Problem 57452. Design a well field in an infinite aquifer

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q_d\"/></w:customXmlPr><w:r><w:t>Q_d</w:t></w:r></w:customXml><w:r><w:t> (i.e., volume of water per time) with the constraint of lowering the water table by no more than </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"s_max\"/></w:customXmlPr><w:r><w:t>s_{max}</w:t></w:r></w:customXml><w:r><w:t>, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"K\"/></w:customXmlPr><w:r><w:t>K</w:t></w:r></w:customXml><w:r><w:t>, the specific yield </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"S_y\"/></w:customXmlPr><w:r><w:t>S_y</w:t></w:r></w:customXml><w:r><w:t>, and the initial saturated thickness </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"b\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t>) and the radius </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"r_w\"/></w:customXmlPr><w:r><w:t>r_w</w:t></w:r></w:customXml><w:r><w:t> of the well. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The Gupta/Chin method for designing a well field has the following steps:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Compute </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q_w\"/></w:customXmlPr><w:r><w:t>Q_w</w:t></w:r></w:customXml><w:r><w:t>, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"r = r_w\"/></w:customXmlPr><w:r><w:t>r = r_w</w:t></w:r></w:customXml><w:r><w:t>) is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"s_max/2\"/></w:customXmlPr><w:r><w:t>s_{max}/2</w:t></w:r></w:customXml><w:r><w:t>. Compute the transmissivity to be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"T = K(b-s_{max}/2)\"/></w:customXmlPr><w:r><w:t>T = K(b-s_{max}/2)</w:t></w:r></w:customXml><w:r><w:t>. Evaluate the drawdown at a time </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"t = \"/></w:customXmlPr><w:r><w:t>t =</w:t></w:r></w:customXml><w:r><w:t> 1 year. Realize that for small values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"u = S_y r^2/4Tt\"/></w:customXmlPr><w:r><w:t>u = S_y r^2/4Tt</w:t></w:r></w:customXml><w:r><w:t> the unconfined well function* can be approximated and compute the pumping rate from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"s_max/2 = (Q_w/4 pi T) W(u_w)\"/></w:customXmlPr><w:r><w:t>\\frac{s_{max}}{2} = \\frac{Q_w}{4\\pi T} W(u_w)</w:t></w:r></w:customXml><w:r><w:t> where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"W(u) = integral(exp(-x)/x,{x,0,infinity})\"/></w:customXmlPr><w:r><w:t>W(u) = \\int_u^\\infty \\frac{e^{-x}}{x} dx</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"u_w = S_y r_w^2/4Tt\"/></w:customXmlPr><w:r><w:t>u_w = S_y r_w^2/4 T t</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Compute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"ceil(Q_d/Q_w)\"/></w:customXmlPr><w:r><w:t>N = \\lceil Q_d/Q_w\\rceil</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Set the pumping rate to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q_0 = Q_d/N\"/></w:customXmlPr><w:r><w:t>Q_0 = Q_d/N</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Arrange the wells so that they are equidistant from the central well.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Determine the distance </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"R\"/></w:customXmlPr><w:r><w:t>R</w:t></w:r></w:customXml><w:r><w:t> between the central well and others so that the total drawdown at the central well is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"s_max\"/></w:customXmlPr><w:r><w:t>s_{max}</w:t></w:r></w:customXml><w:r><w:t>. In other words, add the drawdown from the central well to the drawdown from the other wells. If </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"u_R = S_y R^2/4Tt\"/></w:customXmlPr><w:r><w:t>u_R = S_y R^2/4Tt</w:t></w:r></w:customXml><w:r><w:t>, then </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>s_{max} = \\frac{Q_0}{4\\pi T}\\left[W(u_w) + (N-1) W(u_R)\\right]</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> Write a function to design a well field using this method.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" 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<div 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; "><div style="block-size: 895.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 447.692px; transform-origin: 407px 447.692px; vertical-align: baseline; "><div style="block-size: 87px; 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 43.5px; text-align: left; transform-origin: 384px 43.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.242px 8px; transform-origin: 375.242px 8px; unicode-bidi: normal; ">A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand <img src="data:image/png;base64,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" alt="Q_d" style="width: 19.5px; height: 20px;" width="19.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292.875px 8px; transform-origin: 292.875px 8px; unicode-bidi: normal; "> (i.e., volume of water per time) with the constraint of lowering the water table by no more than <img src="data:image/png;base64,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" alt="s_max" style="width: 25.5px; height: 20px;" width="25.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8333px 8px; transform-origin: 47.8333px 8px; unicode-bidi: normal; ">, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity K<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.175px 8px; transform-origin: 57.175px 8px; unicode-bidi: normal; ">, the specific yield <img src="data:image/png;base64,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" alt="S_y" style="width: 15.5px; height: 20px;" width="15.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; ">, and the initial saturated thickness b<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 8px; transform-origin: 50.5667px 8px; unicode-bidi: normal; ">) and the radius <img src="data:image/png;base64,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" alt="r_w" style="width: 15.5px; height: 20px;" width="15.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; "> of the well. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.008px 8px; transform-origin: 226.008px 8px; unicode-bidi: normal; ">The Gupta/Chin method for designing a well field has the following steps:</div><ol style="block-size: 231.783px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 115.892px; transform-origin: 391px 115.892px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 104.05px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 52.025px; text-align: left; transform-origin: 363px 52.025px; white-space: pre-wrap; margin-left: 56px; ">Compute <img src="data:image/png;base64,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" alt="Q_w" style="width: 20.5px; height: 20px;" width="20.5" height="20">, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance <img src="data:image/png;base64,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" alt="r = r_w" style="width: 40.5px; height: 20px;" width="40.5" height="20">) is <img src="data:image/png;base64,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" alt="s_max/2" style="width: 40.5px; height: 20px;" width="40.5" height="20">. Compute the transmissivity to be <img src="data:image/png;base64,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" alt="T = K(b-s_{max}/2)" style="width: 116.5px; height: 20px;" width="116.5" height="20">. Evaluate the drawdown at a time <img src="data:image/png;base64,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" alt="t = " style="width: 22px; height: 18px;" width="22" height="18"> 1 year. Realize that for small values of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKMAAAAqCAYAAADf0+uQAAAH7klEQVR4Xu2bR6stRRDH3/sAIoaliBh2iiImRF24UFEQRcWIPFAwIIILsxsx68KVEd0ZUTdieCroQhFMoCC4MHBxbeDpB9D6PaYedft2qJo5YeD0QHHOmenprq7+d8U+u3f1q0tgJhLYPRM+OhtdArs6GDsIZiOBDsbZLEVnpINx/Rg4TFg4Xej4gZW35fO39bO1eg46GFcvczviifLjM6FfhQ4ROmZ4eLd8PjmCNYD9jNBVI95d+ysdjOtbAoDzldAeoS8GNgDR68P3s819L5c3ScM7hY71vjCndh2M61sNgHeC0P0JC2/I7yuFHs08a3H7jTR4SeiFVsM5Pt9kMGIizxA6eFiY3+UTIHBdOHx+sMRFO0v6/knoz2SMu+T3EyPAeLS8g7nH1Ed8TuaKv1pyC+j38olyeDkzzx1dbiIYASGLfb7Qt0IfC+0TOkoIbcWCniJ0s9A6NIyC8SIZP7IZHpH25wmdGgAOG+Jzob+FDi28p/zwGHmhfbeGtvfIJ74u10dCnw7fT5ZPtLvev8DD06aBkV2OQBHgm0Kpo299tpPk+Q8eIS64zV7p77QKOErD/SIPHhBS7d5iS31WNGkNjMrPxdJOfVv65v0/zCCpj4v/+ryQOxjbNDA+K8K5ZRBgyZyx83l2nFBqQlsLPPW5mtqoVkTbfy90eIBn9U3huQRGBVyOH7txeT8nr//kvjsQ2zQwoj00fVJaOMzSFUIRczcVhPo+APlL6NZgh2wyzKw3pYPWekzoOaH7KmDEn7y+0K/d2DkrwxSYSwpS+nwwJ99NAyM7Va+SGQaMBDVplBvER7g5QLokACg7AIt+nZDHx9TcJu0JXPCfS5oRTc2VC4jsxi7518zJug06Nvd2bLhNAyMmmOCEC4c751jXFiCMMOcLLNI7QlRioq4BmuYVoVIAkrKADAja2GwanNR8xtwU1J3QZx7/WvnEX8+6IS0wEm0dIfSPULrr6Pz2gRtQHkknONdo4c2sn0PnY3J5HqZUbrRVzcC9M4V+TGQJEMkNsjEsELVM2NJ2EdOuEbeONRaMVo5kH2pJduZ9m5BG18iEoIbrS6EDQVEOjAjhBiEbtufUsDrAkV21iJzVjkl40GHaEB2S1tHLHe01xmFugBvNm5b1rH9FN+qvqkbcYxdFvrMGDwm9ltxPWdAAw6OZNI1jA7exYLTzwe+s+biMwaV4ArwvDve21eFrmpFdhHPLlUaeVk23mLECVIE01rX5eEoOkAUEkGquGWxKfymzdo5EktcIIS/GZUyNPHmPcqACN+2npXFoj4Z6WKhV/mPsn4XuFbK507FgxEfV/OLV8r2VTrJpoOLmr4FRNUhOKJpDQiAeZlTQi9KM+HtTcoDLBKSaMECHxlCwqMVR06SVj9LO22bCCo3w/94Sah2qULCk0fYYMGoaSVnyVHyY6/vDC8VUTw2MGnnmNJ+NpDzMlAS+zvspIAFPmtgdw5+aMDYMGuuyiRunxIO3/KdpnFwecAwYrSKigOBJgalMqi5dCYzW1KSRT8R5HbOYq3zHVmQY1yvcGo+6URE8G3lZKSJPPlRTKaVNNgaMNlnuDQBVJqV85H55lsBo65FpcthqxYi/uEqQRcZK/dgpmt6aMMCIj7isLIOn/IcZ58KU565z5SbBHLw+bhrUzL71Fz3VFRtfVH3zEhjVX0xzcary1XmNlq0W5TN6/CmVrSeJbXd7dE52ka0J82qNyMbRtt7yn03ye8epmVK7cUslwHQca0mrG70ERp2EjXxs9lzru5FaKEyuI5rGX0FwNXNpLcEUMNq00RQN2wKOt/ynaZVSf6oZea65P04wlU4rWTmVigbpWLrRm9mBHBjT1ARJSXX275DvTwthftS/4hnlM485WpRmjETTAISrdozJprGiG0yFb9MXVd+ohTTHc61ft1Iqra6iPqPdbN50mJp1denAAIDfUWnKgTHHIDtxSwhfwmpNDk2+OuyqKamWltCmPFdh1Pwbj4ONZfg32XT2gKxNX0TSXdG5Rct/tf4jYEyPjHkS7daHRiafCAHotNq0n8ccGK1a5bAmvg8Xtt9qTTo/RwgQruMQqmcRrQDR5DcO/Np3Ne2AGcnVhvEDLxXC0bemSRdSXRmbvljm8TPG4Yqe7MnJKwLGtJTqsSDWh8ZtwWJgXe25yAN81cCojWzEnCY8l22OPICrtWHzvCvEBiMfhnvBfLaEcC2olyIkQHatUO2QAtqTwwgaIQN0rMJ3Qvijql29vtSYuenm8kSxnv69YLSHHLRfj29tfUz89rQCtI3HUm1a//OAWk19QXbIkUKRiNYjmGW0YfMcJKQ7Mf2PMv97+Tozxxwv6ldaX4l7HwrxXxbq+VzLlIu3/OeVpR7eKAUtHh+/Nl+tOsFP8//grVM73kltQju1CtYakMfzVCAWJR/8LdXEi+pzNv10MMaWgmAIwrdEE9p/FMZ6irf2lv/iPc/kjQ7G2EJocEckyRnEVWpFggECsFWOGZPOxNYdjDEBanRI5M3B4tbB11jv9dYESE8JzTVzMXmuHYwxEWpqa9VZBG/5LzabmbXuYIwtyLpAQYqEP8Z7//0Xm9VMWncwxhaChPN7KzbPcFgsocXYn3frDkb/+mh+tXWq2t9jb7lNAh2MdUCQ1OaEElH0llAH4hI3UAdjXbj4iNSkm9WDJa7RxnTdwbgxSz3/iXYwzn+NNobDDsaNWer5T/R/IincOrb9C9QAAAAASUVORK5CYII=" alt="u = S_y r^2/4Tt" style="width: 81.5px; height: 21px;" width="81.5" height="21"> the unconfined well function* can be approximated and compute the pumping rate from <img src="data:image/png;base64,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" alt="s_max/2 = (Q_w/4 pi T) W(u_w)" style="width: 111.5px; height: 38px;" width="111.5" height="38"> where <img src="data:image/png;base64,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" alt="W(u) = integral(exp(-x)/x,{x,0,infinity})" style="width: 112px; height: 35.5px;" width="112" height="35.5"> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAsCAYAAAAuJIllAAAIxUlEQVR4Xu2cOcslRRSGZ36AiEvkkrgEBqLgBqKCBq6JorgHA4ormLmbiLtmgjqKwgTuC4i4JhooghtoIAYuiWLk7g/Q84z9DmdqqrqquqvvvQ7VcLj3u119qurUW2et/rZu6VeXwF4iga17yTz6NLoEtnQwdxDsNRLoYN5rlrLZRK41Tj8avd2M44oYdTCvSNALdXPKwPcb+/y1UR+/GZ8bjF5sxG9lbDqYVybqph3dZ9zucBx/t++3G706E9Tn2vPPGu3fdLQrYtbBXC/ow+yRg4bH/rbPr4bvB9jnUUYf1bOsegIgHz6A+U/7vMho+8Dhspka9fGBD5q55sJC/Gz0Q+KhY+z3fWoYBm29nJNsOpjLJXypNb13ANL39vmdEQDmesXomuG3s8tZVrekv2+NQs0pTf2e3ZvaP7x/MTrPqMZfVt/X2XNPJmaE67Kfu8c4uejzePf75/Yddyn8vWiTdjCX4QmNdf3Q9Fj7lDbmJ0D+wnDvVvt8uIzlpFZouIMjYEMzfmgEGE6YxPm/ebBZj6h4Xv3ySArMjPlLIxTAhYHsbrG/Hxr6C8fOcx8YsQkONMrGBB3M+ZUrWTCBvVar5Xsva6ExPmHNa10E9UDAB+DuLOtyp/bESkjjpsBMduQBoyMjgPzMfpNmvj/SN1r/TKOiDdrBnF85H2ylwErg9FapBsl3Wd0CwOA3T91MxAEAObQ6YwN5127+YXTJ0CgFZto9ahS6LnJr1Mep9iWMN9Dc+0ZAjhXh993cmg7mPG5YjLOGZinfDc24w6jGROd7Lm/BGLmm+stshquNijSgtaP9zUZoTTYBVwrMADLmekkBaJYxLAJa0o7erZP7Qfamg7kcIztben+ZwOUKo9B/Q7OdaLSO3KxcjCK/MjF3zP3TITgSbeUDS5P+kwFzStze4pUGrsz1DSNcGzI6u2VPSjQzC0Vaxe8OBsikpLHIb6bSMpXY2bjm3mdmcHP80tzklN7zRRD6T6WmaP+JURhY5frx9wXOPcARYUJ/WAGyN9K2U8Hs/eWxTAjDAINXGSm3jjXYNoxvV0owBmYGzINnOLDGonSvsUo2RY2Aw7Zz85TiNzUHjMaVbwivnPBr5oocpdnROIrqmfNrRoCMK+ZTAqwdRnMsgvLWmPTcRdvjjLx1mgLm0F8e89WRjfLfUp4UiT4dBrvLtRoDoTcDYWc+kn3JmJYIIieosfveb53KBwFMrWxJI/mcaMs0nF9covqXjUhLkZ8VmMPgjgXGWoa5XTZBaEXHZEa+/K6CDaHq4OkB/ylg9unM0nXxFjIa6I6BWQCKdeYH01JLpYQujTAVyDxH5D1n08UA3WruHswEmeR7bzLChXhsALVPuaUqdQCZ4Kw0PSeAxtJmXtZSXrEzG1PA7K16qTL0OelofDAGZlVtYp15TVmTzpkDxk14NgbomPmvHauP7NHMXKl8rxZVVTTfF2a4Zj1Ky9dKw8WUwRQwYw1kcYqqe9ZePnYyWEyBWUEBggo78+q+1ETULu4mtw+LBQQjJxllK1Qjk5JLBy9coZQ7xLqoYhZjRxBeqpU1jyvtmbHytdJwqTnWglk5bY2/NPCk1M6VdO9SYFYSnofDzrxWLjURmwzOKWPzm53npxYr1LfXVK1cl9y8SsrXmidj+jrBkDI6FxblneH72KEj76KyeUty895yJS1hCsyK3sPOwjRVqYnICTZ3f9XZjBLf0wfIsVJsbk667zXVKi1dSfna+6ml86Hd2Ib0maFSuUnWo/JJgVn+su9MZonB6NBNiYmoEUKq7aqzGWiCu43GKmJ+Y5cuSmx+3gquSiuXlq/RotsyC6h0mU4S0jxWvhYbf4Ku1KLJco16AjEwexPqOwPEpIsuMGICpSaiBZhXnc1AI3Gkc8wX9mCeY6G8pppTxauRs/zgEhOf41vjM4fuWUl9wluu0c0eY+Y1he7zG/lFdqoGr0oYEfGbRjVnYHMCWvf9klNw3s2YA0LJc5XxR035OrcWNWD22CotYXsfm0zNT0ZY6j2sZgzMWkhVonw0e4gx4WwqF1r7UCN2GxE0nxcbUSl7ysgfLkHT8VaEEvxoIwoQc7MAOUFPvS+3BuvDYZqwVO/P2sa0BQtw9CAL/DyqVGQ79BzzR2Y+sJmj3WvmKU3XykWsAXPuyGdsHsKjskasDYei9igMxcDs/VOdiBLovGnVPW+qZEa8ltFv/kyDdtscjVazgLVtWSBAqOtB+/Lx8Mc59knMQOk55+NKlorAiTueM0JmUCvtXjM/uWxTT9iFfZWC2WtYeJSecfHFO/ztR4yib7SkfGaO13G9bhTW/XWW4H2794xRmF9lct6f1mD84LWorQRas5i5toztHiPla9nAJxtxVoWLSiKxQ8nLo1pAHyDCjw1BUUSy/GL4Oze2FvdLy9elfen4aSroQwanGWERwot5Y7HH3s5REIrcOeSfLNWXOOClk1I7hMWFNufAEoPdbuR9JNwONN3Ugz+1Y1pXe5Wp/eYGwM+vae4tjouuS5bZfpcAszQxPjXnCzhhRfVGC4pALzcqrVRlJ7HhDSQPlW/R0lPPiMyNS0rL1xsu0vjwlgSzf4GRBcVHJJhCoLED7v9LARYMWoUHAjzM7VytPCcuwefMla8LprSZTZYAs6JP7yPnsgObKZ02o5Jpx82ae3JPI5oSl2ANWJupx2DbSGNBLkuAGU10m5E/ViiAtzhhtqA4FmOtiL9VOmxKXFJSvl5MAKtgvASY0QB/GfkiinzEOW9ErEIeS/WBed/jBcwZnU2JS9hQNcdDZwxvPY8uAeb1zGRze8XHBcg3Gs05Jupn6N02vf+Xi0tq30DZXIkmRtbBvOySKZ9O5qblC789LomsWwdzezDrAP0OY32+EW8UtwQyI+5xSQdze+RGOArMVEiX+hcMPS7pYF4JmHsna5JAdzPWJPjebXsJdDC3l2nnuCYJdDCvSfC92/YS6GBuL9POcU0S6GBek+B7t+0l0MHcXqad45ok8C/K/zBLpkS27wAAAABJRU5ErkJggg==" alt="u_w = S_y r_w^2/4Tt" style="width: 89.5px; height: 22px;" width="89.5" height="22">. </li><li style="block-size: 42.15px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.075px; text-align: left; transform-origin: 363px 21.075px; white-space: pre-wrap; margin-left: 56px; ">Compute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: <img src="data:image/png;base64,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" alt="ceil(Q_d/Q_w)" style="width: 88.5px; height: 20px;" width="88.5" height="20"></li><li style="block-size: 21.7167px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; ">Set the pumping rate to <img src="data:image/png;base64,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" alt="Q_0 = Q_d/N" style="width: 73.5px; height: 20px;" width="73.5" height="20">. </li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; ">Arrange the wells so that they are equidistant from the central well.</li><li style="block-size: 43.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.7167px; text-align: left; transform-origin: 363px 21.7167px; white-space: pre-wrap; margin-left: 56px; ">Determine the distance R between the central well and others so that the total drawdown at the central well is <img src="data:image/png;base64,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" alt="s_max" style="width: 25.5px; height: 20px;" width="25.5" height="20">. In other words, add the drawdown from the central well to the drawdown from the other wells. If <img src="data:image/png;base64,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" alt="u_R = S_y R^2/4Tt" style="width: 91px; height: 21px;" width="91" height="21">, then </li></ol><div style="block-size: 37.9px; 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 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3px 8px; transform-origin: 23.3px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 227px; height: 38px;" width="227" height="38"></div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.133px 8px; transform-origin: 174.133px 8px; unicode-bidi: normal; "> Write a function to design a well field using this method.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; 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transform-origin: 384px 189.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 389px;height: 374px" 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A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand  (i.e., volume of water per time) with the constraint of lowering the water table by no more than , the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity , the specific yield , and the initial saturated thickness ) and the radius  of the well. 
The Gupta/Chin method for designing a well field has the following steps:
Compute , an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance ) is . Compute the transmissivity to be . Evaluate the drawdown at a time  1 year. Realize that for small values of  the unconfined well function* can be approximated and compute the pumping rate from  where  and . 
Compute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: 
Set the pumping rate to . 
Arrange the wells so that they are equidistant from the central well.
Determine the distance  between the central well and others so that the total drawdown at the central well is . In other words, add the drawdown from the central well to the drawdown from the other wells. If , then 
            
 Write a function to design a well field using this method.

*http://www.aqtesolv.com/neuman.htm

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Problem 57452. Design a well field in an infinite aquifer

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Problem 57452. Design a well field in an infinite aquifer

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