{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":55825,"title":"Measure the hydraulic conductivity with a constant-head permeameter","description":"A constant-head permeameter is a device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . By supplying a flow  to a standpipe, water is maintained at a constant level so that the head difference , or the difference in water levels between the standpipe and outlet, is constant. \r\nThe hydraulic conductivity can then be determined from Darcy’s law\r\n\r\nwhere the head gradient  is simply . Darcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\r\n\r\nwhere  is the acceleration of gravity and  is the porosity of the soil \r\nWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use  and .\r\n\r\n                              ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.2px; transform-origin: 407px 419.2px; 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: 256.342px 8px; transform-origin: 256.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 8px; transform-origin: 65.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. By supplying a 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: 75.8417px 8px; transform-origin: 75.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah\" style=\"width: 21.5px; height: 18px;\" width=\"21.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.533px 8px; transform-origin: 188.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.533px 8px; transform-origin: 209.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4167px 8px; transform-origin: 77.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the head gradient \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: 18.5px;\" width=\"39.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 8px; transform-origin: 30.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is simply \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah/L\" style=\"width: 38.5px; height: 18.5px;\" width=\"38.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 214.6px 8px; transform-origin: 214.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.025px 8px; transform-origin: 91.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.417px 8px; transform-origin: 175.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.733px 8px; transform-origin: 114.733px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 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: 371.492px 8px; transform-origin: 371.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.55px; text-align: left; transform-origin: 384px 18.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K = (gd^2/(180nu))(n^3/(1-n)^2)\" style=\"width: 114px; height: 37px;\" width=\"114\" height=\"37\"\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: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity 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);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.95px 8px; transform-origin: 78.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the porosity of the soil \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.683px 8px; transform-origin: 363.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-6} m^2/s\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 338.7px; 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 169.35px; text-align: left; transform-origin: 384px 169.35px; 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: 494px;height: 333px\" 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Xn311cf3+fHHH+8bgotUzRKkonc7l17+Y9Whb3z9lO187Wtfq974xjfWIaQ3xPR7bkW/ZdlWKnrZVm/wLevffffd1a233lrPK+Ev+3rZFX+9eurJk4/t6Wyv9xjPduz7Hd/8U5ATlrLNHMNUD0fdl9kkwL797W+v3vOe99S3B70Hii7PDZhHCZOMj2l6SY6F4nkfpsVCvs5dtv3tb3/76LEwUN93lOHYl3Zzz6NH169fX887FpyaOSfs27evXrZ27dpmzmBZ99zzzjtl3bL9Y4GkmXNC7pP9PhYkmjmDddlO5r/uwv77P+x591s223F62XknP07Zp9ynn67b63essizb6l027DHa5rovw2T97MfXnv1uM+dFx8Jg/Rh33HFHM+eELs8NmD/6TI6hVJYmfWhXnOZbms/6PeYkDZGKzbgo/SEj1Z1jfxv6DqlQ9Xrqz79Rj3fu3FlXlNpDKlLxuc99rj6Bpy3VrFSN2ut+/3vfq+e3HQsD9TiVpUFGOZu7nDAzbDvRu52c5f3sd37Q3Doh78NB+i0rjz/oOH3ney82xfYatL9dt3csdDVTJ+TzWl7b9vM/+JffqseXX355PR6kvEbD9iXVw9leo3jkkUeqn/qpn6pevey8Zs6L0n8yPvrRjw7czlyeGzCPjn1BMEbaFZ9JlrdWv8ri6Q5l25NuIV/nLsenVCYzDNu3fuuUitGwYVDFq9/QW8Eq2z8WjJo5JwyrSPXqsp3M71ctjWHVuH7L5nqcyj4NqujN9/Z6n39e48xLZba3Stiry3tgkGPBb+B7MPuTbfUe87k+N2B+qUyOmWF9vpge4/Y6t8/UHqbfOuW5pAp27G9K36FdIfvQhz5Un9CRatGxEHB8nS9/+ct1Zam3ejTqsZqPqlNvhTPXL3z5sWPTb9tzrUzO9TgVsz2v+dpeXtv288/+po9pzvD/8/2fq+cN0vW59cpJPOljOug1T6UzUtXvrXTHqM8NmF/CJHDSNSSHyTq9SnB66qmn6vFsvvjFL9bjcrmZ4oUXXryGYG+QmG37JdwOCiBFOYFj2H72Xq8y1y/ML+P02/aw60z2WzbX4xS55NGg5zXK8+n17WOvc7/tJWTlte19/qPu86tf/ep6PJd96ZV9yKWVfumXfqmZc6r169fX79GcdNXv7PC5PDdg/giTwJwqk73yBR+D+oAmNJazwKN8ofcGrlQr8/i91aNB2y9n8MYoVae1a9fW40HbKc+9dzvz1WdylOOUvqVt55577sDnNej5FL3bO+ecc+oqa7/nktckr20uOVRCfVxzzTX1uN9jtLf/vve9rx4P25f2e6Cfhx9+uK5K5r04SP75KNXJXMO0V79jVZ5bzPYeAboRJoH6S3a2yuSgdRLEcmHpVItyclEqZuXki9xOU2m7YlUuz5P11q1bVw8JX+Vknd7qUbZ/7bXXHt9+tpvrDub6jwkJWTZK1WmU7UTvdvLLKhe+7NQ/lXOtTI5ynHrDZAx6XtleAuqo20tIHPRcIq9tLvWT0Fkk3LWPWV6rftsf9NwSMsu6s1Ut77vvvuMBeZh3v/vd9Tjhsx18Y9CxynOL2d4jQEdHYQHkrdXvBJrTHcq2Gazr8cmJD7nv4SEn4AxbZ/fu3fVJDllehtze0+eEl5xAcSyUnrJetn8svDRrnexYWDlp28fCZz0/J13k/sP2u23YdnpP/viLv/iLej9vuOGGZs4JZTv9TsAZtmzU41ROKhl0PIpRt/f5A39Vb+9nfuZnmjkne81rXjPwON59990nvV45TuW4tc3lPdD2h3/4hyfdZ9QhxzlmO1bZ397XFpg/LlrOgkg14lj4a27Nn9VXLK237W07mOMDwJmkmRsAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmgYmxbt26ZopJ47WD6TVz9JhmGubNzMxMtfvJQ82t+bP6iqX1tr1tB5vm4+O1n1xeO5heKpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQAd7N+/v5qZmamuu+66Zg4sTsIkADSOHDlSLVu2rA6Jg4as07ZkyZJmarwl/G7YsOGU57Nq1apq7969zVowd8IkADQSDC+44IJ6evny5dXKlStPGq699trq8OHD9fKlS5fWQ2+4HEf33HNPdckll1T33ntvfbs8n0iQTKBct25dfRvmSpgEYOJ95evPN1OnJ8Hwueeeq0Pi448/Xu3Zs+ek4dFHH61WrFhRr5tQmWHcK5MJkhs3bqyn77///uro0aPHn0+md+/eXS976KGHqs2bN9fTMBfCJAAT7/3b/rTa8hufP+1QWSqTpfo4zKRUJrds2VKPEyRvuummerpt9erVdbCMu+66ayIqrYwXYRKAqfDZLxw+Hiq7BqJ2ZXI2s1UmH3vssbr5eLb+iVkvy/qdyJOq4mzLhlUTs072MU3a/YJkUZrw4+GHH67HMCphEoCpklC57p/9f9XHdzw950rlXCqTMSh0JsStWbOmDo5r166t1q9fX4e10j8xy4tUBtM/c9euXaeE4DS1R/Zn0LJsf5CyzihnnN9yyy31+L777qvHMKqZo+kwAfMs/y3vfvJQc2v+rL5iab1tb9vBpvn4eO3Pnrv//f7q3/3RV5tbk+Vv/w+vqza++8V+jqPI2dwJbwlpmW67+uqrq1tvvbWeztnROakl6z344IP1vEilMUEy9u3bd7yPZbSXtauaOcs6J8f0NkWXfYk0RZeTZiLL8vilibqfhMiE1EFN3G0JuOlb2ft8YDbCJAtCmDx7hEnG0UK/dtd9+I+bqRNecf451fve/erqp9+yvJkzmoS/AwcONLdOlupiTsKJVAoT5hLwyrxIs3P6Hg4KcP2WlyDX3n6pYqaqmaC5adOmauvWrScta6/fz1zC5KjbhF6auQGYKgmRW/7uj1af+pW3zjlItvtMpiKYANwe2iEry9vVxaJUCi+//PJ63Oviiy+ux0888UQ9jhL0ShUyPvvZz9bjhMnsT/uxyyV+StP0fCiPN6gPKAwiTAIwFdoh8pqrf7iZOzdz6TOZgNevz+TTTz9djy+99NJ6PEi7eTqPm+blVAczxM6dO+uqZ7ZT+l+WfpOHDr3Y8nPDDTfU40FSaYx2cB3k4MGD9fiyyy6rxzAqYRKAifcPb/qR0wqRRbsyOZtSmexVwtgzzzxTjwdJc3Jb6UuZ6z2mP2bCY5qpEzTLspxpnWVZJ+FztipiqYKWgDtMCbdXXXVVPYZRCZMATLy5NmcPMpfKZCR09p5lXaqBTz31VD3uVS4SXoJekabubG/Hjh11YMw+lGBXluVM60ceeaSed+ONN9bjYa6//vr6fgmfpeLZT/pspm9lzFbthF5OwGFBOAHn7HECzvx6z0f3Vl879N3m1nCvWfbS6rfvOHG2LSdM0vuynMGdM7GHVf4S+NIMnarhXM/mzv36nYWdSmRCX9ZJAEygLPtQluW+CX7tZcOUM8Wj34k427Ztq0/uiVFO1IFeKpMAQ7z/nW9opmY3l3UZX3OpTEZvZTLXjSzhLGd75zevE+hSsSwhc/v27fW4V6qNeex+zdi5f5YlSI7SxF3ksbJ+3HzzzXWwz7YScjNd9jV6nwuMQpgEGCJ98FJxnE3WOd3+epx9pc/kXPQLdbmET5qzczHyBMNUBlNVzJnZqVamuthPaZaO3hNhUpksRmnibkvlNPtT+mlmX3L5o+xfLlOUZXncXJ4oITNVVxiVZm4WRP7b1cx9ZuRLIZWFVCzyZZCqRb6oMp15t91229Q0W52t1/4PHv/L6s5Pfqm51V/OIhYmB/O5HX8J0qmilr6T7etawjAqkzDhEhxzpmZCZfkSKNOpgOj/dPoSEl9/0fnNrVOpSjINUmHNtSxLRXXUZnQQJmEKDPot3TvvvLOZ4nS95x2vb6ZOdeu75+dMYhgH6fOZZu7bb7+9mQPDCZMwBfLHP5WEtjRzl98Q5vQNqk6mKvm2N13Y3AJYfIRJmBK91UlVhfnXrzqpKgksdsIkTIl2dTJVSWFy/vVWJzOtKgksdsIkTJFSndRXcuG0q5O/8K5zmymAxUuYhCmS6mSuI6ev5MIp1ckMb3rTm5q5AIuX60yyIFxncu42b95cXzy4aF/jzbITy977D26v/t4tH66Onn9O9f3vfa867wc/VM/P7SNff75a+sr/pp6eef6F6nsv+a+ntbzMz3TGxZcO/lU9/tGL/1o9Lsvb4yjTp7sfk7484zVXLnOdSZhSwiQLQphkISzU+2q+JeSee955zS1CmITppZkbYJ4JksBiIkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnc0cPaaZhnkzMzNT7X7yUHNr/qy+Ymm9bW/bxclrP7m8djC9hEkWhDDJQshrz+TyuYXpJEyyIIRJFkJe+z3bmxtMlFUb5h4mjxw5Ui1ZsqS5BYwrfSYBGDsJkldffXVzCxhnwiQAY2f79u3VgQMHqm3btjVzgHElTAIwVlKVLCFSmITxJ0wCMFZ27NhRHT58uJ7OWKCE8SZMAjA2UpXcsmVLc+tFwiSMN2ESgLGRvpKlKlmoTsJ4EyYBGAvtvpK9hEkYX64zyYJwnUkWgutMTq5RrjO5f//+6nd+53eOX19y06ZN9ZDpzFu7dm21cuXKZm1gXAiTLAhhkoUgTE6uLhct91mHyaCZGwCAzoRJAAA6EyYBAOhMmAQAoDNhEgCAzoRJAAA6EyZhDDzwwAPVnXfe2dwCgMkhTMIYeOaZZ6o77rijuQUAk0OYhDGwZcsWF2cGYCIJkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAAdCZMAgDQmTAJAEBnwiQAAJ0JkwAwIfbv31/NzMxU1113XTMHzj5hEoCptGzZsjp4JYBNk6VLlzZTp2dajw9nnjAJwNQ5cuRIPU7wmq/wdSZkv1N1TMjbu3dvM/dkhw8frpYsWdLc6mZSjw/jSZiERSRfIOVLpNBsxjRK2Lrgggvq4DVJ2iHxueeea6ZOKOGv93M8V5N6fBhPwiSMmQ0bNtThrgyrVq2qduzY0Szt7rHHHhv4RZR5p1vpgHGS93jCWN7bkyphr1fC33xVJif9+DA+hEkYI+nDdO+991bLly+v1q9fXw9p6rr55ptPO1CWL6Zsu98X0elWOmCctCtvo1Tf8s9W/nFr/yO3efPmUz4XpZKfZZlu//O3YsWKejuD9P6j2B7SMlCW79q1q16/vT/33HNPPS/aAXAuj9821+MDwwiTMCbyZZE/6mvXrq2/pLZv314PmXfttdc2a3W3cuXK6ujRowM726tMMm1K5W226ls+e2vWrKn/ccvnL//E5T533XVX/dnr94/W008/XX+m8s9f1s96Bw4cOL6dtty//KOY+2T9jIvcTjj9uZ/7ueOPHWVfMlx//fX1vMjfhD179hzfZpYPe/xBRj0+MBthEsbEzp076/GNN95Yj4uEvEcffbS66aabmjkLY9oqk199tplg0RqlT2D+udqyZUtdsc8/Ww8++GD9T9yhQ4eqTZs21cHs4YcfbtY+0WfxoYceOv4PWtbPZ/T++++v18n92tKqkP1IOE0IzPoZJyxGwuDq1avrIcsSCCPbye0MqTpGefwEx1Eff5BRjg+MQpiEMZEmrXjiiSfq8Sj6Nc3ldr/qY+Zl+bp165o5J5u2yuTv/V9V9dNbqurTx8YsPvnnqN8JLL0S8BKotm7d2sw5ISEvyj96kXUzJMglwLW99a1vrce9Ae3xxx+vx70tDCU0PvXUU/W4GPaPXZfH72fU4wOjECZhTJQqRb7cRukf2a9pLl9WuX3JJZec1MeqSEVj0BfVtFUmI9XJf/qbQuViVPoEzmbfvn31OIEx/Q/bQz6LkX/E2p+PfI5KpbAt81LhjPb6aY6ei9n+sZvt8Z999tlZP8+jHh8YhTAJYyKVhtI8lRNuUkVMqOz3pZCK5MaNG+vpfBmWprlUKnbv3l3Pz/J+9x30RTVtlck2oXLxyXt/Lmcrp9k6/Q97h6L9+RhW+SvVvvb6F198cT0uJ9YUpeJ5+eWX1+NitiA4TB7/wgsvnPXzPNfjA8MIkzBG0tSWMFiawxIq88e+t8pYmrfSR6q3QpF+VyWUtvt6FYO+qPrNz0kB7Sb0sz3Eqg2jDff+Xr36SdqhUp/K6ZYwNUqfwBK60ocx/Q/7DVlW5PM4LIDlMXsrgzl5JvfJ5zLdUFL1zDjhMq0K+UeybbYgGIM+x6XaOGh5MerxgVEIkzBmEgYTFlNxLF8yqTIm2BXly623olGUSki//peDvqj6zU+47ffleraG2LN9tGH9T9Wrn+Jv/c2quufDVfW6C5sZTK1R+gSWJujefouDJHwNCmAJcP0qg+mCkvtknM91Kp7pjpJm9LQq9JotCEa/z2t5/Bj0OW8b5fjAKIRJGFOpOCY0ljM088VTvmRyWZK49NJL6/EgZb22QV9Uo3yBTbKEyN+9s6r+8f8sSC4Wo/QJLCfZtP9Za0uXkt5L7aTK2O/zkgBXKpNt+RymL+O2bdvqs8TLP0e33357s8bJysl4wwLusMePUT7PoxwfGIUwCWMulwQqzWrPPPNMPb7sssvqcbk9SFmvbVDFYpRKxiQSIhenhKlSebv66qvrgNYeylUNSl/lXGonXSmyrJyAk9s5ya1fqBv0eSmVybb0x8z8fI7b3TbKfvRefaG0LKSbS/YjFzTvPSlv2OPHbJ/nUY8PjEKYhAnQW0HIH/sYVLkoJ+FcddVV9ThKIB1UsRilkjFJVv6YELmYJUyVz02CYqqL7aF9hnbpq5xgmWXl5JvcTutAv2u8Dvq89KsMJkymmTvVyVRCy1CW5eoL7V+uufXWW4/3e85+pG/lqCfp5PHnejZ3v+OT5z3bNqCYOVo6IsE8yn/du5881NyaP6uvePE/+2l72+aLLZWA22677ZQvrlQm2l9skS+eco269MFqn4RTlrXXjzxGvrTS4b/dTyvzs27u06//1jjJa5/+kEyenBQ118/tNHzWy+ex93NX5OS69IlON5ZBzd4w7lQmYUwkFJZLAiUcpvqY6QTJyKV/ivYZ2wmICaLlDNESMtvrF6U62Y8qBMy/Uv0bdK3JgwcP1uPStA2TSJiEMZDwmKalNH0l8JVmp8i8VGdSPWxrN82Va+SVbbTPBG8bdhmQ2fpYAXOXk+Tymc7nM/8clv6Y+QcwATMVyXxWF/rnUmEhaeZmQeSPpmZu5ltee83ck2mxNnNHqv45kzuX/Cr/JEZCZLq23HDDDf6ZY6IJkywIYZKFIExOrsUcJmHaaeYGAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQDGwt69e6tVq1ZV1113XT2O9u0dO3bU84DxMnP0mGYa5s3MzEy1+8lDza35s/qKpfW2vW0Xp7z2e7Y3N5goqzZUI31uV6xYUR04cKC5dcLSpUurQ4fm/28KcPpUJgEYG/fdd18zdbI777yzmQLGjTAJwNhYvXp1tXz58ubWi1KVvPXWW5tbwLgRJgEYK73Vydtvv72ZAsaRMAnAWGlXJ1OVFCZhvAmTAIydUp3UVxLGn7O5WRDO5mYh5LVncs31c5tLAj366KPNLWBcCZMsCGGShbBQ76vF6lvffK768r6nqjde9eI1HRfSmiuX+dzClBImWRDCJAtBmJx/7/7vVtShMn0UV7zxb1SvX3F59Zb/fk31mh95Q7XsVRc1a50+YRKmlzDJghAmWQjC5Pzb+Vt3V//71juaWyc797zzqgf/wxeqV7zygmZOd8IkTC8n4AAsYmvXfWBgWPz7v/DL8xIkgekmTAIsYkfPP6d674d+sbl1wtvWvKu68b0bm1sAgwmTAItcQmNvBfLwN/5zdegbX29uAQwmTAJwUnXyf9vxmep/fOfPVu9751urRz71b5u5AP0JkwAcr05+cPNH60sF5fbW33iw+o1//kvV//pPP1zNPP9CsybAyYRJAGoJj+1+kgmVO3d/sTr0l1+v/s7fWlVfkxKglzAJQK3fxctzgs7/8i9/u/rb791Q/cOb3qHZGziFMAnArFKxTF/K3/rEx6pf/tB7NHsDxwmTAIzkDZdcXv3bT++pL2au2RsohEkARpZm74/86r+q3vsPfrF637uc7Q0IkwB0cP3P/p3qX//+f6ybvX/lw3+//n1vYHESJgHoJM3e/+eu/6c697yXVht+9ierzz+xp1kCLCbCJACn5Rfv/Jd1s/cvb/y56tM7/nUzF1gshEkATluavf/FJx+ufu+Bf1Pd8b53avaGRUSYBGBepNl7+6f+sPrh5VfWP8Wo2RsWB2ESgHn1j/7xr1b/6J/8at3svfO37m7mAtNKmARg3r1tzbuqe3/3/64+86kd9UXOgeklTAKwIJa96qK62fs1P/KG+vaf/Mmf1GNgugiTACyoD27+aD3+iZ/4iWrbtm31NDA9hEkAzojDhw9XDz74YLVq1arqyJEjzVxg0gmTAJwRS5Ysqfbs2VNdd9111SWXXFI99thjzRJgkgmTAJxRW7durR599NFq7dq11ebNm5u5wKQSJgE441auXFnt27evDpWavWGyCZMAnBWl2XvdunV1s/eOHTuaJcAkESYBOKtuv/32ukL5wQ9+ULM3TCBhEoCzrjR7p1KZZu/9+/c3S4BxJ0wCMBbS7J0KZZq9Ey6d7Q2TQZgEYKyUZu+c7b1hwwYn58CYEyYBGDul2fvQoUPVtddeq9kbxpgwCcBYSrN3fjGnNHs72xvGkzAJwFgrzd4503vv3r3NXGBcCJMAjL1UJtPUnTFnV16HSenHmn2dmZmpf8KThSNMAjBxEhJyck6CQhlWrFhRN4mrXi6cnGGfC8wvXbp0ok6MSpeJxWTbtm3HPxf33HNPM3fhCJMATJR8OSbQ3HvvvfXtVCszHDhwoHrooYdcp/I0pYqXENLv0kwXXHBBPV6+fHk9HncJvZMWfOfDrl27mqmq2rlzZzO1cIRJACZGAs7GjRvr6fvvv786evRofaHzDJnOGeC5pFACBHPXDl0lOLYltOc4J6xPQrXv8OHD9bCYKpN5bVKdz1UQEvoTLBc6TAuTAEyMBMVIkLzpppvq6bY0decM8MXWrDlfctym7dgttsrkI488UgfoW2655fhn5OGHH67HC0WYBGAipCqZL8lUx/oFyX7KCRg5EzzTaQIv/SvbASOXHSrNu2XIuoP6X2b9sq0ypL9m7zZnW2eQUe/bb730lxv0GFk/z72sm+myfumDmq4C0d5u7hfleGZf+sl6ox7H3tem3Qc2+zXo2Peum2HQYxSzBeS5bLN3v8tx6veeah/DDINemy7PaZDSrH3DDTcc/+droX/zfuZo6tUwz/JB2P3koebW/Fl9xdJ62962i9NCva9YeGuuXHban9t8Id51113Vpk2bqq1btzZzh8uXdMLnmjVrjoek3M6XdGn+TB/M0nSeL99ly5bVzeWl39ndd99d3XrrrfV05L75oo/2+tle7pNtjrLOIIPu+/TTT9fPp+i336UfaZo3H3/88ZMepxy/6F0/ld6LLrqoeuCBB+rKbvazrBPr16+vj1s5nhlyuaa2uR7H9muze/fu+jHzOO37ZP7q1avr6cixSVjNumnGTd/ZYesP29+i6zbn+p4a9NrM9fGHyT9c2a88Zl7HSPDPfs5lO3MlTLIghEkWgjA5ueYjTOYLN1+wg5q4+8kXf76cI1/46VvZVr58I1/gqS4V7WUlJKSqlC/n7Efv+m1lX4et08+o2y/Pq99zKqGxfZzKc0mQyX3bsiyPUx6r7Hu2m+23tYNUCSsx1+MY7demHX6ihLGEq3YIzLYSSj/2sY+d9BiD1i+P0bv9tq7bjH7Hvyyfy2szl8cfJtXNhNb2a1e2k8fNNVsXgmZuAKZWOZs3EpB6lS/pfLm3v8gjVZxUQaP0OUsQKmEoP/U4m1HWaRt1+6XKddttt9XjtlT38pzvu+++Zs6J59mvopvn2X7u5fGH6W2qHfU4lubyKK9NAm5v0EvQyrKEz/ZjZVtZt/cxyvq9+14eo1/TctF1mxn6vafm+trM9fGH+cxnPlMfz/Y/AWU7CZXDjsPpECYBmFoJIxlSmer3pVwqR5dffnk97nXxxRfX4yeeeKIeR6o8kaboVIJSiepVmpOHrTPIKNsv+53+cVmnPeSxy/MuZnuebaMEjt5jOepxfO655+pxlH0sTfqD9Hvdso8JpuU5f+ADH6i31bvv5TFGCWRz3WaqrcPeU6O+NsWojz9IKpy5PFa7K0FkHxMus2yhTsQRJgGYCCV0tIPdKFKVGST9EOPSSy+tx4OUgBCpJKX/WZofU4VKk2aqSu3Qly/vfuukf9xsRtl+kb5wWad3iGefffZ4EBn1ecaowatt1O33VvIGvTbZh3Jpot7HStDK/W6++ebjz7f0Xey378Ne/6LLNgeFvLL+qK9NzPXx+ynV4VQ5SyBNl4mMi3ZFdD4JkwBMhFLdGrX/WNGvClRcdtll9fiZZ56px4Mk2LUl8GU/su004abqk9DXDov91kkgHjVQzrb9SMhNX9R+Q8JnCSKjPs8YFJLaegNO1+M47LUpVcz2YyUYJWglrKdvZnmumR4W8IY9p67bHBTyyvqjvjZdH78t2yvV8LxH2oE04xLiMx5le3MlTAIwEa6//vr6yzVflun/NYqsn2GQUu186qmn6nGvVAijBNleCQTph5gTKKLfdkZZZ5BB951tv3vNZf1BIamtN5B0OY7ltRkUblKZ7K3gJWDF9u3bT+ljGIP2fdhz6rrNQfs919em6+O35dqSkUDZDq3tIV09YiGauoVJACZCvmjL9Q3Tr7B9MkeRCk3ORi4VvFS+hlW/sm6kebG3GTl90FLZScUoJzEUuU/vugcPHmymXjTKOv0koIxy3xIMPv7xj9fjXtn39jZKiOu3ftZtVzzL5YCGhaHegNPlOJbXpl9YynFIZfLCCy8cKUyVvoj9DHv9hxm2zRi0X+VYjPraDFIef1BobSvXluyt/LaVM+oXoqlbmARgYqR6U84MTnDJ5aJSCcqQ6TQF9+uXN+gLOc3JZXu5b+ljlu2VL988ZluCV9bNOmXdfPEnLOVC0aOu008CyqD75izdEsaynex31i3HIOtm/3M7+16qVZGTMhI0yvrleZZ128Hxmmuuqcc5vlkn4ag3uPcezy7HMQZVjXMcSmWyLb/qEtluHiND+xqOvfs1W/Uz5rrNYrb31KivTe/jl9elPP5sYTrBNI/VexZ3r7wHsk4+H1l/PgmTAEyUNPuWE1QiX4zlyzSXXkmzYe+X6rAv5LK93L/0Mcv2Bm2rLMu4vW76yJXHyf1mW2eQQfftrWa197usm/3Pcck2es/qTR/MNJcnXJXnmfsmqLYrhpkuwTDrJHz0nqXd7zmU/cnxGuU4xrDKX6lMtmXfcvmh8hwyZLs5rnkuvfuV7WcYdsznus1i2Dbn8tr0Pn7WzXp5/MybTfn5xN7Xu593vOMd9TiPM59mjqYhHeZZ/qty0XLm20K9r1h483HRcmA8qUwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMMlEmpmZMSzCAYDxM3P0mGYa5k2++Hc/eai5BSx2a65cVvm6gemkMgkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0NnP0mGYa5s3MzEzlrcVCeOwLh5spJsmaK5f5mwBTSphkQSRMArT5uoHpJEwCANCZPpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHRUVf8/76ZBHolDVTQAAAAASUVORK5CYII=\" 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margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = CHP(Q,L,D,dh,n)\r\n   K = f(Q,L,D,dh);\r\n   isDLvalid = true;","test_suite":"%% Coarse sand #1\r\nQ  = 8.92e-6;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #1--larger cylinder area\r\nQ  = 3.57e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.1;                   %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #2\r\nQ  = 2.44e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 9.69e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1\r\nQ  = 1.52e-5;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.1;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1--reduced head difference\r\nQ  = 7.61e-6;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Medium sand #2\r\nQ  = 7.08e-7;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.3;                   %  Porosity\r\nK_correct = 1.2e-4;         %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Fine sand \r\nQ  = 3.57e-7;               %  Flow (m3/s) \r\nL  = 0.075;                 %  Sample length (m)\r\nD  = 0.075;                 %  Diameter of cylinder holding sample (m)\r\ndh = 0.4;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-5;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Silt \r\nQ  = 1.17e-7;               %  Flow (m3/s) \r\nL  = 0.05;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 3.88e-6;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nfiletext = fileread('CHP.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-08-18T23:24:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T14:41:04.000Z","updated_at":"2025-12-01T14:29:21.000Z","published_at":"2022-09-17T14:42:34.000Z","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 constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\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. By supplying a 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\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 a standpipe, water is maintained at a constant level so that the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can then be determined from Darcy’s law\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 the head gradient \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 is simply \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=\\\"Deltah/L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h/L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = (gd^2/(180nu))(n^3/(1-n)^2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = \\\\frac{g d^2}{180 \\\\nu}\\\\frac{n^3}{(1-n)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity 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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the porosity of the soil \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 as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\rm\\\\,m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-6} m^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56205,"title":"Measure the hydraulic conductivity with a falling-head permeameter","description":"A falling-head permeameter is another device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . Unlike the constant-head permeameter, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area ) that falls. In other words, the head difference , or the difference between the water levels in the tube and the outlet, decreases in time. \r\nThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\r\n\r\nDarcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nDerive and solve an ordinary differential equation for the head difference . Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the previous problem. Use  and .\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 902px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 451px; transform-origin: 407px 451px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82px 8px; transform-origin: 82px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_c\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37px 8px; transform-origin: 37px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Unlike the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003econstant-head permeameter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_t\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147px 8px; transform-origin: 147px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) that falls. In other words, the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145px 8px; transform-origin: 145px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116px 8px; transform-origin: 116px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDerive and solve an ordinary differential equation for the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eprevious problem\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 981 cm/s^2\" style=\"width: 90.5px; height: 19.5px;\" width=\"90.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-2} cm^2/s\" style=\"width: 94px; height: 19.5px;\" width=\"94\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 359px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.5px; text-align: left; transform-origin: 384px 179.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 401px;height: 359px\" 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alt=\"falling-head permeameter\" data-image-state=\"image-loaded\" width=\"401\" height=\"359\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n)\r\n  K = f(delta,t,L,Dc,Dt);\r\n  isDLvalid = (Re \u003c 1);\r\nend","test_suite":"%%\r\nDc = 11.28;                                 %  Diameter of cylinder holding sample (cm)\r\nDt = 2.26;                                  %  Diameter of tube (cm)\r\nL  = 10;                                    %  Sample length (cm)\r\nn  = 0.15;                                  %  Porosity\r\nt  = [0 1 2 5 10 15 20 25]*86400;           %  Time (sec)\r\ndelta = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];    %  Head difference (cm)\r\nK_correct = 3.08e-7;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                %  Diameter of cylinder holding sample (cm)\r\nDt = 2;                                                %  Diameter of tube (cm)\r\nL  = 15;                                               %  Sample length (cm)\r\nn  = 0.25;                                             %  Porosity\r\nt  = 0:60:420;                                         %  Time (sec)\r\ndelta = [25 20.63 17.03 14.05 11.60 9.57 7.9 6.52];    %  Head difference (cm)\r\nK_correct = 3e-3;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 7.5;                                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.75;                                             %  Diameter of tube (cm)\r\nL  = 7.6;                                              %  Sample length (cm)\r\nn  = 0.2;                                              %  Porosity\r\nt  = [0 1.25 2.36 3.74 5.40 7.20 9.28 12.08];          %  Time (sec)\r\ndelta = 88.9:-10:18.9;                                 %  Head difference (cm)\r\nK_correct = 5.25e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                                                               %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                                                               %  Diameter of tube (cm)\r\nL  = 7.5;                                                               %  Sample length (cm)\r\nn  = 0.2;                                                               %  Porosity\r\nt  = [0 1.06 2.11 3.62 4.88 6.53 8.39 10.67 13.52 17.37];               %  Time (sec)\r\ndelta = [56.02 50.36 44.7 39.05 33.39 27.73 22.07 16.41 10.75 5.09];    %  Head difference (cm)\r\nK_correct = 3.89e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                              %  Diameter of tube (cm)\r\nL  = 7.5;                              %  Sample length (cm)\r\nn  = 0.2;                              %  Porosity\r\nt  = [0 2.28 5.13 8.98];               %  Time (sec)\r\ndelta = [22.07 16.41 10.75 5.09];      %  Head difference (cm)\r\nK_correct = 4.79e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                      %  Diameter of cylinder holding sample (cm)\r\nDt = 2.5;                                                    %  Diameter of tube (cm)\r\nL  = 15;                                                     %  Sample length (cm)\r\nn  = 0.18;                                                   %  Porosity\r\nt  = 0:7200:50400;                                           %  Time (sec)\r\ndelta = [50 43.15 37.23 32.13 27.72 23.92 20.64 17.81];      %  Head difference (cm)\r\nK_correct = 2.99e-5;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-01T17:35:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-01T17:35:38.000Z","updated_at":"2026-02-10T14:28:46.000Z","published_at":"2022-10-01T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Unlike the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econstant-head permeameter\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) that falls. In other words, the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDerive and solve an ordinary differential equation for the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 981 cm/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 981\\\\rm\\\\,cm/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-2} cm^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 10^{-2}\\\\rm\\\\,cm^2/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"401\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"falling-head permeameter\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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vfvUrWbBggdxzzz3eWgAAsgcjdFaz06dPy3e/+1359NNP5Yc//KH069fPWwMAQHai5qKa2H4VhYWFMmjQIPn1r39NsAAA5ATCRTV45ZVXTBPI9evX5dSpU/Lcc895awAAyH40izi0Z88e0wTStGlT0wRSUFDgrQEAIHcQLhz46KOPTKjQ/hUaKgYPHuytAQAg99AskgLbr+KRRx6R7t27myYQggUAINcRLpJk+1VowNDOmi+88IK3BgCA3FZr4WLChAnenHvVue2DBw/KQw89JJs2bZJf/vKXUlxcbPpYAACA22qtz0VeXp5U166rY9s6ToX2q9Bwof0qhg8f7q0BAAB+NItUQW8nnTt3rmkC6dy5s+lXQbAAACA2wkUcGzdulFatWskHH3xgQoX2q6hXr563FgAARJPT4UI7ZUajTR96B8iPf/xjKSkpkQ0bNtCvAgCAgHI2XPzkJz+Rp556ygx8ZWm/itGjR8uIESPk2WefNX9grEePHt5aAAAQRE6GC9s5U+n//n4Vbdu2lXPnzsmoUaPMegAAkJicvFtEaye0P4Wl/Sh08Cu9C+TLX/6ytxQAACQj58KFhgoNF37an0I7bN5zzz3eEgAAkKycahbxN4f46fJ58+Z5jwAAQCpyKlxosNAgEY3eOVJaWuo9AgAAycqZZhENDnpr6f333+8tEdO/wt/HIvIxAABIHMN/AwAAp3J6EC0AAOAe4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE7llVfw5mtUXl6eRO76yWWl8ttPrnqP4nvgvgbyyowHvUfhom0bAADUjLSquRj7aAtvrmqJlAUAADUnrcJFrw5/Y2okqqJltCwAAEg/adfnIkiNBLUWqEnnzp2Txo0bS9euXeXatWve0sTF286FCxdibnv79u3medrcV7duXVm3bp23Jv46xKbnyZ43e+7GjRsnJ0+e9EoASEXahYuqai+otchc169fl/vvv1/uvvtuuXTpkrc0XJAy2Wb//v3SvHlzadKkSaVj1kAyevRouXr1qvn/iSeekN/+9rdVrkNsq1evlj179sjHH39s+maVlZVJz549TeDo3r17zvzcAdUpLe8WiVczQa0FslXbtm2lQYPwYL179265cuWKvP7667J+/XpzYZw7d26V6xDf1KlTpX79+ma+RYsWsmPHDhk6dKh5DCB1aRkuYtVeUGuBbNS7d2/zDfro0aOhC54Vr5qeKvzkFBYWyne/+105fPiwt0SkTp06smXLFvnzn/8s9957r7cUQLLSMlyoaDUU1FoASFWrVq3kpz/9qQwePFgmTZqUUj8aANGlbbiIrL2g1gJq165d5punvyPeokWLol4gtJPkiy++GNZxr1+/fmHfWP1u3bolr7zySlgHye9///umT0MiEt2O7eg5YsQIb8ntfgH63GXLlpnH2qdCH2tflAULFsRcZ/sLBD1Pdt/anKLz9jna6dTf9yCZ7Z0/f16mT58eek6nTp1innulnVO7desWKt+uXbuo+0jkZyAWDRgXL140zVCNGjVK+PkAqlBeS4Lsev/xP5T/7Yz9ZtL5oGrxsBDHX/7yl/KWLVuWV3ygl1d8sHtLw8Ur89prr5n3Nj8/v7ziglo+ZcqU8ooLg1nWpUuX8oqLt1eyvPzgwYOhdX379jVlBw0aFHr+oUOHvJJ3zJgxI7TeX95OkfuIJdHtnD171rzW4cOHe0tuv359bsVF3jzHHsOzzz5bvnPnzpjrdLuJnCe7by1ny+h2/ec/le1FngN9XNW5j9zHhg0bvFKJvZaqnDp1qvyZZ54p79mzp3l+x44dy0+cOOGtBZCKtA4XaurSX5spEUG3jZplg4O+PwUFBeZDPXKyF8zIcGEvWpEXkJs3b4YuTP6L0L59+8rHjh1b6WJhL07+C7nS8tH2W1ZWFnrNQS5eyWwnWriwoh2bFW1doufJlo/2ulQq29Pj8T+nqnOvF/fIQKlByr6Hib6WWPS90LDz0ksvhbazbds28/xooRZA4mo1XOw8dbnKqXjbR2aKti7aZLed6YqKisxx2EkfW+m0LhH+cFHVFPkhH+/iYS860S7OkWKVtduPdmyxLmrRJLOdeK8/3nFHW5foebLLYl1Uk91eIkEl3j78En0t0difwWjvT6zwAyBxadvnwvrq/Z83U67RNuuK9yc0+W8xTHWd3r6YzPOirUtGxYXMtHf7t2mnig9/qfjw90repn0Yzpw5Y+a1R7/eRuif5s+fb45JxyuIbDfXfhdbt26tVNbPbj8/P1+GDBniLU2cq+0kK5XzNHDgwEp3SaSyPX0PI+98adasmTRs2NB7dJv/nLVu3dpbWlkqr8XvpZdekk8//TTq+zNmzBjzut9+++24fUMAVC3twwXc0kGqtDOc/p+JKr61yqpVq8KmNWvWeGvv0IuRdibUwamGDRsWt2w2CnqegnK9PUvfp/fff1/uuusu08kyiGRfiw0osfalt6N27tzZewQgFYSLHKN3MZSWlpr/M41+uz106FDUGg+d/ONEzJ49W5YvXy5dunSREydOhMqcPXvW3B2QzRI5T0G43p6fvaDfvHnT3GlSlVReiw0ysehradOmjfcIQCoIFzlEayv0ljul/2dK7YX90L9x44YJB1Wx31D1QlRcXCzt27f31kSX6PZjcbWdZLnef00cT9B9uHgtuo14Qcb+3HTo0MFMAJJHuMghWluh7c1K/8+k2gs7BsTixYujtqnr2AdVjVipF48VK1ZU6nOhYm1fL0I65kO050TjajvJcnGe/FxvLxob/qLt49133w1tP9XXouFi+PDhJqBov4pIBw8eNP1zZs2alXRNDIDbCBc5wl9rYWVS7YUOkT1jxgw5duyY6RCqg2FpR76JEyeagZQGDBggx48fN2X9F5E+ffqYjnpaTv8wmB14KlKPHj3M35bQ7WuziW5bR3DUToZf+tKXzP6CcLWdZCVynoJwvb1o9K+R+s+Zvl+6Dx2Mq2/fvqHtu3gtdl/z5s0zA5vZkKLBRPvmFBUVyahRo8wyACkoryW662i3kqY62W0j3A9/+ENzXiInXV5T4g2QZVVVRscjsGNh6JSfn28GkSotLfVK3LF27Vpze6Itq+WOHDlith/tdkMdL2HOnDlh216yZIlZXnFBCnQrqkp0O2fj3EYZ7/bLeOuCnqd4+/ZzsT373kY7j3puiouLw94vHQtl4cKFlcom8jMQTbR9JfJ8AFXL038qfrlqnH7TqAgD3iN3+hc0MtuupcNKS1o7ob3jbZOIX9OmTU2Vfb169bwlAACkhnCRA06fPi0bN270HompEtbqX0urgSu+JXqPAABIDeEiB3F+AADViQ6dAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIF8gqEyZM8OaQaXjvgOyRV17Bm69ReXl5svPUZe+RO/0LGplt19JhZYRsPj+895mL9w7IHtRcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwKq+8gjdfo/Ly8mTnqcveI3f6FzQy266lw8oI2Xx+auPYnlxWKr/95Kr3KL4H7msgr8x40HsEP35vgexBzQWQorGPtvDmqpZIWQDIVIQLIEW9OvyNqZGoipbRskAyzp07J40bN5YRI0Z4S4D0RbgAHAhSI0GtBSJdv35d7r//ftMkFG26++675dKlS17pzHL+/HmZPn26CUT2eOrWrSv9+vWT999/3yuFbEW4yAGlpaVSWFgYmpT/8bZt28wyJK+q2gtqLVCVgoIC6dmzZ9j0yCOPeGszy+rVq6Vly5ayfPlyuXLlSuh4bty4IXv37pUHH3xQJk2a5JVGNiJc5AD9Rf7ss89kz549ZlJ2/vTp0+abBFIXr2aCWgvE06BBA3n33XflvffeC5t27Ngh9957r1cqM2iw0OCQn58va9euNZ107fHovH6ZadSokSk3d+5c71nINoSLHFFUVOTNhZs9e7bUq1fPe4RUxKq9oNYCuUKbeebNm2fmX3/9dRk7dqyZ9xs0aJBs2bLFzC9ZsiRjm30QH+EiRwwfPtzUYPg1bdpUnnzySe8RXIhWQ0GtReb7t8t/9ebS165du2Tw4MFhfTa0VvLkyZNeidv2799v1kXrGKq1CVWti1fbsH79eikrK5MuXbrIsGHDvKWV9ejRQ4YOHSpXr16VnTt3ekuRTQgXOSSy9oJaC/ciay+otcgO3/7BEVmy8V/TNmTohX/AgAGyfft2GT16tEyZMsUEC+3f0KFDB9m4caNXUqRbt26mP4Q2uUTWGtggogHh2rVrZt7SddrUMWTIEG9JZfb5Ghzq169v5qOpU6eO+cKjNm3aZP5HdiFc5BB/7QW1FtXHX1NBrUX22P6//q3aQsbNmzfl2WeflalTp4ZN69at80rEpjUR2sdB+22cOHHC1B6sXLlSdu/eHeqsPXny5FCQ0C8UI0eOrFRroE0ab775ppnX7ehk2XUaVHSK5tatW3LmzBkzr51TkdsIFznG1l5Qa1F9bO0FtRbZqTpCht5FsWHDBlm1alXY9NZbb3klYispKTH/v/rqq9K+fXszb2n/hhkzZlQKEracv9bgyJEjpsZCaz309bz99tvemjvrtMYjXo1EIr761a96c8hGDP+dQbSt03aWUhoUbPtnIuu+8pWvyPHjx024cLXNdFo37unZMn7abO9R7fjwd//X/P/V+z9v/kd8+45ekv3HMrNjn9ZOjRvU0nuUGK0RaNu2rfzxj380g2TFuzNE13ft2lX69u0bChRaW/DNb37TNIfs27dPHn74YbPcz9694f+dsdtq1aqVeZ4GBi331FNPmeYS7Yj5hS98IbRu5syZsmzZMhOARo0aZbYRyb6WrVu3xi1n2delNar2eJA9CBc5SD/QsrXWorp+rlD9BrRrnLa/twNnvufN3dG0cT0TLB79WhNvSeJSDRdBnh/tIh4ZSrQDpj7+5JNPTHPKt7/9bdNBVLept43qOvs43mu0IcQfZGJJpCwyD80iOYjmECB5GipmjWoj617qmlKwcEE7Rnbu3Nn02dALfzxazrIdKm3zh46mqX03tCPm5z//ebPONqXYdQMHDqxyzA3b3FLVCJz0z8h+hAsACCCdQoWlIaFNmzYmJJw9e9ZbeodexDdv3mzmIy/iOjqv1kpoM8aHH35oRtK0Zew67ZOhNRm67vHHHzfr4rHP08By+PBhb2llOriW7lc7oepdLsg+hAsAqEK6hQo/OyaF3hESOaaF1jzoRTzauBMtWrSQ3r17ywcffGAu9v4LvV2n/S/0jpWgIUD7cEyYMMGEnT59+oSCjaVhR4cE12YapZ1Qq6oNQWYiXABAFdIxVFgaAuwdIXqb6JgxY8xtrFqLoINq6dgUxcXFle7ysE0j+jy9fdXf7GFrRHSd/pmAIE0i1qJFi0zzigYMDT7aD6pXr15mfI277rrL/DEzpa9Lm3OQnQgXAJDhli5dasa00A6f9pbWAwcOmLs+jh07FvUuEmWbMZS/T4byj9IZpEnE0mCiw3trrYneCqv0tRw9etQ0uyxcuNC8Vq0NGTdunHTq1Im/kpqFuFsEWYW7RTJXOt8tAve0o6iGC/vHFLlrJLtQcwEAqHHar8OOIqo1Lsgu1Fwgq1BzkbmouQCyBzUXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAApwgXAADAKcIFAABwinABAACcIlwAAACnCBcAAMApwgUAAHCKcAEAAJwiXAAAAKcIFwAAwCnCBQAAcIpwAQAAnCJcAAAAp/LKK3jzNSovL092nrrsPXKnf0Ejs+1aOizUMt77zMV7B2QPwgWySoN6eXLtr94DZJT6dUWuXuf3FsgGhAtkFX3vj6z0HiCjdJsqCf/efvbZZ3LPPfd4jwCkC/pcAMhI169fl8LCQvM/gPRCuACQkV555RUpLS01/wNIL4QLABlHaysWLVpk5vV/ai+A9EK4AJBxtLbi008/NfP6P7UXQHohXADIKP5aC4vaCyC9EC4AZBR/rYVF7QWQXggXADJGtFoLi9oLIH0wzgWyCuNcZK4g41ycPn1aNm7c6D0SmTdvnhQVFXmPREaNGiUFBQXeIwC1hXCBrEK4yFzJDKLF7zqQnmgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAgi5w7d04aN24sI0aM8JYANY9wASAnXb9+Xe6//365++675dKlS95SWJwfpIJwAQAZ5NatWzJs2DCpW7euHD582FsKpBfCBcJcuHBBrl275j26jWpWAEAiCBcZRr+1vPjii+Zin5eXZ6Z+/frJ5s2bvRLJ279/vzRv3lyaNGlCNSgAIGmEiwyibaAPPPCALFiwQL74xS/KlClTZMKECbJ3715Tq7Bx40avZGratm0rDRo08B4BULt27ZLCwsJQqNdmiUWLFsWs6Zs7d66cP39epk+fHnpOp06dYjZl6BcHf9nISX/HZ86cKXfddZds3bpVbty4Id27dw+tj/b7H7nNePsHXCJcZJD169dLWVmZDB8+XE6dOiUrV66U1atXm2UjR470SiWvd+/eUl5eLkePHpX69et7SwHo79mAAQPkwIEDMnr0aBPsNYC/8MIL0qdPn0oBQ3344YfSuXNn83uq5QcNGiTHjx835SMv8PaLw/Lly6Vv376mfNeuXc26/Px883j8+PHyjW98w8w3atTIrLOv5emnn5aOHTuaZdbp06dNLWSQ/QOuES4yhH4DsU0fjz/+uPnfatGihfzsZz+TUaNGeUsQxO//6M0AcWhNxPPPPy9dunSRK1eumJCvF+yLFy/KjBkz5NixY7Jlyxav9B0bNmwwQUGfo+W3bdsmr732mqlx0NpHP/vFoaioSPbs2WPKHzx4UIYOHWrWT5o0yXyp6N+/v/zTP/2T+SKgoeO5554zZVesWCHt27c3ZS0NF0H3D7hGuMgQderUkTZt2ph5/dAISqtyBw8eHKoW1Un7aJw8edIrcUeuddz8xQGRYS+KbK34H4hFL9x6gZ41a1ZYjZ7+Tk6bNs3UImzatMlbeoeGkTfeeCPsOdqsouU1SPhrO/T3UcPCkCFDvCW3t6+BQsPA2bNnvaXBJbJ/wDXCRQaxF3391rFu3TozH4+tyt2+fXuo+lSDhfbR6NChg7M+GplMay/mvU7IQHRaY3jmzBkzr7UTU6dODZvmz59vgke0i3XLli0rNS82a9ZMGjZs6D2qXrW9f+Q2wkUG0arQOXPmmG8y48aNMx3KNGRE+waid35oVaq2C584cSJUlbt7925TPaomT57MXSEeQgaqos0cq1atCpvWrFnjrU2NNmno7/Xbb7/tLbnTFKo1Gq1bt/aWApmBcJFhXn75Zdm5c6epgbAhQ6s5I2sySkpKzP+vvvpqpbZY7dilbcVXr14120qF9oj3N7nU9qS6TQ02rfqFKR7GHzLokwFLL/CHDh0yHZ6jTal2grbNFfPmzTO/21or0qNHD3NXiDaVPPzww15JIDMQLjKQdurSGgi9Y8QfMvRCr2xVbrxvPDZwJNJ/IxrdZ7QP29qa1JGVwaYp/9kUr2RoT5FXZoo0/xtvAXKW7euUbL+HIPT39dlnnzVhX28t/81vfmNqRfTOjoULF5p+E0CmIVxksIKCAhMytAe4WrJkiWnm0A+r999/39wP36pVK7MuFi2H2zRUbHlZpGg8wQJ32L5OixcvjtoEqZ2mo3WQDsr+vur4MjpuxuXLl01Q/utf/yqzZ8+uVCNSE4EHSBXhIguMGTPGdN66efOmueNDP3z0/nr7OB4tl+sIFblNawy+/vWvS69evcIm7bOkYUL7OtlbTrUPk222mDhxommK007TWsuQrHr16pnaiY8//tiMS+Fv5tPXobWSkeHF1jzq2Bf6WvSOsOrqoF3V+QGiIVxkoaq+2diOYkprP3JV17aECtymzYM6QJZ/Ki0t9daKLF261HSE1oGt9G4rbbbQQKDjSGi5VMeY0T5SeteJDoSld3XZSWsvtD+V3lbqH/hKg43t3K2vRTtwV2enz6rODxApr9w2VNcwTeU7T132HrnTv6CR2XYtHVa10RoIbY/VQXP03ndLg4JWnS5btsx8AO3bt89Uo+qHjY7Ep9+0tCOav1On3pqq33T85ZXuQz889QPTdghVsZanI33vtT8FMo92sk309zYbftft76r+Xkf7/dJbyrWWQAfYsv2qgHRHzUUG0Y5e2v6rH6jt2rUzVZPar0KDhXbeLC4uDgUFW5WrVZo6poU2nWj1qfZK12ARWR5A7dIB7CLplwfbJJLLtYzIPISLDKEdM7XT1zPPPGNuWbPVlBoStIpUq1Qjb1fzV+Xae/T1OWPHjjXtx9zeBtS+bt26mT5TWkOhY9folwDbp0P7YNhayWHDhnnPANIfzSLIKjSLZK5cbRZRFy5cMH+07J133jFjZlg9e/aUJ598Ur71rW9Ry4iMQrhAViFcZK5cDhdAtqFZBAAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgBkjNLSUiksLAxNyv9427ZtZhmA2pVXXsGbr1F5eXmy89Rl75E7/QsamW3X0mGhlul7f2Sl9wAZpdtUCfR7+9BDD5mQEalp06Zy7tw5qVevnrcEQG2h5gJARikqKvLmws2ePZtgAaQJwgWAjDJ8+HB58MEHvUe3aa3Fk08+6T0CUNsIFwAyTmTtBbUWQHohXADIOP7aC2otgPRDuACQkWztBbUWQPrhbhFklTqfy5N//3/eA2SUz1V81bn174n93j722GNSUlJCuADSDOECWaW6fq5y1Z//9H+k7OwZ+U+du3lLqs+Ado0T/r29fv06wQJIQ4QLZBXChVs3/vpXeeJvO8vlP1yUrxR0lBat20iLVm3kwYd7Vcx/VRp/oYlXMnXJhAsA6YlwgaxCuHDvX9YWy/9Y8JL3KJyGi5Ul7zoJGYQLIHvQoRNAXEMfnxgzPIz6+2ed1l4AyA6ECwBx5deta0JEpF4DviHfGveU9wgA7iBcAKhSZO2FBo4rf/g3+fSTMm8JANxBuABQJX/thc4vfX2r9BwwRJ4Z9ajsfvstsxwALMIFgEBs7cXkGf9gbk0d/ffPybwVP5VXl/2j/GjeTHNnCQAowgWAQLTGQsOEv5+FhoyVJXvl8qWLphZDx8QAAMIFgMCiDaZ1d8P/KP+4Yp08OmKUzBw/VLaXrPfWAMhVhAsATmiNxoL/+TPZ+OqP5b+/OI1mEiCHES4AOKOjeC7f+E5FsLguU7/5dZpJgBxFuADglDaTfH/pqzJq8rOmHwbNJEDuIVwAqBaDRowxtRjaTPLfZk42fwQNQG4gXACoNi1bt5GVb70r+XXrmVqMfz193FuDbHHu3Dlp3LixjBgxwltyx4ULF+TatWveo+ph99+1a9dq3xeCI1wAqFZ6C+v3Xl5hmknm/P1/ka0b13hrUNPOnz8v06dPNxdj/SN/OrVr107GjRsnJ0+e9Eq5sX//fmnevLk0adJELl265C1FriBcAKgR2kyiI3v+YtNP5B+mjaWZpIatXr1aWrZsKcuXL5crV65Iz549zXT69GlZt26ddO/evVpCQNu2baVBgwbeI+QKwgWAGqPNJNoPo/G9TWTqiL7yv98/4q1BddJahEmTJpn5tWvXmj9t/95775lJ50+dOiWPPvqoWe9K7969zbaPHj0q9evX95YiVxAuANQobSZ5rmip/Nc5P5Ciad+Wf1lb7K1Bdbh+/bo88cQTZn7Dhg0yduxYM+9XUFAgb731ltx7773eEiA1hAsAtUL/ZLvWYux5u8Q0k6B6HDlyRMrKyqRLly4ybNgwb2ls2nyifTHmzp3rLQlX1XorVkdPu1yfb/uA2P4fnTp1ksOHD3slw926dUteeeWVUH+RuhUh9fvf/75cvXrVKxHdrl27pLCwMLQPfd6iRYsqdf70vy6dt8/RjqL0GUkc4QJArWl6X0vTD0P/VwcPHjT/w52SkhLz/9ChQwM1T+hFtVGjRrJ169ZKF2C9wG/evFny8/NlyJAh3tLkfPjhh9K5c2dZuXKlTJkyRQYNGiTHjx+XPn36RA0Ys2fPlqeeesqECS2vr/MHP/iBdOzY0fQhiUaD0IABA+TAgQMyevRo8zzt//HCCy+Y/US7u0RflwaKPXv2mP8/+OADbw0SQbgAUKu0mUSbSNRjjz0mCxcuNPNInYaBM2duj5KqTR9BtGjRwvSXOHbsmGzZssVbepuGPw0dGiwefvhhb2lytImmb9++JhhowNi2bZu89tprcuPGDVmwYIFX6jbtM7Js2TITDD7++ONQea2R0U6q0Wjtw/PPP29qbHQf69evN8+7ePGizJgxI+rxKX1drVq1MiFGa33+/Oc/01yUBMIFgLShHQt//vOfm5Dx2WefeUtRk+rUqSPDhw8385s2bTL/W7YW5PHHHzf/p0Iv+m+88UZYbYqtNdHQ4K9VsPvVsOC/0GsQ0hoGfU6kFStWmFAxa9assH3o8U2bNs08J/L4lAYYDS50Qk0N4QJA2mjatKn86le/kgcffNCMv6AXDtS8MWPGmBqBHTt2hPobaMfQN99801x8takhVbr9yAt4s2bNpGHDht6j22ztSyJNMf4aG62dmDp1atg0f/58EzwiQ4waOHAgNRUOEC4ApB2tFtfqaW0nr6rjIGLTb+lt2rQx8zqeRVD16tWTkSNHmqaBnTt3mmW2Y2imXXz152jVqlVh05o1DORW3QgXANJSv3795Ne//rXs3bvXVJd/+umn3hokon379ub/aB0047F3edimA5dNIjVFazsOHTpkxtuINjEGR/UhXABIW9pMsnv3btPx76GHHjJt4UiM7ccQqwNjLN26dQs1jWiNhTaJBL2d1SVb+6IdPc+ePestjS+Z58AtwgWAtKdNI/rNecKECTJnzhxvKYLQOx/0vKnx48ebob4j6XgTequq/++LaNNIUVGRaRrR5ikNGEFvZ3XN1qIsXrw4rPZF7wjR20Wj3Yoa6zmWjn/h+u+p4A7CBYCM0KNHD3M3SWlpqTzyyCM0kyRAB43SUKbf5PWPlOngUL169TKTzmsNxTvvvFNpQCpb66HjRLgY2yJZ+t5rsNHaF3092ilz8ODB0rp1a/nSl75kmtAi6e209pZT7YSqZfR5EydONMesnVJ1XA1UD8IFgIxxzz33yC9/+Uv5u7/7O5pJEqDNBC+//LLpnKmDVSkNDDrp+Bc6JLhehCPHrrBjXqgOHTqYqTbo69fhyW1A0k6Z2ly2ZMkS87oj7zCxli5dan5GtHZD++7o8/T2V21m05A6atQoryRcyyvXXi21QJPjzlOXvUfu9C9oZLZdS4eFWlZdP1eofgPaNU7o91YHdNLqeh2TQe8u0Wp8uDdz5kwzgJXedcHFGEFRcwEgI2lVud5N8tFHH5nqe/0fbrke2wK5g3ABIGNpM4l29NTbI7Ufhv7dC7ijQ2Zn4tgWqH2ECwAZ77nnnjN9MbRNnj9+5ob/j5Rxhw4SRZ8LZBX6XGSuRPtcRKPV+PS9AGofNRcAsgbBAkgPhAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAABOXLhwQa5du+Y9Sm/nzp2Txo0by4gRI7wlcIlwASCrnD9/XqZPn24uHDpiq07t2rWTcePGycmTJ71ScG3//v3SvHlzadKkiVy6dMlbinSzevXq0O/Fxo0bvaXuES4AZA394GzZsqUsX75crly5Ij179jTT6dOnZd26ddK9e3cufEnSvzUybNgwqVu3rhw+fNhbWlnbtm3NX1FF+rF/L8batGmTN+ce4QJAVtBvzpMmTTLza9euNX+n5L333jOTzp86dUoeffRRsx7u9e7d25zno0ePSv369b2lSCdaq6e/J4MGDTIhfMeOHdUWtgkXADKe/sGyJ554wsxv2LBBxo4da+b9CgoK5K233uJPhyNn7d6929Tofec735GRI0fK1atXZefOnd5atwgXADLekSNHpKysTLp06WKq7oOwHfrmzp1r5gsLC007dNeuXcO+ze3atUsGDx4caqfWqV+/fjH7b2h5uy2dtBlBa1T8HR2DlIkl6HOjlVu0aFHMfWzfvl26desWKq/9VGz5mTNnyl133SVbt26VGzdumOYlW86221fVQTKR8+h/b2wfGvucTp06xWyW0Q6lL774Ylh/G91HvGacqiSyzUR+poK+N66OyTaJaJPVgAEDQu/T4sWLA/3cJYo/uY6sUl0/V6h+qfzJdb34LVu2TIqKiswHexD64a8f+nrB27Ztm/lGp4+1f4au0xoO7cNhm1pGjx4tDRs2lA8//FD27NljlmktyahRo8y80irnPn36SH5+vnzrW98y5X/3u9+ZC8u+fftMc0GQMrEEfa593f5yP/vZz8wxagCL3I89f9HK6zFqJ01tn7fL7LnQwPHUU09J+/btQ+ezb9++UlJS4m35tkTPY+R7o9+w9du2HquGIH2degwPP/yw9wyRQ4cOyWOPPWZen74G7fsRr3y812slu80gP1NB3ptE9x+P/dkZPny4OV4NG9/85jfNthLZTlCEC2QVwkXmSjZc2A9J/VYdeZGKx14Ion2oK/thrN/09ENeL6CWfiDrBUTX2YtGkA/rVD7Qgz7XHlerVq3CjkmfP3v2bBMi/OfJHmfHjh1NFbm/2Ui/YX/xi180x17V/u1+Iy/WiZ5H5X9v9GL4xhtvVApO9iJp6X5WrVpljtG/j1jlY71ev2S3Getnyq5P5L1JZP/xaIBcsWJF2Htnt5NIKA+KZhEAOU0vbPot038RUPZD+9VXXw37YFfaIW7GjBnV2madLL2A6MVt1qxZYcdUp04dmTZtmjRq1CjsLgF7nFr17g8Wqn///pWOPVGpnEe9QPuDhdLmBD0GbQbzV+drh1LtyBu5D1s+GcluM9bPVKLvjatj0j5Jb775pnTo0MFMlt2OBnPXTSOECwA5beDAgZUuqvpN8syZM6bquXXr1t7ScPYDX6u8lV4gvve975k+CfpNXb8RfvTRR2adFaRMLEGea1+32rJli0ydOjVsmj9/vrm42QtzkONMRTLn0U/vaIi8QDdr1sw0JcSifRT0Yhl5zKlIdJvxfqZUkPfGL9Vjsn2Shg4dGnY+W7RoYQLMsWPHzGtyiXABIKPpRbdNmzZmPtoFKhl6IXj//fdNnwKtwo5Hy1n6Qa3fwHVsDa1y1udqB0R/p8UgZWJJ5Llava5V6v5pzZo13trbEjnOZCR7HpOh+9KOnzqQl3bqjXXMiaiObaog741ytX9be6R9XPyB5umnn5Y//elPZp3rMS8IFwAynv3266p6VwNL586d5ebNm6adPB4t56dNCXrL3+9//3uZM2eOHD9+3FTv+3v3BykTS5Dnak2B9m/QPizRJjsWRSLHmYxUzmOitF+CDp6m5+LEiROhYz179mzSzSLVsc2g741ysX897zaM7N27NyzQ6GQ71boe84JwASDj2bZjV9W7tjZEmyD0gzySfqO0Ix3q+BnRaPX9yy+/LK+99lrM7QQpE0u051b1uiMlWj5RLs5jELod2/xSXFxcqY9CMlxvM9Fz7Wr/dmwL7bTpDzF20uCnzSWu+w8RLgBkPK1ynzBhgpkfP368Geo7ko6XoB+iQZoflB0HYPLkyZWeox/CWkui3yjtuBraaS7a9v2Pg5SJJehzqxq/QO8A8T/HXrSilX/33XdDZZMNIomeR5f0Am07UbqSyjYTfW+iSWT/WlbDmwaUIUOGeEvD6fuqd50ol00jhAsAWUEHIdJmAr346R8p09uSe/XqZSad186B77zzjvmGFoT2b7B3MmgP+zFjxph2aq0l0dsn7TdKfwe53/zmN6asDnJky+rthf6LZ5AysQR5rn3dWoujdy3YshMnTjTnQQdQ0qYUS8+VhhYtr7U/9jh10Ca9TdNf1gYRDXBaRs9DVX/8KpnzmCh7gdT3Xju76j70eHV8Dj0/yaiObSby3rjYvx3uW8+7TrHotvX34+233w41r2kw0Z8pfV062WAUFOECQFbQD2NtJtBvw3qLozpw4ICZtMpdhwTXD/VExpZYunSpuaVQxyawnfB0e9G2Va9ePfNB/swzz4TatrWsXhDsmAZBysSSyHP9r9uW1Vs6NSyUlpaGjQWi502HRdcLvF7w7HHq+BYLFy4MCzy6LxvgtIy+niB3mSRyHpOlr01v27THoP0MtLOr3imhF85kVMc2E3lvUt2/bRLR8FjVz5YOB67vqwYMDRY6psnnPve5UPOJvs+J/BVVBtFCVqmunytUv1RG6ATgjnYC1TuSfv7znycd/Ki5AAAAIZ988om5RTWV25MJFwAAIOS+++4zA5Wlcnsy4QIAAIToyJ1f+9rXZMGCBd6S23+bJJE+F4QLAAAQop18//mf/9l0trV3i+jtx0H/KKAiXAAAgDB6B4n+eXftZK1T0L++ahEuAACAU4QLAADgFOECAAA4lZXhokePHqFOKEy5NQEAal/WjdAJIDMxQieQPWgWAQAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgVF55BW++Ro0YMUJKSkq8R4A7u05f8eaQSQa0ayy19HEEwLFaCxeFhYWyZ88e7xGAXHf33XfLn/70J+8RgExWa+ECAPyuX78u9erV8x4ByGSECwAA4BQdOgEAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgFOECwAA4BThAgAAOEW4AAAAThEuAACAU4QLAADgFOECAAA4RbgAAABOES4AAIBThAsAAOAU4QIAADhFuAAAAE4RLgAAgEMi/x8lhOZy8L/U+wAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":55825,"title":"Measure the hydraulic conductivity with a constant-head permeameter","description":"A constant-head permeameter is a device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . By supplying a flow  to a standpipe, water is maintained at a constant level so that the head difference , or the difference in water levels between the standpipe and outlet, is constant. \r\nThe hydraulic conductivity can then be determined from Darcy’s law\r\n\r\nwhere the head gradient  is simply . Darcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\r\n\r\nwhere  is the acceleration of gravity and  is the porosity of the soil \r\nWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use  and .\r\n\r\n                              ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.2px; transform-origin: 407px 419.2px; 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: 256.342px 8px; transform-origin: 256.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.7333px 8px; transform-origin: 65.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. By supplying a 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: 75.8417px 8px; transform-origin: 75.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a standpipe, water is maintained at a constant level so that the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah\" style=\"width: 21.5px; height: 18px;\" width=\"21.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.533px 8px; transform-origin: 188.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.533px 8px; transform-origin: 209.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can then be determined from Darcy’s law\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4167px 8px; transform-origin: 77.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the head gradient \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: 18.5px;\" width=\"39.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 8px; transform-origin: 30.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is simply \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Deltah/L\" style=\"width: 38.5px; height: 18.5px;\" width=\"38.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 214.6px 8px; transform-origin: 214.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.025px 8px; transform-origin: 91.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.417px 8px; transform-origin: 175.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.733px 8px; transform-origin: 114.733px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 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: 371.492px 8px; transform-origin: 371.492px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.55px; text-align: left; transform-origin: 384px 18.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K = (gd^2/(180nu))(n^3/(1-n)^2)\" style=\"width: 114px; height: 37px;\" width=\"114\" height=\"37\"\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: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity 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);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.95px 8px; transform-origin: 78.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the porosity of the soil \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.683px 8px; transform-origin: 363.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-6} m^2/s\" style=\"width: 87.5px; height: 19.5px;\" width=\"87.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 338.7px; 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 169.35px; text-align: left; transform-origin: 384px 169.35px; 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: 494px;height: 333px\" 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\" 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margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = CHP(Q,L,D,dh,n)\r\n   K = f(Q,L,D,dh);\r\n   isDLvalid = true;","test_suite":"%% Coarse sand #1\r\nQ  = 8.92e-6;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #1--larger cylinder area\r\nQ  = 3.57e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.1;                   %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Coarse sand #2\r\nQ  = 2.44e-5;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 9.69e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1\r\nQ  = 1.52e-5;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.1;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%% Medium sand #1--reduced head difference\r\nQ  = 7.61e-6;               %  Flow (m3/s) \r\nL  = 0.08;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.05;                  %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 2.42e-3;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Medium sand #2\r\nQ  = 7.08e-7;               %  Flow (m3/s) \r\nL  = 0.1;                   %  Sample length (m)\r\nD  = 0.05;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.3;                   %  Porosity\r\nK_correct = 1.2e-4;         %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Fine sand \r\nQ  = 3.57e-7;               %  Flow (m3/s) \r\nL  = 0.075;                 %  Sample length (m)\r\nD  = 0.075;                 %  Diameter of cylinder holding sample (m)\r\ndh = 0.4;                   %  Head difference (m)\r\nn  = 0.25;                  %  Porosity\r\nK_correct = 1.51e-5;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%% Silt \r\nQ  = 1.17e-7;               %  Flow (m3/s) \r\nL  = 0.05;                  %  Sample length (m)\r\nD  = 0.08;                  %  Diameter of cylinder holding sample (m)\r\ndh = 0.3;                   %  Head difference (m)\r\nn  = 0.4;                   %  Porosity\r\nK_correct = 3.88e-6;        %  Hydraulic conductivity (m/s)\r\n[K,isDLvalid] = CHP(Q,L,D,dh,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nfiletext = fileread('CHP.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-08-18T23:24:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T14:41:04.000Z","updated_at":"2025-12-01T14:29:21.000Z","published_at":"2022-09-17T14:42:34.000Z","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 constant-head permeameter is a device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\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. By supplying a 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\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 a standpipe, water is maintained at a constant level so that the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Deltah\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference in water levels between the standpipe and outlet, is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can then be determined from Darcy’s law\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 the head gradient \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 is simply \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=\\\"Deltah/L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta h/L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Darcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = (gd^2/(180nu))(n^3/(1-n)^2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = \\\\frac{g d^2}{180 \\\\nu}\\\\frac{n^3}{(1-n)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity 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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the porosity of the soil \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 as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\rm\\\\,m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-6} m^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 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OpEm5dynLeGghLdUqtrrR9bP/WYz1+0kdGX/8pzyfCKhJtvIOMOP//iPV29+85vr55zQ+cADDxxflu1lyLI7fvmfVZ/8zX818DhdccUV1ZNPPlkvizx27rtmzZpq9+7dx49ltvvtb3+7DvfDjvso2+s9BrMd+97HSJ/Qm266qV42l32ZTfY1+/boo4/Wt3Ncs495v5R5bVn/TVdeUi2/YlX1F19+ZuTnBswPYXLMCJOLw7iFyUgF58CBA9Xy5cvrZuN+EmQiX9YlHOaL/O1vuaS68HV/vfqzP/uzel6RKlgqTO3QkW1k3sc+9rH6MYtcSieVvN7AkPVT7Yr24ybcXn311cf3+fHHH+8bgotUzRKkonc7l17+Y9Whb3z9lO187Wtfq974xjfWIaQ3xPR7bkW/ZdlWKnrZVm/wLevffffd1a233lrPK+Ev+3rZFX+9eurJk4/t6Wyv9xjPduz7Hd/8U5ATlrLNHMNUD0fdl9kkwL797W+v3vOe99S3B70Hii7PDZhHCZOMj2l6SY6F4nkfpsVCvs5dtv3tb3/76LEwUN93lOHYl3Zzz6NH169fX887FpyaOSfs27evXrZ27dpmzmBZ99zzzjtl3bL9Y4GkmXNC7pP9PhYkmjmDddlO5r/uwv77P+x591s223F62XknP07Zp9ynn67b63essizb6l027DHa5rovw2T97MfXnv1uM+dFx8Jg/Rh33HFHM+eELs8NmD/6TI6hVJYmfWhXnOZbms/6PeYkDZGKzbgo/SEj1Z1jfxv6DqlQ9Xrqz79Rj3fu3FlXlNpDKlLxuc99rj6Bpy3VrFSN2ut+/3vfq+e3HQsD9TiVpUFGOZu7nDAzbDvRu52c5f3sd37Q3Doh78NB+i0rjz/oOH3ney82xfYatL9dt3csdDVTJ+TzWl7b9vM/+JffqseXX355PR6kvEbD9iXVw9leo3jkkUeqn/qpn6pevey8Zs6L0n8yPvrRjw7czlyeGzCPjn1BMEbaFZ9JlrdWv8ri6Q5l25NuIV/nLsenVCYzDNu3fuuUitGwYVDFq9/QW8Eq2z8WjJo5JwyrSPXqsp3M71ctjWHVuH7L5nqcyj4NqujN9/Z6n39e48xLZba3Stiry3tgkGPBb+B7MPuTbfUe87k+N2B+qUyOmWF9vpge4/Y6t8/UHqbfOuW5pAp27G9K36FdIfvQhz5Un9CRatGxEHB8nS9/+ct1Zam3ejTqsZqPqlNvhTPXL3z5sWPTb9tzrUzO9TgVsz2v+dpeXtv288/+po9pzvD/8/2fq+cN0vW59cpJPOljOug1T6UzUtXvrXTHqM8NmF/CJHDSNSSHyTq9SnB66qmn6vFsvvjFL9bjcrmZ4oUXXryGYG+QmG37JdwOCiBFOYFj2H72Xq8y1y/ML+P02/aw60z2WzbX4xS55NGg5zXK8+n17WOvc7/tJWTlte19/qPu86tf/ep6PJd96ZV9yKWVfumXfqmZc6r169fX79GcdNXv7PC5PDdg/giTwJwqk73yBR+D+oAmNJazwKN8ofcGrlQr8/i91aNB2y9n8MYoVae1a9fW40HbKc+9dzvz1WdylOOUvqVt55577sDnNej5FL3bO+ecc+oqa7/nktckr20uOVRCfVxzzTX1uN9jtLf/vve9rx4P25f2e6Cfhx9+uK5K5r04SP75KNXJXMO0V79jVZ5bzPYeAboRJoH6S3a2yuSgdRLEcmHpVItyclEqZuXki9xOU2m7YlUuz5P11q1bVw8JX+Vknd7qUbZ/7bXXHt9+tpvrDub6jwkJWTZK1WmU7UTvdvLLKhe+7NQ/lXOtTI5ynHrDZAx6XtleAuqo20tIHPRcIq9tLvWT0Fkk3LWPWV6rftsf9NwSMsu6s1Ut77vvvuMBeZh3v/vd9Tjhsx18Y9CxynOL2d4jQEdHYQHkrdXvBJrTHcq2Gazr8cmJD7nv4SEn4AxbZ/fu3fVJDllehtze0+eEl5xAcSyUnrJetn8svDRrnexYWDlp28fCZz0/J13k/sP2u23YdnpP/viLv/iLej9vuOGGZs4JZTv9TsAZtmzU41ROKhl0PIpRt/f5A39Vb+9nfuZnmjkne81rXjPwON59990nvV45TuW4tc3lPdD2h3/4hyfdZ9QhxzlmO1bZ397XFpg/LlrOgkg14lj4a27Nn9VXLK237W07mOMDwJmkmRsAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmAQDoTJgEAKAzYRIAgM6ESQAAOhMmgYmxbt26ZopJ47WD6TVz9JhmGubNzMxMtfvJQ82t+bP6iqX1tr1tB5vm4+O1n1xeO5heKpMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQBAZ8IkAACdCZMAAHQmTAIA0JkwCQAd7N+/v5qZmamuu+66Zg4sTsIkADSOHDlSLVu2rA6Jg4as07ZkyZJmarwl/G7YsOGU57Nq1apq7969zVowd8IkADQSDC+44IJ6evny5dXKlStPGq699trq8OHD9fKlS5fWQ2+4HEf33HNPdckll1T33ntvfbs8n0iQTKBct25dfRvmSpgEYOJ95evPN1OnJ8Hwueeeq0Pi448/Xu3Zs+ek4dFHH61WrFhRr5tQmWHcK5MJkhs3bqyn77///uro0aPHn0+md+/eXS976KGHqs2bN9fTMBfCJAAT7/3b/rTa8hufP+1QWSqTpfo4zKRUJrds2VKPEyRvuummerpt9erVdbCMu+66ayIqrYwXYRKAqfDZLxw+Hiq7BqJ2ZXI2s1UmH3vssbr5eLb+iVkvy/qdyJOq4mzLhlUTs072MU3a/YJkUZrw4+GHH67HMCphEoCpklC57p/9f9XHdzw950rlXCqTMSh0JsStWbOmDo5r166t1q9fX4e10j8xy4tUBtM/c9euXaeE4DS1R/Zn0LJsf5CyzihnnN9yyy31+L777qvHMKqZo+kwAfMs/y3vfvJQc2v+rL5iab1tb9vBpvn4eO3Pnrv//f7q3/3RV5tbk+Vv/w+vqza++8V+jqPI2dwJbwlpmW67+uqrq1tvvbWeztnROakl6z344IP1vEilMUEy9u3bd7yPZbSXtauaOcs6J8f0NkWXfYk0RZeTZiLL8vilibqfhMiE1EFN3G0JuOlb2ft8YDbCJAtCmDx7hEnG0UK/dtd9+I+bqRNecf451fve/erqp9+yvJkzmoS/AwcONLdOlupiTsKJVAoT5hLwyrxIs3P6Hg4KcP2WlyDX3n6pYqaqmaC5adOmauvWrScta6/fz1zC5KjbhF6auQGYKgmRW/7uj1af+pW3zjlItvtMpiKYANwe2iEry9vVxaJUCi+//PJ63Oviiy+ux0888UQ9jhL0ShUyPvvZz9bjhMnsT/uxyyV+StP0fCiPN6gPKAwiTAIwFdoh8pqrf7iZOzdz6TOZgNevz+TTTz9djy+99NJ6PEi7eTqPm+blVAczxM6dO+uqZ7ZT+l+WfpOHDr3Y8nPDDTfU40FSaYx2cB3k4MGD9fiyyy6rxzAqYRKAifcPb/qR0wqRRbsyOZtSmexVwtgzzzxTjwdJc3Jb6UuZ6z2mP2bCY5qpEzTLspxpnWVZJ+FztipiqYKWgDtMCbdXXXVVPYZRCZMATLy5NmcPMpfKZCR09p5lXaqBTz31VD3uVS4SXoJekabubG/Hjh11YMw+lGBXluVM60ceeaSed+ONN9bjYa6//vr6fgmfpeLZT/pspm9lzFbthF5OwGFBOAHn7HECzvx6z0f3Vl879N3m1nCvWfbS6rfvOHG2LSdM0vuynMGdM7GHVf4S+NIMnarhXM/mzv36nYWdSmRCX9ZJAEygLPtQluW+CX7tZcOUM8Wj34k427Ztq0/uiVFO1IFeKpMAQ7z/nW9opmY3l3UZX3OpTEZvZTLXjSzhLGd75zevE+hSsSwhc/v27fW4V6qNeex+zdi5f5YlSI7SxF3ksbJ+3HzzzXWwz7YScjNd9jV6nwuMQpgEGCJ98FJxnE3WOd3+epx9pc/kXPQLdbmET5qzczHyBMNUBlNVzJnZqVamuthPaZaO3hNhUpksRmnibkvlNPtT+mlmX3L5o+xfLlOUZXncXJ4oITNVVxiVZm4WRP7b1cx9ZuRLIZWFVCzyZZCqRb6oMp15t91229Q0W52t1/4PHv/L6s5Pfqm51V/OIhYmB/O5HX8J0qmilr6T7etawjAqkzDhEhxzpmZCZfkSKNOpgOj/dPoSEl9/0fnNrVOpSjINUmHNtSxLRXXUZnQQJmEKDPot3TvvvLOZ4nS95x2vb6ZOdeu75+dMYhgH6fOZZu7bb7+9mQPDCZMwBfLHP5WEtjRzl98Q5vQNqk6mKvm2N13Y3AJYfIRJmBK91UlVhfnXrzqpKgksdsIkTIl2dTJVSWFy/vVWJzOtKgksdsIkTJFSndRXcuG0q5O/8K5zmymAxUuYhCmS6mSuI6ev5MIp1ckMb3rTm5q5AIuX60yyIFxncu42b95cXzy4aF/jzbITy977D26v/t4tH66Onn9O9f3vfa867wc/VM/P7SNff75a+sr/pp6eef6F6nsv+a+ntbzMz3TGxZcO/lU9/tGL/1o9Lsvb4yjTp7sfk7484zVXLnOdSZhSwiQLQphkISzU+2q+JeSee955zS1CmITppZkbYJ4JksBiIkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfCJAAAnQmTAAB0JkwCANCZMAkAQGfC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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56205,"title":"Measure the hydraulic conductivity with a falling-head permeameter","description":"A falling-head permeameter is another device for measuring the hydraulic conductivity  of a soil sample. In this problem the sample is placed in a cylinder of length  and cross-sectional area . Unlike the constant-head permeameter, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area ) that falls. In other words, the head difference , or the difference between the water levels in the tube and the outlet, decreases in time. \r\nThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\r\n\r\nDarcy’s law applies when a Reynolds number based on the specific discharge  and representative diameter  of the soil grains is less than (approximately) 1—that is, \r\n\r\nwhere  is the kinematic viscosity of the fluid.\r\nDerive and solve an ordinary differential equation for the head difference . Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the previous problem. Use  and .\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 902px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 451px; transform-origin: 407px 451px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82px 8px; transform-origin: 82px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_c\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37px 8px; transform-origin: 37px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Unlike the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003econstant-head permeameter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"A_t\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147px 8px; transform-origin: 147px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) that falls. In other words, the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145px 8px; transform-origin: 145px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = -K(dh/dx)A\" style=\"width: 85px; height: 35px;\" width=\"85\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"v = Q/A\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and representative diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ed\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the soil grains is less than (approximately) 1—that is, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Re = vd/nu \u003c 1\" style=\"width: 79px; height: 35px;\" width=\"79\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eν\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116px 8px; transform-origin: 116px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity of the fluid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDerive and solve an ordinary differential equation for the head difference \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eδ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eprevious problem\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"g = 981 cm/s^2\" style=\"width: 90.5px; height: 19.5px;\" width=\"90.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nu = 10^{-2} cm^2/s\" style=\"width: 94px; height: 19.5px;\" width=\"94\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 359px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.5px; text-align: left; transform-origin: 384px 179.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 401px;height: 359px\" 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alt=\"falling-head permeameter\" data-image-state=\"image-loaded\" width=\"401\" height=\"359\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n)\r\n  K = f(delta,t,L,Dc,Dt);\r\n  isDLvalid = (Re \u003c 1);\r\nend","test_suite":"%%\r\nDc = 11.28;                                 %  Diameter of cylinder holding sample (cm)\r\nDt = 2.26;                                  %  Diameter of tube (cm)\r\nL  = 10;                                    %  Sample length (cm)\r\nn  = 0.15;                                  %  Porosity\r\nt  = [0 1 2 5 10 15 20 25]*86400;           %  Time (sec)\r\ndelta = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];    %  Head difference (cm)\r\nK_correct = 3.08e-7;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                %  Diameter of cylinder holding sample (cm)\r\nDt = 2;                                                %  Diameter of tube (cm)\r\nL  = 15;                                               %  Sample length (cm)\r\nn  = 0.25;                                             %  Porosity\r\nt  = 0:60:420;                                         %  Time (sec)\r\ndelta = [25 20.63 17.03 14.05 11.60 9.57 7.9 6.52];    %  Head difference (cm)\r\nK_correct = 3e-3;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)\r\n\r\n%%\r\nDc = 7.5;                                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.75;                                             %  Diameter of tube (cm)\r\nL  = 7.6;                                              %  Sample length (cm)\r\nn  = 0.2;                                              %  Porosity\r\nt  = [0 1.25 2.36 3.74 5.40 7.20 9.28 12.08];          %  Time (sec)\r\ndelta = 88.9:-10:18.9;                                 %  Head difference (cm)\r\nK_correct = 5.25e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                                                               %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                                                               %  Diameter of tube (cm)\r\nL  = 7.5;                                                               %  Sample length (cm)\r\nn  = 0.2;                                                               %  Porosity\r\nt  = [0 1.06 2.11 3.62 4.88 6.53 8.39 10.67 13.52 17.37];               %  Time (sec)\r\ndelta = [56.02 50.36 44.7 39.05 33.39 27.73 22.07 16.41 10.75 5.09];    %  Head difference (cm)\r\nK_correct = 3.89e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 7.6;                              %  Diameter of cylinder holding sample (cm)\r\nDt = 1.5;                              %  Diameter of tube (cm)\r\nL  = 7.5;                              %  Sample length (cm)\r\nn  = 0.2;                              %  Porosity\r\nt  = [0 2.28 5.13 8.98];               %  Time (sec)\r\ndelta = [22.07 16.41 10.75 5.09];      %  Head difference (cm)\r\nK_correct = 4.79e-2;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(~isDLvalid)\r\n\r\n%%\r\nDc = 8;                                                      %  Diameter of cylinder holding sample (cm)\r\nDt = 2.5;                                                    %  Diameter of tube (cm)\r\nL  = 15;                                                     %  Sample length (cm)\r\nn  = 0.18;                                                   %  Porosity\r\nt  = 0:7200:50400;                                           %  Time (sec)\r\ndelta = [50 43.15 37.23 32.13 27.72 23.92 20.64 17.81];      %  Head difference (cm)\r\nK_correct = 2.99e-5;\r\n[K,isDLvalid] = FHP(t,delta,L,Dc,Dt,n);\r\nassert(abs((K-K_correct)/K_correct)\u003c0.01)\r\nassert(isDLvalid)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-01T17:35:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-01T17:35:38.000Z","updated_at":"2026-02-10T14:28:46.000Z","published_at":"2022-10-01T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA falling-head permeameter is another device for measuring the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a soil sample. In this problem the sample is placed in a cylinder of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Unlike the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econstant-head permeameter\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which the water level in a standpipe (or tube) is kept constant, the falling-head permeameter has a water level in the tube (of cross-sectional area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) that falls. In other words, the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or the difference between the water levels in the tube and the outlet, decreases in time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hydraulic conductivity can be determined from a statement of conservation of mass (i.e., water volume) by equating the rate of change of volume in the tube to the flow out of the soil sample. The outflow can be computed with Darcy’s law, which states in general\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law applies when a Reynolds number based on the specific discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and representative diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"d\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the soil grains is less than (approximately) 1—that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re = vd/nu \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eRe = \\\\frac{vd}{\\\\nu} \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity of the fluid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDerive and solve an ordinary differential equation for the head difference \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"delta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then write a function that takes as input measurements of head difference as a function of time, as well as the soil’s porosity, diameter of the tube, and length and diameter of the cylinder holding the soil sample. The function should compute the hydraulic conductivity by fitting the solution to the ordinary differential equation to the data and using Darcy’s law regardless of its validity. Also return a flag indicating whether Darcy’s law is valid throughout the experiment; to assess the validity, relate the hydraulic conductivity to the representative grain diameter with the Kozeny-Carman equation, as described in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825-measure-the-hydraulic-conductivity-with-a-constant-head-permeameter\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 981 cm/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 981\\\\rm\\\\,cm/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nu = 10^{-2} cm^2/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 10^{-2}\\\\rm\\\\,cm^2/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"401\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"falling-head permeameter\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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