{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52070,"title":"Compute the effective conductivity of a heterogeneous aquifer","description":"Slow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water  to the gradient in piezometric head  by\r\n\r\nwhere  is the conductivity of the soil and  is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow  (and the specific discharge ) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \r\nSome aquifers, or underground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of  set such that the aquifer produces the same flow under the same total change in head. \r\nFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If  is 2 m/d (meters/day) and  is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \r\nWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 317px; transform-origin: 407px 317px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.833px 7.91667px; transform-origin: 311.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.0083px 7.91667px; transform-origin: 56.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the gradient in piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 19px;\" width=\"39.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 7.91667px; transform-origin: 9.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4167px; text-align: left; transform-origin: 384px 17.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.91667px; transform-origin: 104.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the conductivity of the soil and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.283px 7.91667px; transform-origin: 244.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.1333px 7.91667px; transform-origin: 87.1333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (and the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 19px;\" width=\"57.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 227.95px 7.91667px; transform-origin: 227.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 7.91667px; transform-origin: 57.175px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome aquifers, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.6px 7.91667px; transform-origin: 325.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.433px 7.91667px; transform-origin: 252.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.917px 7.91667px; transform-origin: 376.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.225px 7.91667px; transform-origin: 83.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 m/d (meters/day) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.125px 7.91667px; transform-origin: 251.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.242px 7.91667px; transform-origin: 376.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.458px; text-align: left; transform-origin: 384px 104.458px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 382px;height: 203px\" src=\"data:image/png;base64,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\" alt=\"Aquifers in series and parallel\" data-image-state=\"image-loaded\" width=\"382\" height=\"203\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,1:2) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,3:4) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(1:2,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(3:4,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10*rand;\r\nK  = K1*ones(7);\r\nKeff_correct = K1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,10) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,5) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(10,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(5,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(4:6,:) = K2;\r\nK(7:8,:) = K3;\r\nKeff_correct = 3.875;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(:,4:6) = K2;\r\nK(:,7:8) = K3;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(5:7,:) = K2;\r\nK(8:9,:) = K3;\r\nK(10,:)  = K4;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(:,5:7) = K2;\r\nK(:,8:9) = K3;\r\nK(:,10)  = K4;\r\nKeff_correct = 1.5584;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-17T14:24:44.000Z","updated_at":"2026-03-16T13:48:00.000Z","published_at":"2021-06-17T14:30:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the gradient in piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the conductivity of the soil and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (and the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome aquifers, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 m/d (meters/day) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52070,"title":"Compute the effective conductivity of a heterogeneous aquifer","description":"Slow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water  to the gradient in piezometric head  by\r\n\r\nwhere  is the conductivity of the soil and  is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow  (and the specific discharge ) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \r\nSome aquifers, or underground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of  set such that the aquifer produces the same flow under the same total change in head. \r\nFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If  is 2 m/d (meters/day) and  is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \r\nWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 317px; transform-origin: 407px 317px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.833px 7.91667px; transform-origin: 311.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.0083px 7.91667px; transform-origin: 56.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the gradient in piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dh/dx\" style=\"width: 39.5px; height: 19px;\" width=\"39.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 7.91667px; transform-origin: 9.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4167px; text-align: left; transform-origin: 384px 17.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.91667px; transform-origin: 104.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the conductivity of the soil and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.283px 7.91667px; transform-origin: 244.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.1333px 7.91667px; transform-origin: 87.1333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (and the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 19px;\" width=\"57.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 227.95px 7.91667px; transform-origin: 227.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 7.91667px; transform-origin: 57.175px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome aquifers, or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.6px 7.91667px; transform-origin: 325.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.433px 7.91667px; transform-origin: 252.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.625px; text-align: left; transform-origin: 384px 31.625px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.917px 7.91667px; transform-origin: 376.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.225px 7.91667px; transform-origin: 83.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 m/d (meters/day) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAABfklEQVRYhe2WXZGFMAyFPw91gAEMoAAFdbAOrgMsoAEJeMACGrCw+1AyN+2Gv50L3YeeGR6AtBxyktNAQUFBXjTAa+f6UrF7ce6TpBzQAd/qmoHKiPUqZlnJ3IImIWSRAeh5E67vIgNBGiEzHpAZ+bBEFkZFKJXBAcPGu9ug5WrU8xqYCPXSPkWmJS5UkUNknHlAIg3dYQOxRP2TRASTItQTMrIQe9BjcMT1c+RDtyM1ulnddzkIibeIXNogFzJkSWfEr8+0Jw0n92mTdSN/cPKauG6qjedHG3tCY/iVmHRo6mmH0MfFnLzTUk4H+1gNIKTOZjhaZBVwRagheb/l0o2xFt5me/QzEbQs1gdfxBm84tbSHKczlI4b1scccZauGKXYyek1+rjYS6uOu2ID/brvqaw2xH++YHeSPtOutHPFhQ7zbM/F/mRcGptiJNM5aKEj05FjwRNq59HZaQsee9Z2ZJipxAR7ftfazIOjL4SO0x1rzVX/QsKCgoICwQ+2aq9ZyMmVYQAAAABJRU5ErkJggg==\" alt=\"K2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.125px 7.91667px; transform-origin: 251.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.242px 7.91667px; transform-origin: 376.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. The relative size of each unit is indicated by the number of rows or columns. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.458px; text-align: left; transform-origin: 384px 104.458px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 382px;height: 203px\" src=\"data:image/png;base64,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\" alt=\"Aquifers in series and parallel\" data-image-state=\"image-loaded\" width=\"382\" height=\"203\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Keff = effectiveConductivity(K)\r\n  Keff = mean(K);\r\nend","test_suite":"%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,1:2) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(:,3:4) = K2;\r\nKeff_correct = 3;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(1:2,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 2;\r\nK2 = 6;\r\nK  = K1*ones(4);\r\nK(3:4,:) = K2;\r\nKeff_correct = 4;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10*rand;\r\nK  = K1*ones(7);\r\nKeff_correct = K1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,10) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(:,5) = K2;\r\nKeff_correct = 5.2632;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(10,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 10;\r\nK2 = 1;\r\nK  = K1*ones(10);\r\nK(5,:) = K2;\r\nKeff_correct = 9.1;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(4:6,:) = K2;\r\nK(7:8,:) = K3;\r\nKeff_correct = 3.875;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 4;\r\nK2 = 1;\r\nK3 = 8;\r\nK  = K1*ones(8);\r\nK(:,4:6) = K2;\r\nK(:,7:8) = K3;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(5:7,:) = K2;\r\nK(8:9,:) = K3;\r\nK(10,:)  = K4;\r\nKeff_correct = 2;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n\r\n%%\r\nK1 = 1;\r\nK2 = 2;\r\nK3 = 3;\r\nK4 = 4;\r\nK  = K1*ones(10);\r\nK(:,5:7) = K2;\r\nK(:,8:9) = K3;\r\nK(:,10)  = K4;\r\nKeff_correct = 1.5584;\r\nassert(abs(effectiveConductivity(K)-Keff_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-17T14:24:44.000Z","updated_at":"2026-03-16T13:48:00.000Z","published_at":"2021-06-17T14:30:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlow flow through soil or another porous medium follows Darcy’s law, which relates the flow of water \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the gradient in piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dh/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edh/dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the conductivity of the soil and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area (i.e., the aquifer thickness multiplied by the aquifer width). The flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (and the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is analogous to current in an electrical circuit, and the change in head is analogous to the voltage drop. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome aquifers, or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eunderground water-bearing formations, consist of multiple soil units in series or parallel, as shown below. The analysis of these aquifers is often simplified by computing the effective conductivity—that is, treating the aquifer as homogeneous with the single value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e set such that the aquifer produces the same flow under the same total change in head. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, suppose the soil units have equal size in the two aquifers shown below and flow in both cases is from left to right. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 m/d (meters/day) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 6 m/d, then the effective conductivity is 4 m/d in the parallel case and 3 m/d in the series case. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the effective conductivity of an aquifer whose conductivity (in m/d) is specified as a matrix. Flow is always left to right, and heterogeneous cases involve either units in series or units in parallel. In the series case, the conductivity will be constant in each column, and in the parallel case, the conductivity will be constant in each row. 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