{"id":1408,"date":"2026-05-12T21:47:48","date_gmt":"2026-05-12T21:47:48","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-16\/"},"modified":"2026-05-13T17:02:36","modified_gmt":"2026-05-13T17:02:36","slug":"solution-exercise-16","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-16\/","title":{"raw":"Solution Exercise 16","rendered":"Solution Exercise 16"},"content":{"raw":"
\r\n
\r\n\r\nVariables<\/strong>:\r\n\r\n<\/div>\r\n
\r\n
[latex]T\\ = \\ 2.28\\ x\\ 10^{- 4}\\ \\frac{m^{2}}{s} [\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]S\\ = \\ 0.00003 [\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]Q_{PW - 2}\\ = \\ 500\\frac{m^{3}}{d} = 0.0058\\ \\frac{m^{2}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]r = 260\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]t = 631,152,000\\ seconds\\ \\ \\ (20\\ years\\ with\\ 1\\ year = 365.25\\ days)[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nCalculations<\/strong>:\r\n\r\n<\/div>\r\n
\r\n\r\nPart 1 a:\r\n\r\n<\/div>\r\n
\r\n
[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(260\\ m)}^{2}\\ \\ 0.00003}{4\\left( 2.28\\ x\\ 10^{- 4}\\frac{m^{2}}{s} \\right)\\ 631,152,000\\ seconds} = \\ 3.5x10^{- 6}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]W(u)\\ = \\ 12[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
Drawdown at 20 years:[latex]\\ s = \\ \\frac{Q}{4\\pi T}W(u) = \\ \\frac{0.0058\\ \\frac{m^{3}}{s}(12)}{4\\ \\pi\\ 2.28x10^{- 4}\\ \\frac{m^{2}}{s}}\\ = \\ 24.3\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nPart 1 b:\r\n\r\n<\/div>\r\n
\r\n\r\nChanged Variables:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]Q_{PW - 5}\\ = \\ 200\\frac{m^{3}}{d} = 0.0023\\ \\frac{m^{2}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]r\\ = \\ 150\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]t\\ \\ = \\ 315,576,000\\ seconds\\ \\ \\ (10\\ years\\ with\\ 1\\ year = 365.25\\ days)[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(150\\ m)}^{2}\\ \\ 0.00003}{4\\left( 2.28x10^{- 4}\\ \\frac{m^{2}}{s} \\right)\\ 315,576,000\\ seconds} = \\ 2.3x10^{- 6}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]W(u)\\ = \\ 12.4[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
Drawdown at [latex]10[\/latex] years:[latex]\\ s = \\ \\frac{Q}{4\\pi T}W(u) = \\ \\frac{0.0058\\ \\frac{m^{3}}{s}(12.4)}{4\\ \\pi\\ 2.28\\ x\\ 10^{- 4}\\ \\frac{m^{2}}{s}}\\ = \\ 10\\ m [\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nDrawdown at 20 years due to both wells pumping: 24.3[latex]\\ m + 10\\ m =[\/latex] 34.2 m\r\n\r\n<\/div>\r\n
\r\n\r\nHead is 386.3 n ASL \u2013 34.2 m = 352.1 m ASL which is well above the top of the aquifer at 55 m ASL.\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to Exercise\u00a01<\/span><\/a>6<\/u><\/strong>\u2ba5\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise\u00a016<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Variables<\/strong>:<\/p>\n<\/div>\n

\n

[latex]T\\ = \\ 2.28\\ x\\ 10^{- 4}\\ \\frac{m^{2}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]S\\ = \\ 0.00003[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]Q_{PW - 2}\\ = \\ 500\\frac{m^{3}}{d} = 0.0058\\ \\frac{m^{2}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]r = 260\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]t = 631,152,000\\ seconds\\ \\ \\ (20\\ years\\ with\\ 1\\ year = 365.25\\ days)[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Calculations<\/strong>:<\/p>\n<\/div>\n

\n

Part 1 a:<\/p>\n<\/div>\n

\n

[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(260\\ m)}^{2}\\ \\ 0.00003}{4\\left( 2.28\\ x\\ 10^{- 4}\\frac{m^{2}}{s} \\right)\\ 631,152,000\\ seconds} = \\ 3.5x10^{- 6}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]W(u)\\ = \\ 12[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at 20 years:[latex]\\ s = \\ \\frac{Q}{4\\pi T}W(u) = \\ \\frac{0.0058\\ \\frac{m^{3}}{s}(12)}{4\\ \\pi\\ 2.28x10^{- 4}\\ \\frac{m^{2}}{s}}\\ = \\ 24.3\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Part 1 b:<\/p>\n<\/div>\n

\n

Changed Variables:<\/strong><\/p>\n<\/div>\n

\n

[latex]Q_{PW - 5}\\ = \\ 200\\frac{m^{3}}{d} = 0.0023\\ \\frac{m^{2}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]r\\ = \\ 150\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]t\\ \\ = \\ 315,576,000\\ seconds\\ \\ \\ (10\\ years\\ with\\ 1\\ year = 365.25\\ days)[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(150\\ m)}^{2}\\ \\ 0.00003}{4\\left( 2.28x10^{- 4}\\ \\frac{m^{2}}{s} \\right)\\ 315,576,000\\ seconds} = \\ 2.3x10^{- 6}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]W(u)\\ = \\ 12.4[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at [latex]10[\/latex] years:[latex]\\ s = \\ \\frac{Q}{4\\pi T}W(u) = \\ \\frac{0.0058\\ \\frac{m^{3}}{s}(12.4)}{4\\ \\pi\\ 2.28\\ x\\ 10^{- 4}\\ \\frac{m^{2}}{s}}\\ = \\ 10\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at 20 years due to both wells pumping: 24.3[latex]\\ m + 10\\ m =[\/latex] 34.2 m<\/p>\n<\/div>\n

\n

Head is 386.3 n ASL \u2013 34.2 m = 352.1 m ASL which is well above the top of the aquifer at 55 m ASL.<\/p>\n<\/div>\n

\n

Return to Exercise\u00a01<\/span><\/a>6<\/u><\/strong>\u2ba5<\/p>\n<\/div>\n

\n

Return to where text linked to Exercise\u00a016<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":127,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1408","chapter","type-chapter","status-publish","hentry"],"part":1531,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":4,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1408\/revisions"}],"predecessor-version":[{"id":1887,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1408\/revisions\/1887"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1531"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1408\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1408"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1408"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1408"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}