{"id":1398,"date":"2026-05-12T21:47:44","date_gmt":"2026-05-12T21:47:44","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-9\/"},"modified":"2026-05-13T03:43:32","modified_gmt":"2026-05-13T03:43:32","slug":"solution-exercise-9","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-9\/","title":{"raw":"Solution Exercise 9","rendered":"Solution Exercise 9"},"content":{"raw":"<div id=\"solution-exercise-9\" class=\"level1\">\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\n<strong>Variables<\/strong>:\r\n\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]T\\ = (k)(b) = (75\\ m)\\left( 7.06\\ x\\ 10^{- 6}\\frac{m}{s} \\right) = \\ 0.00053\\ m^{2}\/s [\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]S\\ = \\ 0.0004 [\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]Q\\ = \\frac{545\\frac{\\ \\ m^{3}}{d}}{86400\\ \\frac{s}{d}} = 0.00631\\ \\frac{m^{3}}{s} [\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]r\\ = \\ 75\\ m [\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]t = (36\\ hrs)\\left( 3600\\ \\frac{s}{hr} \\right) = 129,600\\ seconds [\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\n<strong>Calculations<\/strong>:\r\n\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{\\left\\lbrack \\left( 5625{\\ \\ m}^{2} \\right)0.0004 \\right\\rbrack}{\\left\\lbrack 4\\left( 0.00053\\frac{{\\ \\ m}^{2}}{s} \\right)129,600\\ s \\right\\rbrack} = \\ 0.0082[\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>reading from Table 4, [latex]W(u)\\ = \\ 4.26[\/latex]<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\nDrawdown at 36\u00a0hours [latex]s = \\frac{Q}{4\\pi T}W(u) = \\frac{\\left( 0.00631\\frac{{\\ \\ m}^{3}}{s} \\right)\\ 4.23}{4\\ \\pi\\ 0.00053\\frac{{\\ \\ m}^{2}}{s}}\\ \\ = \\ 4.02\\ m[\/latex]\r\n\r\n<\/div>\r\n<div data-custom-style=\"Body Text\">\r\n\r\nFinal head at 36\u00a0hours[latex]\\ = \\ 175\\ - \\ 4.02\\ = \\ 171\\ m[\/latex]\r\n\r\n<\/div>\r\n<div data-custom-style=\"Body Text\">\r\n\r\n<strong><a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-9\/#exercise-9\"><span data-custom-style=\"Hyperlink\">Return to Exercise\u00a0<\/span><\/a><u>9<\/u><\/strong>\u2ba5\r\n\r\n<\/div>\r\n<div data-custom-style=\"Body Text\">\r\n\r\n<a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/the-theis-equation\/#extext09\"><span data-custom-style=\"Hyperlink\"><strong>Return to where text linked to Exercise\u00a09<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div id=\"solution-exercise-9\" class=\"level1\">\n<div data-custom-style=\"First Paragraph\">\n<p><strong>Variables<\/strong>:<\/p>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]T\\ = (k)(b) = (75\\ m)\\left( 7.06\\ x\\ 10^{- 6}\\frac{m}{s} \\right) = \\ 0.00053\\ m^{2}\/s[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]S\\ = \\ 0.0004[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]Q\\ = \\frac{545\\frac{\\ \\ m^{3}}{d}}{86400\\ \\frac{s}{d}} = 0.00631\\ \\frac{m^{3}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]r\\ = \\ 75\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]t = (36\\ hrs)\\left( 3600\\ \\frac{s}{hr} \\right) = 129,600\\ seconds[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"First Paragraph\">\n<p><strong>Calculations<\/strong>:<\/p>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{\\left\\lbrack \\left( 5625{\\ \\ m}^{2} \\right)0.0004 \\right\\rbrack}{\\left\\lbrack 4\\left( 0.00053\\frac{{\\ \\ m}^{2}}{s} \\right)129,600\\ s \\right\\rbrack} = \\ 0.0082[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>reading from Table 4, [latex]W(u)\\ = \\ 4.26[\/latex]<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"First Paragraph\">\n<p>Drawdown at 36\u00a0hours [latex]s = \\frac{Q}{4\\pi T}W(u) = \\frac{\\left( 0.00631\\frac{{\\ \\ m}^{3}}{s} \\right)\\ 4.23}{4\\ \\pi\\ 0.00053\\frac{{\\ \\ m}^{2}}{s}}\\ \\ = \\ 4.02\\ m[\/latex]<\/p>\n<\/div>\n<div data-custom-style=\"Body Text\">\n<p>Final head at 36\u00a0hours[latex]\\ = \\ 175\\ - \\ 4.02\\ = \\ 171\\ m[\/latex]<\/p>\n<\/div>\n<div data-custom-style=\"Body Text\">\n<p><strong><a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-9\/#exercise-9\"><span data-custom-style=\"Hyperlink\">Return to Exercise\u00a0<\/span><\/a><u>9<\/u><\/strong>\u2ba5<\/p>\n<\/div>\n<div data-custom-style=\"Body Text\">\n<p><a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/the-theis-equation\/#extext09\"><span data-custom-style=\"Hyperlink\"><strong>Return to where text linked to Exercise\u00a09<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":120,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1398","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\/1398","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\/1398\/revisions"}],"predecessor-version":[{"id":1848,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1398\/revisions\/1848"}],"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\/1398\/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=1398"}],"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=1398"},{"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=1398"},{"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=1398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}