{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":57532,"title":"Compute steady drawdown in a confined aquifer","description":"A well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance  to the point where the drawdown is wanted is smaller than the radius of influence , then the drawdown  of a well pumping at rate  in a confined aquifer of transmissivity  is \r\n\r\nIf the distance  is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \r\nBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in Cody Problem 57497. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \r\nWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the - and -coordinates of the points where drawdown is requested, the - and -coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of - and -coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head).  ","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: 369.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.95px; transform-origin: 407px 184.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; 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 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.925px 8px; transform-origin: 376.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance \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);\"\u003er\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: 254.008px 8px; transform-origin: 254.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the point where the drawdown is wanted is smaller than the radius of influence \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);\"\u003eR\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: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the drawdown \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);\"\u003es\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: 80.125px 8px; transform-origin: 80.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a well pumping at rate \u003c/span\u003e\u003c/span\u003e\u003cspan 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alt=\"Q0\" style=\"width: 19px; height: 20px;\" width=\"19\" 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: 118.633px 8px; transform-origin: 118.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a confined aquifer of transmissivity \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);\"\u003eT\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: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38.9px; 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 19.45px; text-align: left; transform-origin: 384px 19.45px; 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=\"s = (Q0/2piT) ln(R/r)\" style=\"width: 97px; height: 39px;\" width=\"97\" height=\"39\"\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: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the distance \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);\"\u003er\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: 310.4px 8px; transform-origin: 310.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.892px 8px; transform-origin: 378.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57497-locate-image-wells\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 57497\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: 317.433px 8px; transform-origin: 317.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 323.875px 8px; transform-origin: 323.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the \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);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 189.05px 8px; transform-origin: 189.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates of the points where drawdown is requested, the \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);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 257.883px 8px; transform-origin: 257.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 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 s = drawdown(x,y,xw,yw,Q0,R,T,varargin)\r\n%  s = drawdown\r\n%  (x,y) = points where drawdown is requested\r\n%  (xw,yw) = coordinates of real wells\r\n%  Q0 = pumping rates\r\n%  R = radii of influence\r\n%  T = transmissivity\r\n%  varargin:\r\n%     (xb,yb) = coordinates of two points on the boundary\r\n%     btype = type of boundary ('NF' = no-flow, 'CH' = constant-head)\r\ns = (Q0/(2*pi*T)*ln(R/hypot(x-xw,y-yw);\r\nend","test_suite":"%%  Single well in an infinite aquifer\r\nx  = 50;                        %  x-coordinate of drawdown point (m)\r\ny  = 100;                       %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinates of wells (m) \r\nyw = 0;                         %  y-coordinates of wells (m)\r\nQ0 = 800;                       %  Pumping rates (m3/d)\r\nR  = 910;                       %  Radius of influence (m)\r\nT  = 150;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = 1.7797;             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Single well in an infinite aquifer, drawdown requested at multiple points\r\nx  = [50 400 93];               %  x-coordinate of drawdown point (m)\r\ny  = [100 818 45];              %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 800;                       %  Pumping rate (m3/d)\r\nR  = 910;                       %  Radius of influence (m)\r\nT  = 150;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = [1.7797 0 1.8468];             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Single well in an infinite aquifer, drawdown requested at random points\r\nx  = 200*rand(1,8);             %  x-coordinate of drawdown point (m)\r\ny  = zeros(1,8);                %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 1200;                      %  Pumping rate (m3/d)\r\nR  = 450;                       %  Radius of influence (m)\r\nT  = 175;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\nassert(all(abs(s(2:end)/s(1)-log(R./x(2:end))/log(R./x(1)))\u003c1e-3))\r\n\r\n%%  Three wells in an infinite aquifer\r\nx  = 0;                         %  x-coordinate of drawdown point (m)\r\ny  = 0;                         %  y-coordinate of drawdown point (m)\r\nxw = [150 200 -300];            %  x-coordinates of wells (m) \r\nyw = [200 -150 100];            %  y-coordinates of wells (m)\r\nQ0 = [1000 1500 2000];          %  Pumping rates (m3/d)\r\nR  = 450;                       %  Radius of influence (m)\r\nT  = 430;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = 0.8050;             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Two extraction wells and one injection well in an infinite aquifer\r\nx  = [0 50 270];                %  x-coordinate of drawdown point (m)\r\ny  = [0 100 -180];              %  y-coordinate of drawdown point (m)\r\nxw = [150 200 -300];            %  x-coordinates of wells (m) \r\nyw = [200 -150 100];            %  y-coordinates of wells (m)\r\nQ0 = [1200 -500 800];           %  Pumping rates (m3/d)\r\nR  = [450 280 620];             %  Radius of influence (m)\r\nT  = 340;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = [0.5558 0.8643 -0.2365];             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Well near a slanted boundary\r\nx  = 350;                       %  x-coordinate of drawdown point (m)\r\ny  = 100;                       %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 300;                       %  Pumping rate (m3/d)\r\nR  = 1000;                      %  Radius of influence (m)\r\nT  = 210;                       %  Transmissivity (m2/d)\r\nxb = [-550 1050];               %  x-coordinates of points on boundary (m)\r\nyb = [900 -50];                 %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = 0.2298;\r\nsNF_correct = 0.2911;\r\nsCH_correct = 0.1684;             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%  Wells near a boundary parallel to the y-axis\r\nx  = [20 50 -320];               %  x-coordinate of drawdown point (m)\r\ny  = [30 46 -300];               %  y-coordinate of drawdown point (m)\r\nxw = [50 75 85 43];              %  x-coordinate of well (m) \r\nyw = [10 35 67 91];              %  y-coordinate of well (m)\r\nQ0 = [150 600 420 80];           %  Pumping rate (m3/d)\r\nR  = 670;                        %  Radius of influence (m)\r\nT  = 195;                        %  Transmissivity (m2/d)\r\nxb = [140 140];                  %  x-coordinates of points on boundary (m)\r\nyb = randi(1500,[1 2]);          %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = [2.4837 3.0597 0.2509];\r\nsNF_correct = [3.7791 4.5365 0.3138];\r\nsCH_correct = [1.1884 1.5830 0.1880];             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%  Wells near a boundary parallel to the x-axis\r\nx  = [0 -20 -40 370];            %  x-coordinate of drawdown point (m)\r\ny  = [0 25 -40 90];              %  y-coordinate of drawdown point (m)\r\nxw = [-72 13 50 -20];            %  x-coordinate of well (m) \r\nyw = [14 28 0 -14];              %  y-coordinate of well (m)\r\nQ0 = [230 410 380 215];          %  Pumping rate (m3/d)\r\nR  = 450;                        %  Radius of influence (m)\r\nT  = 81;                         %  Transmissivity (m2/d)\r\nxb = randi(982,[1 2]);           %  x-coordinates of points on boundary (m)\r\nyb = [-43 -43];          %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = [5.8499 5.4446 4.4620 0.4481];\r\nsNF_correct = [9.4217 8.4800 8.7657 0.7035];\r\nsCH_correct = [2.2783 2.4091 0.1584 0.1927];             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('drawdown.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-08T16:30:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2023-01-08T16:28:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-08T02:57:32.000Z","updated_at":"2026-02-12T14:29:49.000Z","published_at":"2023-01-08T02:58:04.000Z","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 well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance \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=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the point where the drawdown is wanted is smaller than the radius of influence \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=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the drawdown \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=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a well pumping at rate \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=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a confined aquifer of transmissivity \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=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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=\\\"s = (Q0/2piT) ln(R/r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = \\\\frac{Q_0}{2\\\\pi T} \\\\ln\\\\left(\\\\frac{R}{r}\\\\right)\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\u003eIf the distance \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=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \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\u003eBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57497-locate-image-wells\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 57497\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates of the points where drawdown is requested, the \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59109,"title":"Check a scheme to dewater a construction area","description":"In addition to supplying water and capturing contaminants, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation  at least a value  over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than . \r\nThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\r\n\r\nwhere  is the hydraulic conductivity,  is the pumping rate of the th well,  is the radius of influence, and  is the distance from the th well to the point in question. \r\nWrite a function that takes the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\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: 825.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 412.8px; transform-origin: 407px 412.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 65px; 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 32.5px; text-align: left; transform-origin: 384px 32.5px; 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: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57452\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esupplying water\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59104\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecapturing contaminants\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: 205.442px 8px; transform-origin: 205.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.95px 8px; transform-origin: 50.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at least a value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24\" height=\"20\" alt=\"smin\" style=\"width: 24px; height: 20px;\"\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: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87\" height=\"20\" alt=\"hmax = H - smin\" style=\"width: 87px; height: 20px;\"\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\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: 373.417px 8px; transform-origin: 373.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48.9px; 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 24.45px; text-align: left; transform-origin: 384px 24.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAX0AAABiCAYAAAC8jgOrAAAYeklEQVR4Xu1dX+h2RRH+vC+yulLEorpI+qNgpWlJRRZEIiX0x0KkQksIiVIsIkxCo4yQoiwKxKLMsBBDKMFCEcoKNJS6KFCIuqqMuq95/N7Hb37rOWdnd2fPn/edA4Ofv3fPnt1nd5+dnZ2dPelYPIFAIBAIBAIHg8BJB1PTqGggEAgEAoHAsSD96ASBQCAQCBwQAkH6B9TYUdVAIBAIBIL0ow8EAoFAIHBACATpH1BjR1UDgUAgEAjS79MHPiTZnt4n68g1EAgEAoEiBH4lqSFPP0H6RdiZEz8oKd9gTh0JA4FAIBDoh8DnJevrg/T7ARw5BwKBQCCwWgRC0/dvmrdJljeInOufdeQYCAQCgUAbAkH6bfgNvf0l+eOZIm/3zzpyDAQCgUCgDYEg/Tb8ht7+tfzxAZFr/bOOHAOBQCAQaEMgSL8Nv6G3/yZ/vFzkF/5ZR44bQ+AFUt4rRT4j8hyRO0Xem9Tho/L/V4u8fPf7zfLf326snlHcDSEQpO/bWBjk/xB5mchffLOO3DaMAEx+1+zKPzTm8PsHRV4p8s8N1zOKvgEEgvR9GwmbuHeJPNc328ht4wjA5HfOrg5flv+mpr8/yt9gEsSqIJ5AoCsCQfq+8EJju0AkPHd8cd1yblz9fVsqcYXI30VOVRXi79j4D5Pgllt6I2UP0vdtqB9Jdk8OaHK+X4nctoQAbPhfFYHpBn0Dtn1N8Pz9jfL3MAluqWU3WtYgfd+GwzL9FpFbfbON3DaMABQBPCB32vZ/I//mahC/n7ybCDZczSj6VhAI0vdtqf9Jdq8TCe8LX1y3nBu8uXBYD4rAS0X+vKsMN/v171uuZ5R9IwgE6fs1FDZxfy4SmPphuvWcXisVuF/kLBGabqDZv0cEG7rfEnkk+X3rdY7yrxyBICi/BoK/9eUisYnrh+nWc/q0VOAykTNURagc4E/w309/33qdo/wrRyBI36+BoLXBNpsevvH7QuS0NQTgqvmoSOqKib0fHMb6r8g3ReL09tZadsPlDdL3azwM8LtFbvLLMnLaMAJTrphYFYLs8cQe0IYbeYtFD9L3azVs4oavtR+eW8+JxD52Ovs/UkFInMLdektvrPxB+j4NRq+MwNMHz63nAls+4+3gwNX7RdLwCnDffJ5InMLdemtvrPxBUj4NxgM2+qSlT86RSyAQCKwBAZjr7hUZ2qPxLB9DubxFMu3i+h2k79NcEUPfB8fIJRBYIwIg/IdE/iAyh6MGTINw6e1C/EH6Pl0sYuj74Bi5BAJrQ4CEj3KdP2Cm61VeeANe2oP4g/R9mgwbcpeIRMAsHzwjl0BgLQhAoTtdZIkNdxz2PM+b+IP027tWxNBvx7A0B2B+nQhi0Mc+Sil6kd6KAE9Pl7jV6ktxpr4DBfGnIlNxurqsMoL0rc0/ni5i6LdjaM2BZP8xeQHRKnG4qffdBToWvrWcPdOBLOL+5Z4IH88btvs7ROCFVXP2hgfwkBfCaV8sgo1ZePp9QwS8wd+mVhEI5fGwiFu7B+m3d56Iod+OoSUHDMJ3izwlgrj0eOYgfdhW+T2W80/yj3sshS5I8yJJC4EbJ07rTj1xM1sBsBVJQcyIifS4SG1YFa0s4C6F1DVX/54jdEZnrZ2AjkAQpF/RI5JXYHeDG1ccpW/HcioHDEQGLeOAmYP0ucROibj3QTxogmeLIDZP+u0hEumL/mHlzv7VMrlinw+rUTzvE2GIbSKpT2Xjby8UmboqE9FYsarVwfuqWiVIvwq2Iy9FDP12DEtzmJP0UTZGy+Qgxt8w4UAzn+NOW0x4N4ogOufc3y5tm62np1mnZWLVQfXG+olOA8xyEwzT51YFWfyD9LMQZRNEDP0sRO4J5iZ9VACnbEG8+tGXobhXciBDTD63i0Dzx75GXNbjizpWdY+JQKNumdBpjkHpxvqI1vStCgT7fdMqM0i/rdNEDP02/GrfXoL0UVaY8rgBx7K72FkLgAAxIVgbrlcMz6UC4AxJSdZDl9cbXn8mibbXj+Wl09wpb1oOfZFvmpSNIP2Spnx2Wmh/2JWv3exp+/rhvr0U6VMTPCWBvsSlz6vVYFa8WiTOhvggirblHcY5+/rUF+nCzTRDfYOuoEgDp4B3iljvR27W9oP02zrMWmLoa+0PhLTvcdqXIn30FrrQ6Z4Dl7y5D+/Q9S/cN9vGMN+m+c6qdY99lXsC+F2bbdBeF4pcLnLO7mVo7B8oIHy8RrNQtbYfpN/WYdYQQ5/eJQ9IVe4SgccHIzxWd4w2WLq/vSTpo3LaZsvKNm+wVaAGAgi7fgVwA6/AOwYKU+uqbcjFV38Omj3Hau0qjZ5BVbb9IP22DrOGGPrQUF4sov2AtTba2onbEOrz9tKkj1oNHdqKzdU+7d07V2rnIGR9tWXNdzl54F32B70X1LpfgHw5sVStSkpIH8sTPFbbUw1gW3qHxFqCYY/6oUNdNdAuPBE45CPcoxxz5rkG0tc2YNYdy/kukRHnBHfGb4FT4IYKEpvD9XWsarSxt27K814Nfod7A6nJp/UUuVbqivcfpggLO8VvFblA5BUi8FH2mKVm7FNdP1UaQx8dAtr4RSLpYRuYYbDk+6Lq/MD/w7tBoSsC+zFOg0LDnxooJMbQ9Pt1Az2Y+RUPbbFfiZ+dMyYvEO+7RF4lwk1qTGCIH/9dkVozxFA90K8RnBC8wnGwZB/VG685X/lcu2g3zLQf6MNaVWaZ5ONcURSvLnNaKgD5oQjd1DwKmwNuK7+3xNCHWYgPlmhouDEC1zZCDETriTx0CjxzbzDO0X5r0PRZzyEbbsvBnjnw4zfQh9H38MAN9McivLgDBAYlD8pelRlhpCLQUp8vcpsIJ5glSZ9EDWWq1QVWe+WkfUD3E4/9H+ZXnFeO9NFurMgSHgpzDoDSb4F4oJ2Xhl+wuHTpstR0Fi4zi7WAUhAWSr8m0gcEOrgWIVmzWQ3942ci0LShkSLUw9AtTfrUqPdEpjfDlyR98ptH/aZCL6ReXxbunRpeepVZlJclMZcRxTPKQoQw12drY+jrxrJMpJpQrDZHdOSTRYbuZp0Ln57fWRvpj4VpsK7KemKV5q3Lalk56v7nSc5rIX0SdeskrUl97IStxtJDIaPFoKjsOdLXFfEo5Jydu+e3WmLol2ju6arAYnOEdnaLSMmBj55Y9ch7baSPOqYBtPC3tbnMppvPFrLQ5Oxp5lkD6TdtiCYdW4fpGGt3S5qS8cJxULRKyZG+LqSFcEoKvOW0LTH0S2Z7vSrAMjx3XRuW7Q+K4Ij+PntZrZH00Z+1TZf9e03OD7rvWVfumpw97N7EZQ2kT37zqJd24R0j4RolboonqUAWKRc50qd/qYVwtkzipWWvjaGfunTlJlJNIjktCx0K3hafE/H0tijFpnf6VFstdlnrWMCxMA1rcIDQJGsx6wyRM/7mhfcU6WuPovPkm3BxhKL1yd1/UY7S8AVDzU5+s06AY10ntddPad7aZz83pnNdVa8uc1z+TF65hLR36UrQfIBNoEP1S0bD1cTQT126cpr70EGPoY7AU7nX77RNnQaDS3tl5DrSWn+nC+s7pIBpiOMfyN/uH6j7EnUZCtNgjaLYq7zpRFlCcunqpTfpQ/vGXogOIw3PIrg6w3ECz6W7PtCKK8dX7WoMShwcOVge3X7gTJyQTxWw1M0Xv39lIJ2lL+i+ZlYscn76IDc8tP1hOQHwvy/CK+tKlhZpDGlLxYbSWDc0a/PPvVcbQ79Ecx876DFUNpQHNy6hXfTD25hAlEsefsnhuW+/a7Mo61ZCtN54pGEjzAQhBdEmIc8zCDnzTmqK0k4JWnmq3WvUppYSPLzbpjU/buaacZgifTYKZ1PMtnhAuLAXc5Y8RNKvjaGvNfeSxp4abEN2ZJ330hNkST33Ke1QmIal2kL3uxJTbWqD9py4cqQ/tW+jy1VrItEKqKdX0tx9uHi1MkX6BB2kfrfIm0Q42+plRdHO8dyIdPhebQz9dNmfi44IDxyeWDw0jDs02+xZDoVpMGtjjqVNV4wlJJmaIjwnrRbSBzzUcGsnoip7uGO7eGWledoU4n2M9NOZFN4g2iNEL18tbl9eFVxDPqh7TQx9jZllmex9bDuHnT4lnEs79Psc99XWlGvJd3oebrLWKyXukvGqV5Elm7+Wsi1N+vr7ub1NS32WSsM2MltcxiqbdpTU5sUd6NaNlKWAavku9jVw8Mly043+jt61z20cabKYC+Mg/ZZeMfwuJ/oS7dq7FKk9P+cxxu+nph3v1ebSpF9Mlt4N45Rf8eQ1Rvr6ANFQY1MLNc8uThX0zAbEWuPaiOUUzF03FRZGk2pu40g35JYxLoRor5LrcL05L62eFU9J3+p9U+PiyXcsq4mlSb/YLNKzkRrydiN9bg4MLem0bbrUxrcW7x3aW2tCnNbE0C/V3LXnQm5V0NBf4tVOCDDUAbJvuWDbo3jpqt1C+ul+hHUvgsqihReC9D1a97jF4Y5dVpa2PTak6euNn6Flacsp3bWQPjtc6a59bQz9Es29NCCbT9eZJ5cb5TOvn+dTRV/5uqSGT7XHQ8JEXmuIrV96IBDl1qZIb7MOMV6a9Iu9XlTngIPF9zw6S5IH/PVJ4NbsNafmLAhP5zlE+npXeygTdgiaHUCEiLtfau6wVso7ndZiLMtQ/f3SGPp8tyRoWmlANm98eua376TPQ3IghdK+1RN37T6a09q1UgelD+l7nPFYmvRpbq1ZSe8d6edCKdOejyUclnOPiWwp1overyhtcHTUM0Vy7pZ6AJdq7tpjotYdrSeBRN7jCFAhyhHr3Bhqk+yU55gmfIuJhvWAoviS3dh4Sv5rcXLYMunP3X5T33PR9EnqQ4SjOw80fTxbivWCpS60zVeLYLYuJdWaGPol3hNpiN5eS+s1ddp9KQsn6yU9daawBDHzUhSMXX1KG8Rxg8g5Ivjt4yJD8fWn8ucK1Tqm9OpjaFWkD5SltmpNdBb356Fyt2j6a+qzzaSfC6XMKI6n7DrHlggfDYWBCQ0GxI/YHqUdpiSGPmPFMIYIOwoi+iFcgr58BWlxhdxQDA+QyC9Fbl1TT4uyHEGAJlEr4S0FH5UerMwxhnWfRHTWn+zGSE35qNzkVgjA6moRHjzEt3g1483yb9yqxQlIl+9r8j8wIWM1gm/o+Es1E1WQfk0rb+wddnhoJMVuTvJOSwz9jUEVxS1AYC2umdYi8wrU8+SFkkteMH6mwnVTcy91jrCW2ztdkL43oivMD6sYbEih49bE3cA78PCocfNcIRxRJAcElnbNhNZcsgLUG80w9WB/y3LvAveydNCzFD6QqOUmOAfYXbII0neBcTuZaDc266YbOv4FIqb4FtuBYtMlJRlhQtYPTWgMKT1mPoPprNakwdj5UAKWcM3EhPMFEatTAZUWbRYhZjBz3iPye5H7RKAcoX4XinxCBBFcp25ioxK1dvOW7iNB+pse+nWFL2302hj6daWLt0oQSMP/jhEU08GG/BER7PHUPFpjtioNNd8Ze2fq/oShd2jOpPMFSFzb1KfKBmcC2NGn3Dat9nxPDFrzKh3/rd/r9X7zRm6vgq0x39Jj2LUx9NdY930rk+UcBL1rPG5cYl65TcseOGubvMXUiBXB2SLQ4LUph7dTvVn+jlPD8Nzhg8kBF5ZYL9/Zmj0f9aSXYqnbdo82bckzSL8APX0e4VTDe7Ux9A1ZR5IGBCwnTtnWFq01VxSe81jCNRMEfrsItPQ1ufNuzZ6PNi5V+nL9Yqnf9WHa6jAMSxV+7u+WePDUxtCfu06H+D3d6dMLQmgGOU2AgZtu66lxfmvuIHgg+0+JaPfftXjJ0HtpTZOQZRzsC+mX8NjTuGw5jrSlYafSlCyLamPot5Yx3s8joE8wa+0bZPQdkb+KwC+8JqKq/jr7S8nNU/nSD6fA6uU1ItgghvNAan8vPV9SWw7Le1j54HwJzpm0Ymz5nleaCK3sheSG8tHhEXKbcdzwsxwv3xAEe1FUfdkM25EmGJDQVSIWt8QpMPRJaUwsTzohhw1VhPXgY91gXWIvQVeZ4SYQm/8RkXtFtjY2ijVkpzb3zqZ48jpkTR/gWzdzamPoezfwvuWHifc6kYtELN4k6aZbegUlTB60eTM2VGuwMLpm6hOsS7eDyXbbsZD6BPIT8p2cd0/HolRnreMMtfCgjjt0+q40uD8BD+4Vh0nO+9YxXWmaqczusi2VrUZ7RS9a7Xo1MfRXVM1VFiWNM2QpZGrH1gMXAwsP/NA9NWEdZthSxt5pzIO7d0E2nn/NAc2hKiMfhI5gSGRGJn1I/qYVmV5RV4tDRB866dMMMHW/a20M/Y2Pia7FB6a4fQzxVHAg6DYRaNIYGP9Sgwi2a9jj+fxO/qE19zFCXpPNuyuQkXk1Atq860HI9PuHifFyEbq83i//hkWhVyRi/V3T6exDJ32tKY4tmbF8Q2A5i1tndQ88sBcx2SKkBbRWulzqDVKaD3JukfoKSgw2RpEEnB4D+cCa5eCqazXv5oDRqwZ4Mb1YZCpkRS4/6+/avGn25jp00rd48NTE0Lc2WqQ7fioWdk9tr+dhq6mbgIauoMT+wDU7UBGKISbq6GFTCBTbw0cy46Yw+hyeXlp9+nntrmzmcnPCPe07eok3ZgeuiaG/p3C5V0vfYkZNhZp/LniXvgyHfvPp3a6etn33yhsy5E1tiH9TGzLC8JmDTaLJukVB0CfC5zyvwDFQdG7k0EkfvZ0bIWONhSVgS5yWgx1RhopTU9GmHQ7E3Ibl2OXxWvvBXs1cF5Oz3B5mJQaIu2KHoUeehuY4uCR6tVjrEaUVxxovnZZ+w5VKUSiJIP3p49jUOuGP3OrrfXAjylBhEre23XMSnjo7kbuCUt+6NJfmRa3LY3UBWy1uruKgDtI3dKbKJNwXqsVYKxk1fa2l37DspgvRiU+Q/okLVYY8eCKGfuVIMrw2tJ+i/8aJFgQPlzg96eqBNmQG0vmgKFudtIP0DR2pMQk9wGoIG5/WJ8LNm6mNZcbr7ONTnoeDnwnSP3ZME0hKDhFD36F3DmShQxPr+1r1KUkut0F86bWceqCNmYFImPh8zlTUp5btuQbpt2OYy4Hjv3bjnx5ARXb1XKEMv1cH/gvSP3qLVrpMghbwhMiVhkaIJDYEQOww3fAyD23G0UQNkw/s8Xj0Jd74f22+GTOnpNp+0RLYVpWnU+kTmU/J/3uGIwjSL2iIyqTaVFiqqWuXyVKzXmu/4RgoNksF6R/vKWMXKgBYXNJsOvRQ2ekO6bU0bAI0cO3PrDV44IKla3orVUrmU7Z/7cdfq8lZ2oeRJvWKQk9gljyGBm+QvgW59jQ08ZQSt16Z1pgQh/qNpTYcR8WmHWQepH8cYs6a6WGgiKFv6YJlaTjAhoKh8aQuTudiuazNOthUv1YEER31lX/o+IhxwvtekQ4rM0Sn1BeDcBLRactKPp566OYo1AV7EdYHexaps0CQvhW9tnQk31LFgI4ItZFXa28co2mnah8iSP94ZxmKwRMx9NsG0iG9zf5Tah7IYRSkn0PI73cqfr3MgEMlre03LGvN6iI0/V1LDIVZRYiGy0TO8OtXkdOeItDr5qgg/fk6DDkgF/rDs0Q1/YarkuqN49D0jzchgcS/OXtGDH3P7r2/eXFFmHoIhU1/W22uT3NXadCF1R3rN7ls2K+qVyRB+sch1huM3FADuIgE2XrFXq4R4/dtIzBmlw2b/vbalW1ZdMK1spo19nxOFNVaPsoapH+ixVIPnoihX9mbD+y1WrusBSZuFBa75VkyjzTPQoDaPn7oHb6jpt80a/lB+kfbnAMMy/TPijwsUhuPI8bT4SBQY5fNoYNVAuI9MfYOvEOuF7lPpPUmsNy3D/13Htbqbdsv7TfU8pvLFZr+iS5OV0IMsFtEIob+oQ//fP25F1TlOpfPPlIshECNFl5S1Jp+A6X0NI8VSJD+iabSHjyw6eHCamyWxBMIjCEAf2mcG7hEBCvEePYDAZz1wIXvj4uc26FKpf2mJRLns4ofpH8CEu3BwwM/OAwUTyCgEeCKEB4eIIZ7RTxDLwTa60CAZh6vTd3afkMnk2azDmEN0j/RwdIQAbF5to7Bt7ZSkAyg2T8hgvMcYWdfWyv5lIdhQTwO3dX0GwYmRG3O9+pnQfpHO4eO1TKHr65P14xcAoFAoBcCbrb0igJi0kGwwbNE3O7zCNI/2hLcwKkKZFTRqPFKIBAIrBuBLtq2ocq0+6cBBw2vTicJ0j+KD5dzTYcfmlslMggEAoE1IUDi/7cUqsfGblpXmIKwl+BO+PhQkP5RuLlLHi54axpyUZZAYHkEQPzYtH9UpOf9GvDHv03kYhFcmen+BOkfhZQHIKZitLs3QmQYCAQCgcBcCPwfl1s3vebRmgcAAAAASUVORK5CYII=\" width=\"190.5\" height=\"49\" alt=\"h = sqrt(H^2 - (1/(pi K) sum(Qj ln(R/rj))\" style=\"width: 190.5px; height: 49px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; 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);\"\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: 90.5px 8px; transform-origin: 90.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic conductivity, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Qj\" style=\"width: 19px; height: 20px;\"\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: 82.8417px 8px; transform-origin: 82.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the pumping rate of the \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);\"\u003ej\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.725px 8px; transform-origin: 23.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth well, \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);\"\u003eR\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: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of influence, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" alt=\"rj\" style=\"width: 14px; height: 20px;\"\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: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the distance from the \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);\"\u003ej\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: 96.075px 8px; transform-origin: 96.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth well to the point in question. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.117px 8px; transform-origin: 379.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 476.7px; 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 238.35px; text-align: left; transform-origin: 384px 238.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"614\" height=\"471\" style=\"vertical-align: baseline;width: 614px;height: 471px\" 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\" alt=\"dewatering scheme\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin)\r\n% tf = true if well system achieves minimum drawdown everywhere, false otherwise\r\n% smin1 = min drawdown achieved\r\n% xmin, ymin = coordinates of the minimum drawdown\r\n% xw, yw = coordinates of the wells\r\n% Q0 = common pumping rate OR vector of pumping rates\r\n% R = radius of influence\r\n% Lx = length of construction area\r\n% Ly = width of construction area\r\n% K = hydraulic conductivity\r\n% H = initial elevation of the water table\r\n% smin = minimum drawdown required\r\n\r\n   h = sqrt(H^2-Q*Lx/K*Ly);\r\n   tf = all(H-h\u003csmin);\r\n   [smin1,[xmin ymin]] = max(H-h);","test_suite":"%% Prep assignment--modified\r\nxw   = -50;                     %  x-coordinates of the wells (m)\r\nyw   = 0;                       %  y-coordinates of the wells (m)\r\nQ0   = 661.6;                   %  Pumping rates (m3/d)\r\nR    = 450;                     %  Radius of influence (m)\r\nLx   = 250;                     %  Length of construction area (m)\r\nLy   = 100;                     %  Width of construction area (m)\r\nK    = 0.1;                     %  Hydraulic conductivity (m/d)\r\nH    = 85;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\ntf = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nassert(tf)\r\n\r\n%% Fall 2020, exam 2, problem 4a\r\nxw   = [0 200 400];             %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125];         %  y-coordinates of the wells (m)\r\nQ0   = 1331.2;                  %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\ntf = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nassert(tf)\r\n\r\n%% Fall 2020, exam 2, problem 4c--with pumping rate from part a\r\nxw   = [0 200 400 1000];        %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125 -125];    %  y-coordinates of the wells (m)\r\nQ0   = 1331.2*[1 1 1 -1];       %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 100;\r\nsmin1_correct = 4.723;\r\nassert(~tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% Fall 2020, exam 2, problem 4c--with higher pumping rate\r\nxw   = [0 200 400 1000];        %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125 -125];    %  y-coordinates of the wells (m)\r\nQ0   = 1410*[1 1 1 -1];         %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 100;\r\nsmin1_correct = 5.02;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% Fall 2022, exam 2, problem 2\r\nxw   = [100 100 700 700];       %  x-coordinates of the wells (m)\r\nyw   = [-200 200 -200 200];     %  y-coordinates of the wells (m)\r\nQ0   = 944*[1 1 -1 -1];         %  Pumping rates (m3/d)\r\nR    = 650;                     %  Radius of influence (m)\r\nLx   = 200;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 2;                       %  Hydraulic conductivity (m/d)\r\nH    = 35;                      %  Initial saturated thickness (m)\r\nsmin = 4;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 200;\r\nymin_correct = 0;\r\nsmin1_correct = 4.001;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 135 450 210];       %  x-coordinates of the wells (m)\r\nyw   = [-80 200 135 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 640;                     %  Pumping rates (m3/d)\r\nR    = 910;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 0.8;                     %  Hydraulic conductivity (m/d)\r\nH    = 90;                      %  Initial saturated thickness (m)\r\nsmin = 6;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = -150;\r\nsmin1_correct = 6;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 135 450 210];       %  x-coordinates of the wells (m)\r\nyw   = [-80 200 -50 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 638;                     %  Pumping rates (m3/d)\r\nR    = 910;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 0.8;                     %  Hydraulic conductivity (m/d)\r\nH    = 90;                      %  Initial saturated thickness (m)\r\nsmin = 6;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 150;\r\nsmin1_correct = 6;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50 100 200 300 450 450  100  200  300];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 5.5;\r\nassert(~tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3 \u0026\u0026 abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50  50 200 350 450 450   50  200  350];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 5.62;\r\nassert(~tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3 \u0026\u0026 abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50   0 200 400 450 450    0  200  400];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 82.4;\r\nymin_correct = 150;\r\nsmin1_correct = 5.66;\r\nassert(~tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-2 || abs(Lx-xmin-xmin_correct)/xmin_correct\u003c1e-2)\r\nassert(abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxL   = 80:80:320;\r\nyL   = 200*ones(1,4);\r\nxw   = [-50 -50 xL 450 450  xL];     %  x-coordinates of the wells (m)\r\nyw   = [-75  75 yL -75  75 -yL];     %  y-coordinates of the wells (m)\r\nQ0   = 200;                          %  Pumping rates (m3/d)\r\nR    = 910;                          %  Radius of influence (m)\r\nLx   = 400;                          %  Length of construction area (m)\r\nLy   = 300;                          %  Width of construction area (m)\r\nK    = 0.8;                          %  Hydraulic conductivity (m/d)\r\nH    = 90;                           %  Initial saturated thickness (m)\r\nsmin = 6;                            %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 6.65;\r\nassert(tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3)\r\nassert(abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-16T05:19:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-16T05:10:49.000Z","updated_at":"2026-02-12T14:57:15.000Z","published_at":"2023-10-16T05:19:15.000Z","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\u003eIn addition to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57452\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esupplying water\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59104\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecapturing contaminants\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at least a value \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=\\\"smin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{min}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than \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=\\\"hmax = H - smin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_{max} = H – s_{min}\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:r\u003e\u003cw:t\u003eThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\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=\\\"h = sqrt(H^2 - (1/(pi K) sum(Qj ln(R/rj))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\sqrt{H^2-\\\\frac{1}{\\\\pi K} \\\\sum_{j=1}^N Q_j \\\\ln\\\\left(\\\\frac{R}{r_j}\\\\right)}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the 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=\\\"Qj\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the pumping rate of the \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=\\\"j\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ej\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth well, \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=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of influence, 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=\\\"rj\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the distance from the \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=\\\"j\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ej\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth well to the point in question. \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 the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\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=\\\"471\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"614\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"dewatering scheme\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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steady drawdown in a confined aquifer","description":"A well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance  to the point where the drawdown is wanted is smaller than the radius of influence , then the drawdown  of a well pumping at rate  in a confined aquifer of transmissivity  is \r\n\r\nIf the distance  is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \r\nBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in Cody Problem 57497. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \r\nWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the - and -coordinates of the points where drawdown is requested, the - and -coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of - and -coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head).  ","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: 369.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.95px; transform-origin: 407px 184.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; 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 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.925px 8px; transform-origin: 376.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance \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);\"\u003er\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: 254.008px 8px; transform-origin: 254.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the point where the drawdown is wanted is smaller than the radius of influence \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);\"\u003eR\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: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the drawdown \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);\"\u003es\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: 80.125px 8px; transform-origin: 80.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a well pumping at rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q0\" style=\"width: 19px; height: 20px;\" width=\"19\" 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: 118.633px 8px; transform-origin: 118.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a confined aquifer of transmissivity \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);\"\u003eT\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: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38.9px; 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 19.45px; text-align: left; transform-origin: 384px 19.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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alt=\"s = (Q0/2piT) ln(R/r)\" style=\"width: 97px; height: 39px;\" width=\"97\" height=\"39\"\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: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the distance \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);\"\u003er\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: 310.4px 8px; transform-origin: 310.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.892px 8px; transform-origin: 378.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57497-locate-image-wells\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 57497\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: 317.433px 8px; transform-origin: 317.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 323.875px 8px; transform-origin: 323.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the \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);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 189.05px 8px; transform-origin: 189.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates of the points where drawdown is requested, the \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);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- 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);\"\u003ey\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: 257.883px 8px; transform-origin: 257.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 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 s = drawdown(x,y,xw,yw,Q0,R,T,varargin)\r\n%  s = drawdown\r\n%  (x,y) = points where drawdown is requested\r\n%  (xw,yw) = coordinates of real wells\r\n%  Q0 = pumping rates\r\n%  R = radii of influence\r\n%  T = transmissivity\r\n%  varargin:\r\n%     (xb,yb) = coordinates of two points on the boundary\r\n%     btype = type of boundary ('NF' = no-flow, 'CH' = constant-head)\r\ns = (Q0/(2*pi*T)*ln(R/hypot(x-xw,y-yw);\r\nend","test_suite":"%%  Single well in an infinite aquifer\r\nx  = 50;                        %  x-coordinate of drawdown point (m)\r\ny  = 100;                       %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinates of wells (m) \r\nyw = 0;                         %  y-coordinates of wells (m)\r\nQ0 = 800;                       %  Pumping rates (m3/d)\r\nR  = 910;                       %  Radius of influence (m)\r\nT  = 150;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = 1.7797;             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Single well in an infinite aquifer, drawdown requested at multiple points\r\nx  = [50 400 93];               %  x-coordinate of drawdown point (m)\r\ny  = [100 818 45];              %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 800;                       %  Pumping rate (m3/d)\r\nR  = 910;                       %  Radius of influence (m)\r\nT  = 150;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = [1.7797 0 1.8468];             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Single well in an infinite aquifer, drawdown requested at random points\r\nx  = 200*rand(1,8);             %  x-coordinate of drawdown point (m)\r\ny  = zeros(1,8);                %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 1200;                      %  Pumping rate (m3/d)\r\nR  = 450;                       %  Radius of influence (m)\r\nT  = 175;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\nassert(all(abs(s(2:end)/s(1)-log(R./x(2:end))/log(R./x(1)))\u003c1e-3))\r\n\r\n%%  Three wells in an infinite aquifer\r\nx  = 0;                         %  x-coordinate of drawdown point (m)\r\ny  = 0;                         %  y-coordinate of drawdown point (m)\r\nxw = [150 200 -300];            %  x-coordinates of wells (m) \r\nyw = [200 -150 100];            %  y-coordinates of wells (m)\r\nQ0 = [1000 1500 2000];          %  Pumping rates (m3/d)\r\nR  = 450;                       %  Radius of influence (m)\r\nT  = 430;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = 0.8050;             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Two extraction wells and one injection well in an infinite aquifer\r\nx  = [0 50 270];                %  x-coordinate of drawdown point (m)\r\ny  = [0 100 -180];              %  y-coordinate of drawdown point (m)\r\nxw = [150 200 -300];            %  x-coordinates of wells (m) \r\nyw = [200 -150 100];            %  y-coordinates of wells (m)\r\nQ0 = [1200 -500 800];           %  Pumping rates (m3/d)\r\nR  = [450 280 620];             %  Radius of influence (m)\r\nT  = 340;                       %  Transmissivity (m2/d)\r\ns  = drawdown(x,y,xw,yw,Q0,R,T);\r\ns_correct = [0.5558 0.8643 -0.2365];             \r\nassert(all(abs(s-s_correct)\u003c1e-3))\r\n\r\n%%  Well near a slanted boundary\r\nx  = 350;                       %  x-coordinate of drawdown point (m)\r\ny  = 100;                       %  y-coordinate of drawdown point (m)\r\nxw = 0;                         %  x-coordinate of well (m) \r\nyw = 0;                         %  y-coordinate of well (m)\r\nQ0 = 300;                       %  Pumping rate (m3/d)\r\nR  = 1000;                      %  Radius of influence (m)\r\nT  = 210;                       %  Transmissivity (m2/d)\r\nxb = [-550 1050];               %  x-coordinates of points on boundary (m)\r\nyb = [900 -50];                 %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = 0.2298;\r\nsNF_correct = 0.2911;\r\nsCH_correct = 0.1684;             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%  Wells near a boundary parallel to the y-axis\r\nx  = [20 50 -320];               %  x-coordinate of drawdown point (m)\r\ny  = [30 46 -300];               %  y-coordinate of drawdown point (m)\r\nxw = [50 75 85 43];              %  x-coordinate of well (m) \r\nyw = [10 35 67 91];              %  y-coordinate of well (m)\r\nQ0 = [150 600 420 80];           %  Pumping rate (m3/d)\r\nR  = 670;                        %  Radius of influence (m)\r\nT  = 195;                        %  Transmissivity (m2/d)\r\nxb = [140 140];                  %  x-coordinates of points on boundary (m)\r\nyb = randi(1500,[1 2]);          %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = [2.4837 3.0597 0.2509];\r\nsNF_correct = [3.7791 4.5365 0.3138];\r\nsCH_correct = [1.1884 1.5830 0.1880];             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%  Wells near a boundary parallel to the x-axis\r\nx  = [0 -20 -40 370];            %  x-coordinate of drawdown point (m)\r\ny  = [0 25 -40 90];              %  y-coordinate of drawdown point (m)\r\nxw = [-72 13 50 -20];            %  x-coordinate of well (m) \r\nyw = [14 28 0 -14];              %  y-coordinate of well (m)\r\nQ0 = [230 410 380 215];          %  Pumping rate (m3/d)\r\nR  = 450;                        %  Radius of influence (m)\r\nT  = 81;                         %  Transmissivity (m2/d)\r\nxb = randi(982,[1 2]);           %  x-coordinates of points on boundary (m)\r\nyb = [-43 -43];          %  y-coordinates of points on boundary (m)\r\nsNB  = drawdown(x,y,xw,yw,Q0,R,T);\r\nsNF  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'NF');\r\nsCH  = drawdown(x,y,xw,yw,Q0,R,T,xb,yb,'CH');\r\nsNB_correct = [5.8499 5.4446 4.4620 0.4481];\r\nsNF_correct = [9.4217 8.4800 8.7657 0.7035];\r\nsCH_correct = [2.2783 2.4091 0.1584 0.1927];             \r\nassert(all(abs(sNB-sNB_correct)\u003c1e-3))    \r\nassert(all(abs(sNF-sNF_correct)\u003c1e-3))    \r\nassert(all(abs(sCH-sCH_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('drawdown.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-08T16:30:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2023-01-08T16:28:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-08T02:57:32.000Z","updated_at":"2026-02-12T14:29:49.000Z","published_at":"2023-01-08T02:58:04.000Z","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 well extracting water from a confined aquifer will lower the piezometric head and create a cone of depression. In steady state, if the distance \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=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the point where the drawdown is wanted is smaller than the radius of influence \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=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the drawdown \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=\\\"s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a well pumping at rate \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=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a confined aquifer of transmissivity \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=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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=\\\"s = (Q0/2piT) ln(R/r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es = \\\\frac{Q_0}{2\\\\pi T} \\\\ln\\\\left(\\\\frac{R}{r}\\\\right)\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\u003eIf the distance \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=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is greater than the radius of influence, then the drawdown is zero. If multiple wells are pumping, the drawdown at the requested point is the sum of the drawdowns from the individual wells. \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\u003eBoundaries, such as no-flow and constant-head boundaries, can be modeled using the method of images, as described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57497-locate-image-wells\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 57497\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Each real well will have a corresponding image, and the drawdown will be the sum of the drawdowns from all wells—real and image. Recall from the previous problem that for no-flow boundaries, the image wells pump in the same sense as the real wells, whereas for constant-head boundaries, the image wells pump in the opposite sense as the real wells. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute steady-state drawdown in a confined aquifer. Input to the function will be the \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates of the points where drawdown is requested, the \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates of the real wells, the pumping rates and radii of influence of the wells, and the transmissivity of the aquifer. If a boundary is present, it will be specified by two pairs of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\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=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-coordinates as well as a character string (‘NF’ for no-flow, ‘CH’ for constant-head). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59109,"title":"Check a scheme to dewater a construction area","description":"In addition to supplying water and capturing contaminants, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation  at least a value  over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than . \r\nThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\r\n\r\nwhere  is the hydraulic conductivity,  is the pumping rate of the th well,  is the radius of influence, and  is the distance from the th well to the point in question. \r\nWrite a function that takes the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\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: 825.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 412.8px; transform-origin: 407px 412.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 65px; 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 32.5px; text-align: left; transform-origin: 384px 32.5px; 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: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57452\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esupplying water\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59104\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecapturing contaminants\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: 205.442px 8px; transform-origin: 205.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.95px 8px; transform-origin: 50.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at least a value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24\" height=\"20\" alt=\"smin\" style=\"width: 24px; height: 20px;\"\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: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87\" height=\"20\" alt=\"hmax = H - smin\" style=\"width: 87px; height: 20px;\"\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\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: 373.417px 8px; transform-origin: 373.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48.9px; 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 24.45px; text-align: left; transform-origin: 384px 24.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"49\" alt=\"h = sqrt(H^2 - (1/(pi K) sum(Qj ln(R/rj))\" style=\"width: 190.5px; height: 49px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; 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);\"\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: 90.5px 8px; transform-origin: 90.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic conductivity, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Qj\" style=\"width: 19px; height: 20px;\"\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: 82.8417px 8px; transform-origin: 82.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the pumping rate of the \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);\"\u003ej\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.725px 8px; transform-origin: 23.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth well, \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);\"\u003eR\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: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of influence, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" alt=\"rj\" style=\"width: 14px; height: 20px;\"\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: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the distance from the \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);\"\u003ej\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: 96.075px 8px; transform-origin: 96.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth well to the point in question. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.117px 8px; transform-origin: 379.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 476.7px; 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 238.35px; text-align: left; transform-origin: 384px 238.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"614\" height=\"471\" style=\"vertical-align: baseline;width: 614px;height: 471px\" 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cTIma/gu2WYhpLuqeNmgt99+O2zXrl173HHHjR8//qmnngpxNGwnTpxYXFz86KOPxmlRaWlp2O68885xuJWWLVu2bds2FBs3bowdcs5nq0vESwAg23y25vMlysZlLyZj+NpImNukvLw8JsyVK1eGWHjqqadecMEFQ4cOPeqoo0Iz5MkrrrjiF7/4ReXcz23evDls27RpE4c1xVubbNq0KQ4bVFSvZBLbUemyl5IKACDLbFn9QVKxHSVL8zokk5oQCXObLF26tKysLBSdO3eePXv2TTfdNHr06CuvvPK+++6bNm1a/BLaCRMmhPxZOT2x1157JVUN+fn5SdU4y+uVTAIAAHaQZGleh2RSE+JzmA2r53OY69atW7JkyYYNG4455pg99tgj6X7hoYceine5HDp0aIidoYj/qQ4dOsydO7dyyta6d+/+8ccfn3DCCbfddlvSqluRz2Fmnw1zH/xw8kWxbrXnfv93vLubAgA70gfXnf7ZmuQ7CPcZ9bP2fc6MNVmi6S3pJcyG1f9NP/UoLy8//PDDN23adOCBBz7xxBOhM3LkyGeffXb33Xd/8cXaL4I/4ogjPvnkk5NOOunmm29OWnWTMLNQ9YRZcEiP/cY/HGsAgB1ixcijJcxs1vSW9K6S/Rq1bNkyfiDzj3/8Y+wUFBSEbT1f5BM/qBkvrwUAAMgtEubXK94hs0WLFnEY74FZWlpaXl4eO9WFeLlly5ZQdO7cOXYAAAByiIS5TZ577rlx48ZdddVVybiGkpLPr0no2LFjHB566KGxWLJkSSyqq7p0trCwMBYAAAA5RMLcJk8++eQDDzzw8MMPb/VtsVGIl++++24o4rWyQc+ePfPy8kLx0ku13NNi8eLFYZufn9+rV6/YAQAAyCES5jY5+eSTYzF16tRYVDdhwoSwDZHyrLPOip327dv36NEjFPfff//69etjM1q7du3MmTND0a9fv3hXTAAAgNwiYW6T4uLigw8+OBSzZs2aOHFi1acrQ3ocM2bMnDlzQj1s2LD9998/9oNLLrkkbEOeHDFixJo1a2KzpKRk+PDhGzZsaN269fnnnx+bAAAAuUXC3FZTpkzZd999QzF16tQjjjhi5MiR55xzzjHHHDN79uzQPPHEEy+99NLKiYmDDjoofm5z8eLFvXv3DpPPPvvsMO3NN98Mzeuvv77qQ5sAAAC5RcLcVnvvvfcjjzwSUmJ+fn5paemzzz47f/78LVu2dOjQYdy4cbfccksyr5qQKidNmhQmhGlh8oIFC8rKyjp16jRt2rT+/fsnkwAAAHJNi4qKiqQk1zS927M2ARvmPvjh5ItiXXBIj/3GPxxrAIAdYsXIoz9b8/ndDYJ9Rv2sfZ8zY02WaHpLeu9hAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwmzY+vXri4uLL7300mRch8cff/zCCy8cWGns2LFPPvlk8kAdMp0PAACQ5STMhl1++eV/+tOfNmzYkIxrWLdu3RlnnHHZZZc9/fTTyyo99dRTF1988eDBg2v9XZnOBwAAyAkSZgNCvJw3b14yqE15efl55533+uuvh3rIkCF33HHH5MmTBw4cGIYLFy4cNWpU5ay/yXQ+AABArpAw67R+/frhw4c/9thjybgO06dPX7ZsWShuvfXWq6++uri4+Pjjj58wYUKoQ3PBggUPPfRQ5cREpvMBAAByhYRZu9mzZ/fv3/+FF14Idbt27WKzVjNmzAjbXr169e3bN3aiIUOGdOvWLRQhUsZOlOl8AACAXCFh1mLYsGFjxoxZvXp1QUHBj3/84xj8arVo0aJVq1aFYsCAAbFT3aBBg8L2rbfeeu+992In0/kAAAA5RMKsxTvvvBO2xcXFv/nNb7773e/GZq2WLl0ai65du8aiui5dusQiXhYbZDofAAAgh0iYtejTp8+DDz54xx13dOjQIWnVIUbBvLy8WmcWFhbGYuHChbHIdD4AAEAOkTBr8YMf/KDq7cT6lZaWhu3OO+8ch1tp2bJl27ZtQ7Fx48bYyXR+g4rqlUwCAAB2kGRpXodkUhMiYW6TzZs3h22bNm3isKZWrVqF7aZNm+Iw0/kNWl6vZBIAALCDJEvzOiSTmhAJMwV77bVXUtWQn5+fVNVkOh8AACAnSJgpWL9+fVI1TqbzAQAAcoKEuU1atvx8B8ZrX2v16aefhm1eXl4cZjofAAAgh0iY26SgoCBs6/linhgm27VrF4eZzgcAAMghEuY2iTcdKS0tLS8vj53qQlzcsmVLKDp37hw7mc4HAADIIRLmNjn00ENjsWTJklhU9+KLL8ai6kaXmc4HAADIIRLmNunZs2f8zORLL70UO9UtXrw4bPPz83v16hU7mc4HAADIIRLmNmnfvn2PHj1Ccf/992/1DbFr166dOXNmKPr16xfvchlkOh8AACCHSJjb6pJLLgnbkA9HjBixZs2a2CwpKRk+fPiGDRtat259/vnnx2aU6XwAAIBcIWFuq4MOOuiqq64KxeLFi3v37n3OOeecffbZJ5544ptvvhma119/fceOHSsnJjKdDwAAkCskzBSElDhp0qQOHTps2bJl/vz5CxYsKCsr69Sp07Rp0/r3759MqibT+QAAADmhRUVFRVKSa4qKipYvX54MyA4b5j744eSLYl1wSI/9xj8cawCAHWLFyKM/W1MS631G/ax9nzNjTZZoekt672ECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWHy1b3//k7jxu3Up89Ow4btdO+9O82bl/QBACA7xRVsWL6GX6Gwgk2dhMlXEV6ZIVh26rTT+PGfvyxDvAwv0dAJr1IAAMhOYbEaV7Bh+Rp+hSKsYMOvsLglLRImGQuvwPDKrPXfe8KrNDwEAADZJiTJsFitKSxrhcwUSZhkbNiwpKhVeHHWPwEAALaz+i+ItYJNkYRJZhrzecswocE5AACwfYQAWeu7l9VZwaZFwiQzzz2XFPUIr2GXGQAAkCUaGR0lzFRImGSmkS88CRMAgCzRmPdIgkZOo34SJpkpLEyK+q1cmRQAALBjdeyYFPVr5EKX+kmYZOa445Kifo2cBgAAX7fevZOC7UDCJDONfH16GQMAkCUa+eak90hSIWGSmRAdG0yP113nGgMAALJFWJqGBWr9whJ36NCkZltImGTsnnuSolbhBTxuXFIDAEA2COmxnrdJwgq2/iUujSdhkrHwClyxovZ/BwrN8BAAAGSVmCFrXcGG5BlWsGECqZAw+SriG5Vz537+Qh069PNfMVt69xIAgOwUV7BhyRpXsCFYhhVsWNCGX6SoRUVFRVKSa4qKipYvX54MyA4b5j744eSLYl1wSI/9xj8cawCAHWLFyKM/W1MS631G/ax9nzNjTZZoekt672ECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApKNFRUVFUvJVlZSUvPzyy8mghhYtWgwaNCgZVPP444/PmTPngw8+CHVhYWFxcXG/fv3iQ41UVFS0fPnyZEB22DD3wQ8nXxTrgkN67Df+4VgDAOwQK0Ye/dmakljvM+pn7fucGWuyRNNb0kuYKbjlllsmT56cDGpo3br10qVLk0GldevWjRgx4vXXX0/GX+jWrdvtt9/evn37ZNwQCTMLSZgAQFaRMLNc01vSu0o2Be+8807Y5uXlhTBZU6tWreK0qLy8/LzzzovxcsiQIXfccUdIpwMHDgzDhQsXjho1qnIWAABA7pEwU7BkyZKwDSlxaW1ee+21OC2aPn36smXLQnHrrbdeffXVxcXFxx9//IQJE0IdmgsWLHjooYcqJwIAAOQYCXNbbd68+cMPPwxF9+7dY6d+M2bMCNtevXr17ds3dqIhQ4Z069YtFCGCxg4AAEBukTC31fz582NxwAEHxKIeixYtWrVqVSgGDBgQO9XFLwR666233nvvvdgBAADIIRLmtlq5cmXY5ufnFxUVxU49ln7xlT9du3aNRXVdunSJRbyMFgAAILdImNsqfmdPCIebNm2aOXPm2LFjR4wYEbZTp05dt25dnFMlRse8vLwOHTrETnWFhYWxWLhwYSwAAAByiIS5rd5+++2wXbt27XHHHTd+/Pinnnpq3rx5YTtx4sTi4uJHH300TotKS0vDduedd47DrbRs2bJt27ah2LhxY+wAAADkEAlzm5SXl8eEuXLlyhALTz311AsuuGDo0KFHHXVUaIY8ecUVV/ziF7+onPu5zZs3h22bNm3isKZ4a5NNmzbFYYOK6pVMAgAAdpBkaV6HZFITImFuk6VLl5aVlYWic+fOs2fPvummm0aPHn3llVfed99906ZNa9euXXhowoQJ8bOaVfbaa6+kqiE/Pz+pGmd5vZJJAADADpIszeuQTGpCJMxtst9++02ZMuUnP/nJvffeG+qkW+nYY4+96qqrQrFly5aZM2fGZrR+/fqkAgAAaEIkzG2y22679enT57TTTttjjz2SVjUDBw6Mn6t88cUXY6dly893eLxWtlaffvpp2Obl5cUhAABADpEwv0YhT8YPZP7xj3+MnYKCgrCt54t8YviMl9cCAADkFgnz6xXftGzRokUcxpuUlJaWlpeXx051IV5u2bIlFJ07d44dAACAHCJhbpPnnntu3Lhx8fOWtSopKQnbjh07xuGhhx4aiyVLlsSiuqqLaatujAkAAJBDJMxt8uSTTz7wwAMPP/zwVt8WG4V4+e6774YiXisb9OzZM37G8qWXXoqd6hYvXhy2+fn5vXr1ih0AAIAcImFuk5NPPjkWU6dOjUV1EyZMCNsQKc8666zYad++fY8ePUJx//33b/WNsmvXro1fOduvX794V0wAAIDcImFuk+Li4oMPPjgUs2bNmjhxYtWnK0N6HDNmzJw5c0I9bNiw/fffP/aDSy65JGxDnhwxYsSaNWtis6SkZPjw4Rs2bGjduvX5558fmwAAALlFwtxWU6ZM2XfffUMxderUI444YuTIkeecc84xxxwze/bs0DzxxBMvvfTSyomJgw46KH5uc/Hixb179w6Tzz777DDtzTffDM3rr7++6kObAAAAuUXC3FZ77733I488ElJifn5+aWnps88+O3/+/C1btnTo0GHcuHG33HJLMq+akConTZoUJoRpYfKCBQvKyso6deo0bdq0/v37J5MAAAByTYuKioqkJNcUFRUtX748GZAdNsx98MPJF8W64JAe+41/ONYAADvEipFHf7bm87sbBPuM+ln7PmfGmizR9Jb03sMEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHVmdMDdv3rxq1arly5cvWrToxhtvfPnll5cuXfr++++vX78+mQEAAEDWyMaEGVLl2LFju3fv/vd///d9+vT5zne+80//9E/Tpk0bMmTI6aeffuKJJx599NFdunQ55ZRTXnzxxeT3AAAAsKNlV8K85557unXrFlLlU0899fHHHyfd2mzatOndd98dNmxYUVFRiKPe1QQAANjhsiVhzpw587DDDvvxj3+8YcOG2Gnbtu2+++7793//99ddd91DDz30yCOPhO0vf/nLww8//IADDthll13itCDE0aOPPvpf//Vf//d//zdpAQAAsN21qKioSModpKSk5B//8R//8pe/xOF+++13wQUXHHvssbvttlvs1KW0tPSDDz645pprFi9enLR22in83tGjRyeDpq6oqGj58uXJgOywYe6DH06+KNYFh/TYb/zDsQYA2CFWjDz6szUlsd5n1M/a9zkz1mSJprek38HvYd52223HH398iJetW7cO4fDVV1995plnTjvttAbjZVBQUNC5c+df/epX4ZDcdddde+21V2jeeuutPXv29GYmAADA9rcjE+bKlStDIAxFyJZLly4dPXr0N77xjfhQpo477rjnn3/+6aef7tChQ8irAwYMSB4AAABge9nB72GeccYZf/jDH9K6rrWwsHDu3LkzZswoKChIWgAAAGwvOzJhduzY8Yc//GHLlin/GY4++ugnnngiGQAAALC97OD3MAEAAGgyJEwAAADSsePvVlKXd955Z8qUKStXriwrK0tatcnLy5s1a1YyaGbcrSQLuVsJAJBV3K0ky7lbyfbw7LPPhh196qmnPvHEE6+//vqyhiS/DQAAgB0q6xLmRx99NHLkyGQAAABA7si6q2S/+93vvvHGG6HYY4897r333m984xv5+fnxobrsueeeSdXMuEo2C7lKFgDIKq6SzXKukv3alZR8/gJo167d7373u86dO3/zm98MAbJ+8TcCAACwY2VdwiwtLQ3bY489Ng4BAADIFVmXMHfeeeewPeGEE+IQAACAXJF1CbNz585hO2XKlDgEAAAgV2RdwrzlllvC9u233/7zn/8cOwAAAOSErEuYe+yxx3XXXReK3r17P/fcc7EJAABA9su6u5VEjz766BVXXBGKvLy8XXfdtZ4blrRs2XLu3LnJoJlxt5Is5G4lAEBWcbeSLOduJdvDbbfdFuNlUFZWtnbt2g/r9tFHH8WZAAAA7FhZlzAXLVp06623JgMAAAByR9YlzEsvvTQWvXv3njdv3uuvv768Xm+88UacDwAAwI6VdQlz7dq1Ybvvvvveeeed3/zmN9u0aRP7AAAAZLmsS5ifffZZ2P7Lv/xLHDZhjz/++IUXXjiw0tixY5988snkAQAAgNyUdQlzl112Cdum/dblunXrzjjjjMsuu+zpp59eVumpp566+OKLBw8evGHDhmQSAABArsm6hHnUUUeF7d133x2HTU95efl55533+uuvh3rIkCF33HHH5MmTBw4cGIYLFy4cNWpU5SxyRqdOnebNm5cM6hbmhJnvv/9+MgYAgKYo6xLmDTfcELZ/+tOfnnnmmdhpYqZPn75s2bJQ3HrrrVdffXVxcfHxxx8/YcKEUIfmggULHnroocqJ5Ia5c+cOGzas/pAZHu3Tp88999xTWFiYtAAAoCnKuoRZUFBwxx13hGLUqFHXXHPNRx99VF5eHh9qGmbMmBG2vXr16tu3b+xEQ4YM6datWyhCBI0dckIIjfWHzBgvw5zevXsnLQAAaKKyLmFeddVVN9988+677x7qWbNmffvb3z7ooIO6dOnyrTocccQR8TfmhEWLFq1atSoUAwYMiJ3qBg0aFLZvvfXWe++9FzvkhHpCpngJAECzknUJ881Kf/nLX5JxpU2bNpXWITyUTMoFS5cujUXXrl1jUV0I0rGIl9GSQ/4WMp/7W8j83RvviZcAADQrWZcwd8lQu3btkt+ZC2J0zMvL69ChQ+xUV/UhvYULF8aCHBJD5vk33rVgzadhGLZnPbRYvAQAoFlpUVFRkZR8/S688MKnn346BONXXnklaX1Zly5dNm3a1L9//4kTJyatuhUVFS1fvjwZkB3+8NQDJ5x59nc7Ftz2h/99aGS/Qbc/kTwAALAjrBh59GdrSmK9z6ifte9zZqzJEk1vSZ9172E2bZs3bw7beu722apVq7Bt/KW/4YysRzKJ7WjfnfMuOHiXEC9/fOT/OWrP1kkXAIDmKlma1yGZ1IRImDvAXnvtlVQ15OfnJ1XjLK9XMont6OW1m694ZX2Il7e+8dd4uSwAAM1ZsjSvQzKpCdmRCbO8vLysrCwZpOoPf/hDUmWl9evXJxVNy7x58/qeOeS+b+/+3Y4F9x23+yX/+fu6bmECAABN0o5MmCUlJQcffPDUqVOTcRr+/Oc/9+nT54ILLkjGWaZly893eLxWtlaffvr5u155eXlxSA6JNyZ5/LqR8eLYfXfOC1GznvtkAgBA07Pjr5KdOHFily5dnnzyyWT8Va1atapv3769e/cOxQEHHJB0s0xBQUHYbty4MQ5riuEzt74gl+Bv97087m/fHNuxsGNyCxMhEwCA5mFHJsyOHTsuXrw4pMFNmzZdfPHFIWdeddVVa9euTR5unNLS0pkzZx5zzDFhfb9y5crQ+clPfnLnnXfGR7NNvElJ+DOXl5fHTnUhXm7ZsiUUnTt3jh1ywt/iZY0bk/ztPplCJgAAzcAOfg+zoKDgN7/5zU9/+tO8vLyQMx9++OGQFY888sjBgwcvX758zZo1tX5Qc8OGDe+8886ll1567LHHfutb3xo/fnzMpWF9//vf//60006L07LQoYceGoslS5bEoroXX3wxFlU3xiT71RMvIyETAIDmY8dfJRv069fvjTfeGDNmTBz+9a9/Xbhw4Xe+851evXodfPDBhx12WLdu3ULy7N69+xFHHFFUVBSGp5566q9//evVq1fH33LIIYe88MILd955Z7zbR9bq2bNn/IzlSy+9FDvVLV68OGzz8/PDE48dsl/98TKqCpnvv/9+0gIAgKYoKxJmdP755y9fvvynP/3pHnvskbQqffrppxs2bFi7du3HH3/8ySefJN1KBQUF/fv3D2ntkUce2XPPPZNuFmvfvn2PHj1Ccf/992/1jbLhCc6cOTMUIW9neU6muoqKivrjZRRC5ooVK7w7DQBA05ZFCTMK+ep3v/vdwoUL77vvvr/7u78LabN167/dtj4/P3/XXXft1KnTVVddNW/evMWLF0+cOHG33XZLHs4Fl1xySdiGPDlixIg1a9bEZklJyfDhw0OQDk82JO3YBAAAyC0tKioqkjK7lZWVNZl7eEyfPv36668PRQjMRx55ZHl5+auvvho/cRoCc//+/StnNayoqKhJ3qQ1p22Y++CHky+KdcEhPfYb/3CsAQB2iBUjj/5sTUms9xn1s/Z9zow1WaLpLemz7j3MujSlW0Sec845kyZN6tChw5YtW+bPn79gwYIQLzt16jRt2rTGx0sAAIBskzMJs4k55ZRT5s6du7ya2bNnH3vsscnDAAAAOUjCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApCPrEuall1763nvvJQMAAAByR9YlzHfffffkk0/u0qXLlVdeuXbt2qQLAABA1svSq2Q3bdr0yCOPHHPMMccee+yvfvWrzz77LHkAAACAbJV1CXPGjBljx47ddddd43D16tXf//73Dz300FNOOeWdd96JTQAAALJQ1iXMb3zjGyNGjJg/f/68efNOPfXU/Pz82H/33XfDsEuXLpdeeumaNWtiEwAAgOyRpVfJBt/85jdvuummZcuW/ed//menTp1ic9OmTb/+9a979ep1zDHHzJw5c/PmzbEPAADADpe9CbPK/vvvP3v27N///vcTJ07cZ599YnPt2rXjx4//+7//+5NOOuntt9+OTQAAAHagHEiYUatWrfr37//cc8+9+uqrt956a1XUXLFiRb9+/Q477LAf/ehHpaWlsQkAAMD2lzMJM1q3bt3dd9/9H//xHx9++GHSqvTpp5/OmDHjW9/61oQJE5IWAAAA21duJMzS0tIQII855pgePXpMnjx59erVsb/vvvuG/oMPPrjffvvFzr333jt48OBYAwAAsD1le8J84YUXjj/++G9961s/+tGP1q5dG5u77LLLqFGjFi5c+Oyzzx599NFdunR55plnwrBt27bh0VA8//zzcSYAAADbTZYmzJUrVw4cOLCoqGj48OElJSVJd6edunbtGsLkK6+8cuGFF7Zv3z7pVgrD//qv/4r1T37yk1gAAACw3WRdwvzBD37QpUuXvn37Llu2LGnttNM+++xz6623/uEPf5g5c2bVBbE17bnnnrEoKyuLBQAAANtN1iXMxYsXb9q0KdZt27Y9++yzX3rppeeeey5kzpYtG/jTVt0es0+fPrEAAABgu8nSq2Q7d+789NNPL1my5Jprrtltt92SbkMKCgrmzp376quvXnrppUkLAACA7SXrEua11177+uuvP/nkk4WFhUkrEx06dPjGN76RDAAAANiOsi5hHn744W3atEkGAAAA5I4svUoWAACAnCNhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkI4WFRUVSclXVVJS8vLLLyeDGlq0aDFo0KBkUM3jjz8+Z86cDz74INSFhYXFxcX9+vWLDzVSUVHR8uXLkwHZYcPcBz+cfFGsCw7psd/4h2MNALBDrBh59GdrSmK9z6ifte9zZqzJEk1vSS9hpuCWW26ZPHlyMqihdevWS5cuTQaV1q1bN2LEiNdffz0Zf6Fbt2633357+/btk3FDJMwsJGECAFlFwsxyTW9J7yrZFLzzzjthm5eXF8JkTa1atYrTovLy8vPOOy/GyyFDhtxxxx0hnQ4cODAMFy5cOGrUqMpZAAAAuUfCTMGSJUvCNqTEpbV57bXX4rRo+vTpy5YtC8Wtt9569dVXFxcXH3/88RMmTAh1aC5YsOChhx6qnAgAAJBjJMxttXnz5g8//DAU3bt3j536zZgxI2x79erVt2/f2ImGDBnSrVu3UIQIGjsAAAC5RcLcVvPnz4/FAQccEIt6LFq0aNWqVaEYMGBA7FQXvxDorbfeeu+992IHAAAgh0iY22rlypVhm5+fX1RUFDv1WPrFV/507do1FtV16dIlFvEyWgAAgNwiYW6r+J09IRxu2rRp5syZY8eOHTFiRNhOnTp13bp1cU6VGB3z8vI6dOgQO9UVFhbGYuHChbEAAADIIe5Wsq1OO+20N998s2PHjh9//PGGDRuSbqWCgoLrrrvuu9/9bjLeaacLL7zw6aef3mWXXV555ZWk9WUxqfbv33/ixIlJq24NvmvqXibbn7uVAABZxd1Kdrjmtmj3HuY2KS8vf/vtt0OxcuXKjRs3nnrqqRdccMHQoUOPOuqo0CwtLb3iiit+8YtfVM793ObNm8O2TZs2cVhTvLVJCJlx2KBwOtYjmQQAAOwgydK8DsmkJkTC3CZLly4tKysLRefOnWfPnn3TTTeNHj36yiuvvO+++6ZNm9auXbvw0IQJE+JnNavstddeSVVDfn5+UgEAAOQaCXOb7LffflOmTPnJT35y7733hjrpVjr22GOvuuqqUGzZsmXmzJmxGa1fvz6pAAAAmhAJsz5lZWUjanPbbbfFCbvttlufPn1OO+20PfbYI3aqGzhwYNu2bUPx4osvxk7Llp/v8HitbK0+/fTTsM3Ly4tDAACAHCJh1qe8vHxebapuOlK/kCfjBzL/+Mc/xk5BQUHYbty4MQ5riuEzXl4LAACQWyTM+oSI2Ls2hx12WDKjIfFNyxYtWsRhvElJaWlpyK6xU12Il1u2bAlF586dYwcAACCHSJj1ycvLu7M2o0ePjhOee+65cePGxc9b1qqk5PPvhu7YsWMcHnroobFYsmRJLKqrupi26saYAAAAOUTC3CZPPvnkAw888PDDD2/1bbFRiJfvvvtuKOK1skHPnj3jZyxfeuml2Klu8eLFYZufn9+rV6/YAQAAyCES5jY5+eSTYzF16tRYVDdhwoSwDZHyrLPOip327dv36NEjFPfff/9W3yi7du3a+JWz/fr1i3fFBAAAyC0S5jYpLi4++OCDQzFr1qyJEydWfboypMcxY8bMmTMn1MOGDdt///1jP7jkkkvCNuTJESNGrFmzJjZLSkqGDx++YcOG1q1bn3/++bEJAACQWyTMbTVlypR99903FFOnTj3iiCNGjhx5zjnnHHPMMbNnzw7NE0888dJLL62cmDjooIPi5zYXL17cu3fvMPnss88O0958883QvP7666s+tAkAAJBbJMxttffeez/yyCMhJebn55eWlj777LPz58/fsmVLhw4dxo0bd8sttyTzqgmpctKkSWFCmBYmL1iwoKysrFOnTtOmTevfv38yCQAAINe0qKioSEpyTVFR0fLly5MB2WHD3Ac/nHxRrAsO6bHf+IdjDQCwQ6wYefRnaz6/u0Gwz6ifte9zZqzJEk1vSe89TAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTL6699/fady4nfr02WnYsJ3uvXenefOSPgAAZKe4gg3L1/ArFFawqZMw+SrCKzMEy06ddho//vOXZYiX4SUaOuFVCgAA2SksVuMKNixfw69QhBVs+BUWt6RFwiRj4RUYXpm1/ntPeJWGhwAAINuEJBkWqzWFZa2QmSIJk4wNG5YUtQovzvonAADAdlb/BbFWsCmSMMlMYz5vGSY0OAcAALaPECBrffeyOivYtEiYZOa555KiHuE17DIDAACyRCOjo4SZCgmTzDTyhSdhAgCQJRrzHknQyGnUT8IkM4WFSVG/lSuTAgAAdqyOHZOifo1c6FI/CZPMHHdcUtSvkdMAAODr1rt3UrAdSJhkppGvTy9jAACyRCPfnPQeSSokTDITomOD6fG661xjAABAtghL07BArV9Y4g4dmtRsCwmTjN1zT1LUKryAx41LagAAyAYhPdbzNklYwda/xKXxJEwyFl6BK1bU/u9AoRkeAgCArBIzZK0r2JA8wwo2TCAVEiZfRXyjcu7cz1+oQ4d+/itmS+9eAgCQneIKNixZ4wo2BMuwgg0L2vCLFLWoqKhISnJNUVHR8uXLkwHZYcPcBz+cfFGsCw7psd/4h2MNALBDrBh59GdrSmK9z6ifte9zZqzJEk1vSe89TAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgNW79+fXFx8aWXXpqM6/D4449feOGFAyuNHTv2ySefTB6oQ6bzAQAAspyE2bDLL7/8T3/604YNG5JxDevWrTvjjDMuu+yyp59+elmlp5566uKLLx48eHCtvyvT+QAAADlBwmxAiJfz5s1LBrUpLy8/77zzXn/99VAPGTLkjjvumDx58sCBA8Nw4cKFo0aNqpz1N5nOBwAAyBUSZp3Wr18/fPjwxx57LBnXYfr06cuWLQvFrbfeevXVVxcXFx9//PETJkwIdWguWLDgoYceqpyYyHQ+AABArpAwazd79uz+/fu/8MILoW7Xrl1s1mrGjBlh26tXr759+8ZONGTIkG7duoUiRMrYiTKdDwAAkCskzFoMGzZszJgxq1evLigo+PGPfxyDX60WLVq0atWqUAwYMCB2qhs0aFDYvvXWW++9917sZDofAAAgh0iYtXjnnXfCtri4+De/+c13v/vd2KzV0qVLY9G1a9dYVNelS5dYxMtig0znAwAA5BAJsxZ9+vR58MEH77jjjg4dOiStOsQomJeXV+vMwsLCWCxcuDAWmc4HAADIIRJmLX7wgx9UvZ1Yv9LS0rDdeeed43ArLVu2bNu2bSg2btwYO5nOBwAAyCES5jbZvHlz2LZp0yYOa2rVqlXYbtq0KQ4znd+gonolkwAAgB0kWZrXIZnUhEiYKdhrr72Sqob8/PykqibT+fVYXq9kEgAAsIMkS/M6JJOaEAkzBevXr0+qxsl0PgAAQE5oXgmzrKxsRG1uu+22ZEaGWrb8fAfGa19r9emnn4ZtXl5eHGY6HwAAIIc0r4RZXl4+rzZVNxHJVEFBQdjW88U8MUy2a9cuDjOdDwAAkEOaV8Js2bJl79ocdthhyYwMxZuOlJaWhuwaO9WFuLhly5ZQdO7cOXYynQ8AAJBDmlfCzMvLu7M2o0ePTmZk6NBDD43FkiVLYlHdiy++GIuqG11mOh8AACCHNK+EmbqePXvGz0y+9NJLsVPd4sWLwzY/P79Xr16xk+l8AACAHCJhbpP27dv36NEjFPfff/9W3xC7du3amTNnhqJfv37xLpdBpvMBAAByiIS5rS655JKwDflwxIgRa9asic2SkpLhw4dv2LChdevW559/fmxGmc4HAADIFRLmtjrooIOuuuqqUCxevLh3797nnHPO2WeffeKJJ7755puhef3113fs2LFyYiLT+QAAALlCwkxBSImTJk3q0KHDli1b5s+fv2DBgrKysk6dOk2bNq1///7JpGoynQ8AAJATWlRUVCQluaaoqGj58uXJgOywYe6DH06+KNYFh/TYb/zDsQYA2CFWjDz6szUlsd5n1M/a9zkz1mSJprek9x4mAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDokTAAAANIhYQIAAJAOCRMAAIB0SJgAAACkQ8IEAAAgHRImAAAA6ZAwAQAASIeECQAAQDpaVFRUJCV1WL9+/cCBA7t27XrjjTcmrS8rKSl5+eWXk0ENLVq0GDRoUDKo5vHHH58zZ84HH3wQ6sLCwuLi4n79+sWHGqmoqGj58uXJgOywYe6DH06+KNYFh/TYb/zDsQYA2CFWjDz6szUlsd5n1M/a9zkz1mSJpreklzAbNmLEiHnz5vXu3fvOO+9MWl92yy23TJ48ORnU0Lp166VLlyaDSuvWrQv/zddffz0Zf6Fbt2633357+/btk3FDJMwsJGECAFlFwsxyTW9J7yrZBlx++eUhXiaDOrzzzjthm5eXF8JkTa1atYrTovLy8vPOOy/GyyFDhtxxxx0hnQ4cODAMFy5cOGrUqMpZAAAAuUfCrNP69euHDx/+2GOPJeO6LVmyJGxDSlxam9deey1Oi6ZPn75s2bJQ3HrrrVdffXVxcfHxxx8/YcKEUIfmggULHnroocqJAAAAOUbCrN3s2bP79+//wgsvhLpdu3axWavNmzd/+OGHoejevXvs1G/GjBlh26tXr759+8ZONGTIkG7duoUiRNDYAQAAyC0SZi2GDRs2ZsyY1atXFxQU/PjHP47Bry7z58+PxQEHHBCLeixatGjVqlWhGDBgQOxUF78Q6K233nrvvfdiBwAAIIf4pp9aHHvssSFeFhcXX3vttR06dKj/m35mzJjxox/9KD8/f+nSpS1bNpDY4+RQzJ07N/yXY7NKCJYnn3xyKCZOnNi/f//YrIdv+slCW33Tzz6jfhZrAIAd4oPrTvdNP9nMd8k2C9///vcHDRrUpUuXOKw/YV5yySVPPPFE165dp02b9thjj73yyiuffPJJu3btDjrooPAf2W233ZJ5lS6//PIwJy8v74033kha1ZSXl4ffFYp//Md//MEPfhCb9ZAws1D1hAkAkFUkzCzku2SbhZDuquJlg95+++2wXbt27XHHHTd+/PinnnoqxNGwnThxYnFx8aOPPhqnRaWlpWG78847x+FWWrZs2bZt21Bs3LgxdgAAAHKIhLlNysvLY8JcuXJliIWnnnrqBRdcMHTo0KOOOio0Q5684oorfvGLX1TO/dzmzZvDtk2bNnFYU7y1yaZNm+KwQUX1SiaxHbXvc+aBD636v+N9ITAAkHUKDumRVGxHydK8DsmkJkTC3CZLly4tKysLRefOnWfPnn3TTTeNHj36yiuvvO+++6ZNmxa/hHbChAkhf1ZOT+y1115JVUN+fn5SNc7yeiWTAABo3lrtud8+o37Waq/9kjHbUbI0r0MyqQnxOcyG1fM5zHXr1i1ZsmTDhg3HHHPMHnvskXS/8NBDD8W7XA4dOjTEzlDE/1SHDh3mzp1bOWVr3bt3//jjj0844YTbbrstadWtyOcws9Vnq5PP0wMAZAPZMms1vSV980qYZWVl559/fjKo5rDDDhs9enQyqKH+b/qpR3l5+eGHH75p06YDDzzwiSeeCJ2RI0c+++yzu++++4svvhjnbOWII4745JNPTjrppJtvvjlp1U3CBACAnNb0lvTN6yrZEPlCVqxp6dKlyYxUtWzZMn4g849//GPsFBQUhG09X+QTP6gZL68FAADILc0rYYbI17s2hx12WDIjbfEOmS1atIjDeA/M0tLSkHVjp7oQL7ds2RKKzp07xw4AAEAOaV4JMy8v787a1HOJbP2ee+65cePGXXXVVcm4hpKSzz+P17Fjxzg89NBDY7FkyZJYVFd16WxhYWEsAAAAcojvkt0mTz755AMPPPDwww9v9W2xUYiX7777bijitbJBz549Q8oNxUsvvRQ71S1evDhs8/Pze/XqFTsAAAA5RMLcJieffHIspk6dGovqJkyYELYhUp511lmx0759+x49Pr8N0f33379+/frYjNauXTtz5sxQ9OvXL94VEwAAILdImNukuLj44IMPDsWsWbMmTpxY9enKkB7HjBkzZ86cUA8bNmz//feP/eCSSy4J25AnR4wYsWbNmtgsKSkZPnz4hg0bWrduXeu33QIAAGQ/98NsWP13K/noo4/OOuusP/3pT6EuKCjo0aPHxo0bX3nllfidPSeeeOItt9xSOfFvpk+ffv3114ciPz//yCOPDLn01VdfLSsrC50QU/v37185q2HuVgIAADnN3UrY2t577/3II4+cffbZIS6WlpY+++yz8+fPD/GyQ4cO48aNqxkvg3POOWfSpElhQpgWJi9YsCDEy06dOk2bNq3x8RIAACDbeA8zh3kPEwAAcpr3MAEAAKB2EiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIR4uKioqkpJr169c/+uijixYt+uCDD8Iu2nfffQ888MDTTz+9Q4cOyYwaHn/88Tlz5oT5oS4sLCwuLu7Xr198qFaZzq+pqKho+fLlyQAAAMg1TW9JL2HW4oknnrj22mtLS0uT8Rfy8/Mvv/zyIUOGJOMvrFu3bsSIEa+//noy/kK3bt1uv/329u3bJ+MvZDq/LhImpOv993cqLExqcogDB0DuanpLelfJbu2ZZ5655JJLQrzcddddL7jggimVLrroot13333Lli0/+tGPHnjggWRqpfLy8vPOOy/GxRA+77jjjsmTJw8cODAMFy5cOGrUqMpZf5PpfODrFvJJnz47tWixU6dOn/8K9bhxyUNks3nzHLicVHXg4rEbNsyByw3hMG114MKhBKhFBdWEDNmrV68DDzywd+/eq1evTrqV/vKXv5xwwgnhoS5duoQ66VZU3H333aEZPP3000mr0vTp02N/1qxZSatSpvPrESYnFfBVXXddRfhBWPNXYWHFihXJHLJQXQdu6FAHLnuFQ9O799aHLP4KB5SsVdeBCz8nHTjYdk1vSe89zC957rnnQrAMxdixY/fcc8/YjHbbbbcrrrgiFKWlpc8//3xsBjNmzAjbkEv79u0bO9GQIUO6desWihAdYyfKdD7w9Rk2bKfx45N6K/GNTbJTODR1Hbh77/38sJKd6nnXKxxQBy5r1XXgws9JBw6oScL8kpdeeikWJ510UiyqO+aYY2Lx6quvxmLRokWrVq0KxYABA2KnukGDBoXtW2+99d5778VOpvOBr09YMIU0Uo+weHLxXhYKB67+a/PCow5cFgovt/oPXJhQ/0uSHSK8mho8cPVPAJobCfNLBg8efNddd918882tWrVKWtV88sknsWjTpk0sli5dGouuXbvGorouXbrEYtmyZbHIdD7w9WnM5QIuKchCjXnDxIHLQnW97VydA5eFGnPgGjMHaD4kzC/p2LHjcccdV+sbmMHTTz8di6p8GKNgXl5erXcxKfziyw0XLlwYi0znA1+fxvyj+/vv+7f5rBMOSoPCnMZMY3tq5IEjqzTyiDhwQHUSZmNt3LjxrrvuCsUuu+zS54uPZ8U7muy8885xuJWWLVu2bds2FOH3xk6m8xtUVK9kElAbS6Jc1PjA7/hmlUYeuHDU/JtOVmn8gfOKg3okS/M6JJOaEAmzsS677LL4EcqLLrqo6irZzZs3h23VsKZ4te2mTZviMNP5DVper2QSsA3caDGrNP5wOHBZxYHLUQ4cpCJZmtchmdSESJiNcs011/z2t78NxT/8wz8MHjw4NqvstddeSVVDfn5+UlWT6Xzg69C7d1LUz7Ipq4TD4cDlIkElRzXycAwdmhQAgYTZgLKysrFjx86aNSvU3bt3nzRpUuxXt379+qRqnEznA1+Hc85JinpYNmWh445Lino4cFmoMQfluuuSgizRyH/T6dgxKQCC5pUwQ1wcUZvbbrstmfFlGzZsOPfcc5966qlQ9+rV66677trqAteWLT/fgfHa11p9+umnYZuXlxeHmc4Hvj5h2dTgysl6NwuFoFL/gQtr4nvuSWqyR3g11f+GWHjUbWayUIOvpvB6dOCA6ppXwiwvL59Xm6qbiFRXUlJy5plnzp8/P9QDBgyYOnVqzc9PFhQUhG09X8wTw2S7du3iMNP5wNcn5pB6lrxz5zawIGaHqP/AxUfJQuHQ1POacuCyVv2HJjzqX+KArTSvhNmyZcvetTnssMOSGV945ZVXzjjjjBUrVoT6oosuuuGGG+Lbj1uJNx0pLS0N2TV2qgtxccuWLaHo3Llz7GQ6H/haxSVvzeVR7947hVd/g+9wsqM4cDmqrgM3dKgDl9XqOkDhUDpwQE0tKioqkpIvvPjii+eff37IgW3btp0wYcIpp5ySPFDD7Nmzx4wZE4pf/vKXhx9+eGxWmTt37ve+971QTJkyJd7gJNP59SsqKmqSXz8F21/8nv158z5fAVst5ZB4j4Twy4HLLQ5cjnLg4OvQ9Jb0zes9zMYIB3j06NEhXrZv3/6ee+6pJ14GPXv2jJ+ZfOmll2KnusWLF4dtfn5+r169YifT+cD2EVZL4VeDH/Aj28RlrgOXcxy4HOXAAY0hYX7J5s2bR40a9cknn7Ru3XratGlHHHFE8kAdQgrt0aNHKO6///6tviF27dq1M2fODEW/fv3iXS6DTOcDAADkEFfJfsntt99+8803h6Jnz56nnnpqbNZUWFh45JFHxvoPf/jDgAEDQvGtb33rtttu23PPPUNdUlIyevToN998MyTVJ598smO1r/HOdH49XCULAAA5rekt6SXMLzn22GNXr16dDOp2xhln/PCHP0wGO+00ffr066+/PhT5+fkheZaXl7/66qtlZWWhM3HixP79+1fO+ptM59dFwgQAgJzmc5hNWWlpaWPiZU3nnHPOpEmTOnTosGXLlvnz5y9YsCDExU6dOk2bNq3WuJjpfAAAgJzgPcwc5j1MAADIad7DBAAAgNpJmAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDDZVkVFRUnFF+yTmuyTmuyTmuyTmuyTrdghNdknNdknNdknNdknXxMJEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHS0qKioSEpyTVFRUVIBAAC5afny5UnVJEiYAAAApMNVsgAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdEiYAAADpkDABAABIh4QJAABAOiRMAAAA0iFhAgAAkA4JEwAAgHRImAAAAKRDwgQAACAdLSoqKpIS6lVSUvLyyy8ngxpatGgxaNCgZFDN448/PmfOnA8++CDUhYWFxcXF/fr1iw81Sc3t+UbOjWj9+vUDBw7s2rXrjTfemLRqk+kTz+kd1eA+aSYnT9gPjz766KJFi8KfOfy1u++++x544IGnn356hw4dkhk1NPnzJKN90kzOk7Vr186aNWvZsmXvvPPO3nvvHfbJgAEDjjrqqOTh2jTt8ySjHdI8/yaaO3fuL3/5yzZt2txyyy1Jq4amfZLUVP8+sWLZPiRMGiu8UCdPnpwMamjduvXSpUuTQaV169aNGDHi9ddfT8Zf6Nat2+23396+fftk3FQ0t+dbnXMjCk9q3rx5vXv3vvPOO5PWl2X6xJvAjmpwnzSHk+eJJ5649tprS0tLk/EX8vPzL7/88iFDhiTjLzSH8yTTfdIczpNnnnnmsssu++STT5LxF8Ja9oYbbtj2455z+yTTHdIM/yYKCTzknI8//rhdu3avvfZa0q2myZ8kNTW4T6xYtg8Jk8a68MILn3766bxKSauaVq1aVX8ll5eXn3766cuWLQt1WCv06NEjdObMmfPII4+EzlFHHXXfffdVTmwimtvz3YpzIwjL4sceeywUdaWpTJ94E9hRDe6ToMmfPGGVPGrUqFDsuuuugwcPPuSQQ0L95ptvhj/qX/7yl1CPGzfurLPO+nxqpUyfY3PYJ0GTP08WLFhw9tlnh2KPPfY477zz9t9//88++yw85V//+tehue3HPef2SaY7JGiGfxMNHz78hRdeCEWtaSrT59gc9klgxbKdhIQJjfHtb3/7wAMPvPrqq5Nxve6+++4wOQgv46RVafr06bE/a9aspNUkNLfnu5Vmfm58/PHH5557bvzDB//2b/+WPPBlmT7xnN5RjdwnQdM+ebZs2dKrV6/wBwsZe/Xq1Um3UohSJ5xwQnioS5cuoU66zeA8+Qr7JGjyP2ROPPHE8AcL69et9snkyZPjn/mJJ55IWpWa/HmS6Q4JmtvfRCHbxD9qcPjhhyfdapr8SVJTg/sksJrdPnzTD42yefPmDz/8MBTdu3ePnfrNmDEjbMMyom/fvrETDRkypFu3bqEIL87YaRqa2/OtrpmfG7Nnz+7fv3/Vv5jGZq0yfeK5u6Mav0+a/Mnz3HPPhfVxKMaOHbvnnnvGZrTbbrtdccUVoSgtLX3++edjM2jy58lX2CdN/jx5+eWXV6xYEYrRo0dvtU++973vtW3bNhTPPvts7ERN+zz5Cjukuf1N9N57791www2hOOCAA2KnpqZ9ktTUmH1iNbvdSJg0yvz582NRz+u2yqJFi1atWhWKAQMGxE518SPUb731VvhZEDu5rrk9360053Nj2LBhY8aMCcvlgoKCH//4x/Hvm1pl+sRzd0c1fp8ETf7keemll2Jx0kknxaK6Y445JhavvvpqLJrDeZLpPgma/HlSVlZ2wgkn7LHHHjX3ScuWLb/5zW+GovrHEZv8eZLpDgma1d9E5eXl4cfsp59+eu655x522GFJ98ua/Emylcbsk8BqdruRMGmUlStXhm1+fn5RUVHs1KPqQ9Jdu3aNRXVdunSJRbyuvQlobs93K8353HjnnXfCtri4+De/+c13v/vd2KxVpk88d3dU4/dJ0ORPnsGDB991110333xzq1atklY1VUvkNm3axKI5nCeZ7pOgyZ8nPXv2vO222373u9/ttttuSesLYd385z//ORTVd0iTP08y3SFBs/qb6MYbbwzBpnPnzpdccknSqqHJnyRbacw+CaxmtxsJk0aJX6IVXk6bNm2aOXPm2LFjR4wYEbZTp05dt25dnFMlvtjy8vJq/dL5wsLCWCxcuDAWua65Pd+tNOdzo0+fPg8++OAdd9xRzz0nokyfeO7uqMbvk6DJnzwdO3Y87rjjan2zLnj66adjUbV8aQ7nSab7JGjOP2Tuueee8KxDUf3WCM3hPKlLrTskaD4nyYIFC+6+++6QkSZNmhSeQtKtoVmdJI3cJ4HV7HYjYdIob7/9dtiuXbs2rAzGjx//1FNPzZs3L2wnTpxYXFz86KOPxmlR/AL6nXfeOQ630rJly/ghio0bN8ZOrmtuz3crzfnc+MEPfhD+okoG9cr0iefujmr8Pgma88kT/px33XVXKHbZZZcQy2Oz+Zwntap1nwTN8DwpKyt7+eWXx4wZ85Of/CQMBwwYUP1jYM3wPKl/hwTN5CTZsGHDpZdeGooQijp37hybtWo+J0nj90lgNbvdSJg0rLy8PL4mV65cGV5Ip5566gUXXDB06NCjKu96HF6BV1xxxS9+8YvKuZ/bvHlz2G51BUt18eKo+M+QTUBze77VOTcaKdMn3hx2VDM/eS677LL4CZ+LLrqo6kk18/Ok1n3SDM+TG2644eCDDx4yZMjs2bPDcNSoUfH7S6o0t/OkwR3SfE6ScePGffjhh926dRs+fHjSqkPzOUkav0+sWLYnCZOGLV26tKysLBSdO3cOP99vuumm0aNHX3nllffdd9+0adPid0VOmDAhvGIrpyf22muvpKohPz8/qZqQ5vZ8I+dGRjJ94k17RzXnk+eaa6757W9/G4p/+Id/GDx4cGxWaZ7nSV37pBmeJx999FFBpTicMmVKWEPHxW51zec8aXCHNJOT5IknnnjqqafC04lv5DZGkz9JMtonVizbk4RJw/bbb7/wAz28eu+9995QJ91Kxx577FVXXRWKLVu2zJw5Mzaj9evXJ1Xz0Nyeb+TcyEimT7xp76jmefKE9c3YsWNnzZoV6u7du0+aNCn2q2tu50n9+6QZnic33njj4krz5s0bMGBA2D8PPPDA9773veThLzSf86TBHdIcTpI///nP48ePD8W1115b68cCa9W0T5JM90kz/GGyA0mYfC78vB5Rm9tuuy08uttuu/Xp0+e0007bY4894vzqBg4cGK9Ef/HFF2OnZcvPz6ua/+Ba5dNPPw3b+j+NnUOa2/OtzrnRSJk+8eawo5rhybNhw4Zzzz33qaeeCnWvXr3uuuuura6/aobnSYP7pBmeJ1V/tm9+85s33HDDd77znVCHJzi78hrRoLmdJw3ukOZwklx88cV//etfTzzxxAa/oztqDidJpvvEimV7+nzfQXl5+bzaLP3im5rrEV6B8RL2P/7xj7ETL2XZWPdHn+PLNV6Q0AQ0t+fbeM6NKpk+cSdV0zt5SkpKzjzzzHg3tgEDBkydOrXmx3ua23nSmH1Sv+bwQ6bq7gvPPPNMLJrbebKVmjukfk3gJPn5z38e7xD77W9/Ozzr6uJHl8vKyuJwyZIllb+j6Z8kX2Gf1M+KJV0SJp8Lr6vetannrrXVhd8eti1atIjDeK1CaWlpCK6xU114QW7ZsiUUnRv6yq9c0dyeb0aa+blRJdMn7qQKmtLJ88orr5xxxhkrVqwI9UUXXXTDDTfEZ7eVZnWeNHKfNKjJ/5DZe++940r3f/7nf2KnWZ0nNdXcIQ3K9ZPkrbfeisXVV1896ssWLFgQ+ps2bYrDqVOnxplN/iT5CvukQU3+h8n29FV+mtP05OXl3Vmb0aNHh0efe+65cePGxSvUa1VSUhK2HTt2jMNDDz00FrX+u1HV5QdVtxLKdc3t+Vbn3GikTJ94c9hRzefkCX+288477+OPP27btu2kSZNGjhyZPFBD8zlPGr9PmsN58qtf/eryyy+/5pprknEdqr5WpMmfJ5nuEH8T1dTkT5KvwHmyPUmYNOzJJ5984IEHHn744a2+XysKL8h33303FPHqgqBnz57xqvSXXnopdqpbvHhx2Ia/GHr16hU7ua65Pd/qnBuNlOkTbw47qpmcPMuXLx89enRpaWn79u3vueeeU045JXmgNs3kPMlonzSH82Tp0qWPPfbYrFmz4tV9W3n//ffDvgrF7rvvHjtN/jzJdIc0+ZPkhhtuCK+aWg0YMCBMaNeuXRzGr88ImvxJ8hX2iRXL9iRh0rCTTz45FrVeaTBhwoSwDS/Cs846K3bCoqFHjx6huP/++7f6Dq61a9fGL+nq169fvI9QE9Dcnm91zo1GyvSJN4cd1RxOns2bN48aNeqTTz5p3br1tGnTjjjiiOSBOjSH8yTTfdIczpOqjD1lypRYVPeTL27DMGjQoFg0+fMk0x3ib6KamvxJ8hU4T7YnCZOGFRcXH3zwwaGYNWvWxIkTq65HD6+3MWPGzJkzJ9TDhg3bf//9Yz+IH8QPr8ARI0asWbMmNktKSoYPH75hw4awsDj//PNjs2lobs+3inOj8TJ94k1+RzWHk+fnP/95+OOF4sgjj3z77bcfqsMrr7wS5wdN/jzJdJ80h/OkZ8+e3bt3D8WvfvWrm2++ufpzvPTSS+Nz7N+//+GHHx77QdM+TzLdIf4mqlXTPkm+AufJ9tSioqIiKaFuH3300VlnnfWnP/0p1AUFBT169Ni4cWNYAcRPOZ944om33HJL5cS/mT59+vXXXx+K/Pz8sJIIr+RXX321rPJet+GFHf5uqJzVdDS351vFuVEl/A00b9683r1733nnnUnryzJ94k1gR9W/T5r8yXPssceuXr06GdTtjDPO+OEPf5gMmvp58hX2SXP4IbNu3brBgwfHi/Tat28f/sx//etfFy1aFJ9jr169br/99q2+aLdpnyeZ7pBm+zfR5Zdf/thjj7Vr1+61115LWtU07ZOkLvXsEyuW7SZv3LhxSQl1+8Y3vnHaaadt3rz5jTfe+PTTT1esWPHBBx+El1mHDh0uvvjiyy67LJlXzbe+9a0DDjhg6dKl//M//xMmh9dzRUVFp06dwgvyhBNOSCY1Ic3t+VZxblR58skn33///cLCwrr+ysn0iTeBHVX/PmnaJ09paelPf/rTZFCvQw45pLi4OBk06fPkq+2T5vBDJix2v/vd74bn+Pvf/z7spfAcV61aFZ7jPvvsM3r06Ouuuy6sbpOpX2jC50mQ6Q5ptn8TPfPMM2+++Wbr1q1HjBiRtKpp2idJXerZJ1Ys2433MMlMWVnZK6+88te//rVly5b/3//3//2///f/kgfqtmzZso8++igU++67b1FRUWw2Yc3t+VZxbjRepk+8ye8oJ0+tnCdbaQ7nSXiOL7/8crwA72s67rm1TzLdIX6Y1KppnyRfgfPk6yZhAgAAkA7f9AMAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACAdEiYAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAWWT58uXPPffcRx99lIzT9vzzz4f/fjIAgLRJmACQLf785z//y7/8y8UXX9ymTZuklbb//u///rd/+7dbbrklGQNAqiRMAMgWl1566V//+tcRI0b8n//zf5JW2kaNGrXLLrtMmTJl2bJlSQsA0iNhAkBWeOihhxYuXLjvvvuee+65SetrELLrv/7rv5aVlV111VVJCwDSI2ECwI63cePGiRMnhmLEiBF5eXmx+TUZOnTo7rvv/uabb86cOTNpAUBKJEwA2PHuvvvujz/+eK+99jrjjDOS1temTZs2//zP/xyKyZMnb968OTYBIBUSJgDsYKWlpSFhhuL0009v2XJ7/NUcEmZeXt7atWt/+ctfJi0ASEOLioqKpAQAGrJ+/fp4OWswaNCgww8/PNZVVq1adfvtt8f6kksuacx39sycOXP8+PGh+M///M/9998/NqtMmDDhk08+Cf9H4f/uz3/+889//vN58+Z99NFHrVq16t69++DBg3v27BlnvvPOOyGp/u53v1u3bl379u1D/9xzzz3ooIPio1v513/91//+7//u2LHjf/3XfyUtANhmEiYAZGbSpElTpkwJxX777ffUU09Vv7NIeXn5WWedtXjx4lCPGjXqwgsvjP36nXbaaW+++WZdYS/EyI8//njAgAEnnnji2LFjS0tLkwe+cNlllw0fPvzhhx++9tpry8rKkm6lvLy8W2655fjjj0/G1fzqV7/6/ve/H4r777//yCOPjE0A2EaukgWAzIwZM+bggw8ORUlJyU033RSb0W233RbjZdeuXRsZL99///0QL0NR9VZkrcKcCy64IMTL8F8OxUUXXRSK+NBPf/rTn//85/G7YU866aRQnHfeeSH9hmEInFdeeWWtH7Y8+uijY/H000/HAgC2nfcwASBjIRaedtppmzZtCvUjjzxyyCGHhGLRokX/9E//FIpdd931iSee2HPPPT+f2pCq9xJvvvnmkA9js7r4HmYo8vLyJk6ceMopp8R+ELLu7NmzY7377rtPnz69c+fOcRhSZfjDvPHGG6Gu6798xBFHfPLJJyGLPvPMM0kLALaN9zABIGOFhYWXX355rC+99NLy8vL//d//HTt2bOxcf/31jYyXwcKFC2NxwAEHxKIu//Iv/1I9XgbnnHNOUu20U4ipVfEyaNOmTdV9NZcsWRKLrcS3MUtKSjZu3Bg7ALCNJEwA+Cr++Z//uXfv3qF49913p0yZ8h//8R+rVq0KwyFDhhQXF1dOaZT33nsvbPPy8hpMmAMGDEiqL3Tp0iUWrVu37tu3b6yr7LrrrrH461//GoutVH0LUVXKBYBtJGECwFc0YcKE3XffPRS33XbbY489Foq/+7u/u+KKKyofbKwQUMO2bdu29d+nJETQmt8KG5qx6Ny5c83f3uCNT6q+t7auCAoAmZIwAeAr2m233X74wx+GIn6Da0FBwc0331yV+hopfpgz/N44rEvr1q3rSYyNvyi3uj322CMWtX4VEAB8BRImAHx1xcXFHTt2jHXnzp0LCwtj3UhVNxf5v//3/8aiLg2+IfkVVP03165dGwsA2EYSJgB8dXfeeefKlStj/frrr99xxx2xbqQWLVrEIn6Gc0eJ1/oCwLaTMAHgK/rDH/5w8803h2KvSqG49dZbQ7PywUZp2bJlfn5+KOK1stvZZ599Fos2bdrEAgC2kYQJAF/F5s2b//3f/z1e5nr99ddXfSAzNDP6WGOMpjvkfiG///3vY9GuXbtYAMA2kjAB4Ku44YYbVqxYEYqBAwcee+yxxx13XLybSGjeeOONlVMa5ZBDDgnbLVu2bP8PQ3788cexaPBGKQDQSBImAGTs+eefv//++0Oxzz77XH311bEZiviBxvvuuy9MiM0GHXjggbFYunRpLLabeEFvQUFB1ZcVAcA2kjABIDPr1q27/PLLY/3DH/7wG9/4Rqzbt28/bty4WIcJ69evj3X9jj766FgsW7YsFtvH//7v/8bvKCouLo4dANh2EiYAZOaaa675y1/+Eop4fWxsRn379j311FNDESaEabFZv27duoVoGor58+fHzvbxwgsvxGKrpwAA20LCBIAMPPTQQ3PmzAlF9etjq/v+978fr5X97W9/+/DDD8dmPVq2bHnaaaeF4rXXXmvk256piM+idevWp5xySuwAwLZrUVFRkZQAwI7w3nvvnXzyyaEYN27cWWedFZtfq7Kysq5du5aWlob/u6orewFg23kPEwB2sP333//b3/52KB588MHY+br9+te/DvEyFEOHDo0dAEiFhAkAO96FF14Ytm+88caiRYti52t13333he13vvOdwsLC2AGAVEiYALDjHXbYYSeddFIopkyZEjtfn1deeWXZsmWtW7f+93//96QFACmRMAEgK1x11VXt2rWbN29evE3l12fixIlhO3LkyA4dOsQOAKRFwgSArLD33nuHkBmK//iP/4idr8Ozzz67aNGiAw888Hvf+17SAoD0SJgAkC1OP/30c889d7fddnv77beTVtpefvnlE0444dZbb23Z0hoAgPS5WwkAAADp8O+XAAAApEPCBAAAIB0SJgAAAOmQMAEAAEiHhAkAAEA6JEwAAADSIWECAACQDgkTAACANOy00/8Psow8KyjsgLcAAAAASUVORK5CYII=\" alt=\"dewatering scheme\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin)\r\n% tf = true if well system achieves minimum drawdown everywhere, false otherwise\r\n% smin1 = min drawdown achieved\r\n% xmin, ymin = coordinates of the minimum drawdown\r\n% xw, yw = coordinates of the wells\r\n% Q0 = common pumping rate OR vector of pumping rates\r\n% R = radius of influence\r\n% Lx = length of construction area\r\n% Ly = width of construction area\r\n% K = hydraulic conductivity\r\n% H = initial elevation of the water table\r\n% smin = minimum drawdown required\r\n\r\n   h = sqrt(H^2-Q*Lx/K*Ly);\r\n   tf = all(H-h\u003csmin);\r\n   [smin1,[xmin ymin]] = max(H-h);","test_suite":"%% Prep assignment--modified\r\nxw   = -50;                     %  x-coordinates of the wells (m)\r\nyw   = 0;                       %  y-coordinates of the wells (m)\r\nQ0   = 661.6;                   %  Pumping rates (m3/d)\r\nR    = 450;                     %  Radius of influence (m)\r\nLx   = 250;                     %  Length of construction area (m)\r\nLy   = 100;                     %  Width of construction area (m)\r\nK    = 0.1;                     %  Hydraulic conductivity (m/d)\r\nH    = 85;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\ntf = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nassert(tf)\r\n\r\n%% Fall 2020, exam 2, problem 4a\r\nxw   = [0 200 400];             %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125];         %  y-coordinates of the wells (m)\r\nQ0   = 1331.2;                  %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\ntf = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nassert(tf)\r\n\r\n%% Fall 2020, exam 2, problem 4c--with pumping rate from part a\r\nxw   = [0 200 400 1000];        %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125 -125];    %  y-coordinates of the wells (m)\r\nQ0   = 1331.2*[1 1 1 -1];       %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 100;\r\nsmin1_correct = 4.723;\r\nassert(~tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% Fall 2020, exam 2, problem 4c--with higher pumping rate\r\nxw   = [0 200 400 1000];        %  x-coordinates of the wells (m)\r\nyw   = [-125 125 -125 -125];    %  y-coordinates of the wells (m)\r\nQ0   = 1410*[1 1 1 -1];         %  Pumping rates (m3/d)\r\nR    = 750;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 200;                     %  Width of construction area (m)\r\nK    = 3;                       %  Hydraulic conductivity (m/d)\r\nH    = 45;                      %  Initial saturated thickness (m)\r\nsmin = 5;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 100;\r\nsmin1_correct = 5.02;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% Fall 2022, exam 2, problem 2\r\nxw   = [100 100 700 700];       %  x-coordinates of the wells (m)\r\nyw   = [-200 200 -200 200];     %  y-coordinates of the wells (m)\r\nQ0   = 944*[1 1 -1 -1];         %  Pumping rates (m3/d)\r\nR    = 650;                     %  Radius of influence (m)\r\nLx   = 200;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 2;                       %  Hydraulic conductivity (m/d)\r\nH    = 35;                      %  Initial saturated thickness (m)\r\nsmin = 4;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 200;\r\nymin_correct = 0;\r\nsmin1_correct = 4.001;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 135 450 210];       %  x-coordinates of the wells (m)\r\nyw   = [-80 200 135 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 640;                     %  Pumping rates (m3/d)\r\nR    = 910;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 0.8;                     %  Hydraulic conductivity (m/d)\r\nH    = 90;                      %  Initial saturated thickness (m)\r\nsmin = 6;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = -150;\r\nsmin1_correct = 6;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 135 450 210];       %  x-coordinates of the wells (m)\r\nyw   = [-80 200 -50 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 638;                     %  Pumping rates (m3/d)\r\nR    = 910;                     %  Radius of influence (m)\r\nLx   = 400;                     %  Length of construction area (m)\r\nLy   = 300;                     %  Width of construction area (m)\r\nK    = 0.8;                     %  Hydraulic conductivity (m/d)\r\nH    = 90;                      %  Initial saturated thickness (m)\r\nsmin = 6;                       %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 400;\r\nymin_correct = 150;\r\nsmin1_correct = 6;\r\nassert(tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-3 \u0026\u0026 abs(ymin-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50 100 200 300 450 450  100  200  300];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 5.5;\r\nassert(~tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3 \u0026\u0026 abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50  50 200 350 450 450   50  200  350];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 5.62;\r\nassert(~tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3 \u0026\u0026 abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxw   = [-50 -50   0 200 400 450 450    0  200  400];      %  x-coordinates of the wells (m)\r\nyw   = [-75  75 200 200 200 -75  75 -200 -200 -200];      %  y-coordinates of the wells (m)\r\nQ0   = 200;                                               %  Pumping rates (m3/d)\r\nR    = 910;                                               %  Radius of influence (m)\r\nLx   = 400;                                               %  Length of construction area (m)\r\nLy   = 300;                                               %  Width of construction area (m)\r\nK    = 0.8;                                               %  Hydraulic conductivity (m/d)\r\nH    = 90;                                                %  Initial saturated thickness (m)\r\nsmin = 6;                                                 %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 82.4;\r\nymin_correct = 150;\r\nsmin1_correct = 5.66;\r\nassert(~tf)\r\nassert(abs(xmin-xmin_correct)/xmin_correct\u003c1e-2 || abs(Lx-xmin-xmin_correct)/xmin_correct\u003c1e-2)\r\nassert(abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)\r\n\r\n%% \r\nxL   = 80:80:320;\r\nyL   = 200*ones(1,4);\r\nxw   = [-50 -50 xL 450 450  xL];     %  x-coordinates of the wells (m)\r\nyw   = [-75  75 yL -75  75 -yL];     %  y-coordinates of the wells (m)\r\nQ0   = 200;                          %  Pumping rates (m3/d)\r\nR    = 910;                          %  Radius of influence (m)\r\nLx   = 400;                          %  Length of construction area (m)\r\nLy   = 300;                          %  Width of construction area (m)\r\nK    = 0.8;                          %  Hydraulic conductivity (m/d)\r\nH    = 90;                           %  Initial saturated thickness (m)\r\nsmin = 6;                            %  Minimum drawdown (m)\r\n[tf,smin1,xmin,ymin] = dewaterCheck(xw,yw,Q0,R,Lx,Ly,K,H,smin);\r\nxmin_correct = 0;\r\nymin_correct = 150;\r\nsmin1_correct = 6.65;\r\nassert(tf)\r\nassert(abs(mod(xmin,Lx)-xmin_correct)\u003c1e-3)\r\nassert(abs(abs(ymin)-ymin_correct)/ymin_correct\u003c1e-3)\r\nassert(abs(smin1-smin1_correct)/smin1_correct\u003c1e-3)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-16T05:19:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-16T05:10:49.000Z","updated_at":"2026-02-12T14:57:15.000Z","published_at":"2023-10-16T05:19:15.000Z","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\u003eIn addition to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57452\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esupplying water\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59104\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecapturing contaminants\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at least a value \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=\\\"smin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_{min}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than \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=\\\"hmax = H - smin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_{max} = H – s_{min}\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:r\u003e\u003cw:t\u003eThe wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with\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=\\\"h = sqrt(H^2 - (1/(pi K) sum(Qj ln(R/rj))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\sqrt{H^2-\\\\frac{1}{\\\\pi K} \\\\sum_{j=1}^N Q_j \\\\ln\\\\left(\\\\frac{R}{r_j}\\\\right)}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the 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=\\\"Qj\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the pumping rate of the \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=\\\"j\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ej\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth well, \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=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of influence, 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=\\\"rj\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the distance from the \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=\\\"j\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ej\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth well to the point in question. \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 the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.\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=\\\"471\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"614\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"dewatering scheme\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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