity2(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 0.1; K2 = 0.2; K3 = 0.01; K4 = 20;\r\no = ones(50,50);\r\nK = [K1*o K2*o; K3*o K4*o];\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.0916;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 5; K2 = 3; K3 = 8; K4 = 6;\r\nK = K3*ones(50,110);\r\nK(1:20,1:50) = K1;\r\nK(21:end,1:30) = K2;\r\nK(1:20,51:end) = K4;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 2.5471;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 0.1; K2 = 1;\r\nK = diag(K2*ones(50,1));\r\nfor j = 1:9\r\n    K = K+diag(K2*ones(1,50-j),j)+diag(K2*ones(1,50-j),-j);\r\nend\r\nK(K==0) = K1;\r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = 0.2945;\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)\r\n\r\n%%\r\nK1 = 1; K2 = randi(9)/10;\r\nw1 = 10*randi(9); w2 = 100-w1;\r\nK = K2*ones(100); K(1:w1,:) = K1; \r\nKeff = effectiveConductivity2(K);\r\nKeff_correct = (K1*w1+K2*w2)/(w1+w2);\r\nassert(abs((Keff_correct-Keff)/Keff_correct)\u003c0.015)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-02-02T15:06:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-28T03:19:00.000Z","updated_at":"2026-04-05T08:16:36.000Z","published_at":"2022-01-28T03:21:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for a function to compute the effective hydraulic conductivity of a heterogeneous aquifer—or the single \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue of conductivity set such that the aquifer produces the same flow under the same total change in head\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In that problem, the aquifer had soil units either in series only or in parallel only. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the effective conductivity for two-dimensional flow in an aquifer with a more complicated distribution of conductivity. Flow is left to right, or to the east, as in the figure below. No flow occurs across the north and south boundaries. Assume the head difference is small enough that Darcy’s law applies. Use the conductivity specified on the equally-spaced grid provided. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if in the aquifer below \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.1 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.2 m/d, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0.01 m/d, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 20 m/d, then the effective conductivity is 0.092 m/d. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The simple formulas that work for soil units either in series only or in parallel only will not work for these more complicated distributions because two-dimensional flow violates assumptions behind the formulas. In this problem, compute the effective conductivity directly from the definition. Darcy's law yields the specific discharges (or flow per unit cross-sectional area) of \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vx = -Kdh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_x = -K\\\\frac{\\\\partial h}{\\\\partial x} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   and   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v_y = -Kdh/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_y = -K\\\\frac{\\\\partial h}{\\\\partial y}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen conservation of mass leads to \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d/dx(K dh/dx) + d/dy(K dh/dy) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial}{\\\\partial x} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial x}\\\\right) + \\\\frac{\\\\partial}{\\\\partial y} \\\\left(K \\\\frac{\\\\partial h}{\\\\partial y}\\\\right) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve this equation for the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the flow through the aquifer, and get the effective conductivity from the definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"241\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57497,"title":"Locate image wells","description":"A mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \r\nIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\r\nWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. \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: 664.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.35px; transform-origin: 407px 332.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.933px 8px; transform-origin: 369.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370.7px 8px; transform-origin: 370.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.892px 8px; transform-origin: 365.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 406.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 203.35px; text-align: left; transform-origin: 384px 203.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 610px;height: 401px\" 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\" data-image-state=\"image-loaded\" width=\"610\" height=\"401\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [xI,yI] = locateImages(x,y,xb,yb)\r\n%  x = x-coordinates of the real wells\r\n%  y = y-coordinates of the real wells\r\n%  xb = x-coordinates of two points on the boundary\r\n%  yb = y-coordinates of two points on the boundary\r\n%  xI = x-coordinates of the image wells\r\n%  yI = y-coordinates of the image wells\r\n\r\n   [xI,yI] = reflectAbout(x,y,xb,yb);\r\nend","test_suite":"%% Vertical boundary, one well\r\nx = 100; \r\ny = 0;\r\nxb = [0 0]; \r\nyb = [0 200];\r\nxI_correct = -100;\r\nyI_correct = 0;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Vertical boundary, multiple wells\r\nx = 100*rand(1,2); \r\ny = randi(100,1,2);\r\nxb = [0 0]; \r\nyb = [0 200];\r\nxI_correct = -x;\r\nyI_correct = y;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Horizontal boundary, one well\r\nx = 100; \r\ny = 50;\r\nxb = [0 200]; \r\nyb = [8 8];\r\nxI_correct = 100;\r\nyI_correct = -34;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Vertical boundary, multiple wells\r\nx = 100*rand(1,2); \r\ny = randi(100,1,2);\r\nxb = [-8*pi 8*pi]; \r\nyb = [0 0];\r\nxI_correct = x;\r\nyI_correct = -y;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% C E 473/573 problem\r\nx = 0; \r\ny = 0;\r\nxb = [-550 1050]; \r\nyb = [900 -50];\r\nxI_correct = 503.4657;\r\nyI_correct = 847.9422;\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #1\r\nx = [150 210 280]; \r\ny = [50 70 95];\r\nxb = [0 200]; \r\nyb = [0 300];\r\nxI_correct = [-11.5385 -16.1538 -20];\r\nyI_correct = [157.6923 220.7692 295];\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #2\r\nx = -[50 65 83 104]; \r\ny = [20 35 49 65];\r\nxb = [-107 -69]; \r\nyb = [57 22];\r\nxI_correct = [-65.4477 -81.6280 -97.0577 -114.7269];\r\nyI_correct = [3.2282 16.9468 33.7374 53.3537];\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%% Slanted boundary #3\r\nr = 100*rand(1,2);\r\nx = -[50 65 83 104]+r(1); \r\ny = [20 35 49 65]+r(2);\r\nxb = [-107 -69]+r(1); \r\nyb = [57 22]+r(2);\r\nxI_correct = [-65.4477 -81.6280 -97.0577 -114.7269]+r(1);\r\nyI_correct = [3.2282 16.9468 33.7374 53.3537]+r(2);\r\n[xI,yI] = locateImages(x,y,xb,yb);\r\nassert(all(abs(xI-xI_correct)\u003c1e-2) \u0026\u0026 all(abs(yI-yI_correct)\u003c1e-2))\r\n\r\n%%\r\nfiletext = fileread('locateImages.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-03T15:19:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-03T15:19:08.000Z","updated_at":"2026-02-12T14:18:55.000Z","published_at":"2023-01-03T15:19:28.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. \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\u003eIf a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. 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