{"id":1409,"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-17\/"},"modified":"2026-05-13T17:03:24","modified_gmt":"2026-05-13T17:03:24","slug":"solution-exercise-17","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-17\/","title":{"raw":"Solution Exercise 17","rendered":"Solution Exercise 17"},"content":{"raw":"
\r\n
\r\n\r\nDrawdown at Observation Well in Figure\u00a055<\/span><\/a> with no-flow boundary<\/strong>\r\n\r\n<\/div>\r\n
\r\n\r\nVariables:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]Q\\ = \\ 1000\\frac{m^{3}}{d}\\ or\\ 0.0116\\ \\frac{m^{3}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]t = 315,576,000\\ seconds\\ (10\\ years\\ assuming\\ 365.25\\ day[\/latex]s per year<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]T\\ = \\ Kb\\ = \\ 0.00002\\frac{m}{s}\\ 20\\ m\\ = \\ 0.0004\\ \\frac{m^{2}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]S\\ = \\ 0.0001[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]r_{pumping}\\ = \\ 200[\/latex] m<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]r_{image}\\ = 300 [\/latex]m<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nDrawdown at OW from the pumping well:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{{(200\\ m)}^{2}\\ 0.0001}{\\left\\lbrack 4\\ \\left( 0.0004\\frac{m^{2}}{s} \\right)315,576,000\\ seconds \\right\\rbrack} = \\ {7.92x10}^{- 6}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]W(u)\\ = \\ 11.17[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]s = \\frac{Q}{4\\pi T}W(u) = \\frac{0.0116\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\pi\\ 0.0004\\frac{\\ \\ m^{2}}{s}}(11.17) = \\ 25.78\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nDrawdown at OW from image well:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{{\\ \\ (300\\ m)}^{2}\\ \\ 0.0001}{4\\ \\ (0.0004\\ \\frac{m^{2}}{s})\\ 315,576,000\\ seconds} = {1.78x10}^{- 5}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]W(u)\\ = \\ 10.39[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]s\\ = \\ \\frac{0.0116\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\pi\\ 0.0004\\frac{\\ \\ m^{2}}{s}}(10.39) = \\ 23.98\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nCombined Drawdown at OW:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]s = \\ 25.78\\ m + 23.98\\ m = \\ 49.76\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nDrawdown at Observation Well in Figure\u00a055<\/span><\/a><\/strong>\r\n\r\n<\/div>\r\n
\r\n
Calculations are identical except Q of the image well is injection [latex]Q = - 0.0116\\frac{m^{3}}{s}[\/latex]. For the total drawdown, the drawdown associated with the image well is subtracted from the real well drawdown rather than added. The solution is:<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]s = \\ 25.78\\ m + ( - 23.98\\ m) = \\ 1.8\\ m[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nReturn to Exercise 17<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise 17<\/u><\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Drawdown at Observation Well in Figure\u00a055<\/span><\/a> with no-flow boundary<\/strong><\/p>\n<\/div>\n

\n

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

\n

[latex]Q\\ = \\ 1000\\frac{m^{3}}{d}\\ or\\ 0.0116\\ \\frac{m^{3}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]t = 315,576,000\\ seconds\\ (10\\ years\\ assuming\\ 365.25\\ day[\/latex]s per year<\/p><\/blockquote>\n<\/div>\n

\n

[latex]T\\ = \\ Kb\\ = \\ 0.00002\\frac{m}{s}\\ 20\\ m\\ = \\ 0.0004\\ \\frac{m^{2}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]S\\ = \\ 0.0001[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]r_{pumping}\\ = \\ 200[\/latex] m<\/p><\/blockquote>\n<\/div>\n

\n

[latex]r_{image}\\ = 300[\/latex]m<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at OW from the pumping well:<\/strong><\/p>\n<\/div>\n

\n

[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{{(200\\ m)}^{2}\\ 0.0001}{\\left\\lbrack 4\\ \\left( 0.0004\\frac{m^{2}}{s} \\right)315,576,000\\ seconds \\right\\rbrack} = \\ {7.92x10}^{- 6}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]W(u)\\ = \\ 11.17[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]s = \\frac{Q}{4\\pi T}W(u) = \\frac{0.0116\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\pi\\ 0.0004\\frac{\\ \\ m^{2}}{s}}(11.17) = \\ 25.78\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at OW from image well:<\/strong><\/p>\n<\/div>\n

\n

[latex]u\\ = \\frac{r^{2}S}{4Tt} = \\frac{{\\ \\ (300\\ m)}^{2}\\ \\ 0.0001}{4\\ \\ (0.0004\\ \\frac{m^{2}}{s})\\ 315,576,000\\ seconds} = {1.78x10}^{- 5}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]W(u)\\ = \\ 10.39[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]s\\ = \\ \\frac{0.0116\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\pi\\ 0.0004\\frac{\\ \\ m^{2}}{s}}(10.39) = \\ 23.98\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Combined Drawdown at OW:<\/strong><\/p>\n<\/div>\n

\n

[latex]s = \\ 25.78\\ m + 23.98\\ m = \\ 49.76\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Drawdown at Observation Well in Figure\u00a055<\/span><\/a><\/strong><\/p>\n<\/div>\n

\n

Calculations are identical except Q of the image well is injection [latex]Q = - 0.0116\\frac{m^{3}}{s}[\/latex]. For the total drawdown, the drawdown associated with the image well is subtracted from the real well drawdown rather than added. The solution is:<\/p><\/blockquote>\n<\/div>\n

\n

[latex]s = \\ 25.78\\ m + ( - 23.98\\ m) = \\ 1.8\\ m[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Return to Exercise 17<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n

\n

Return to where text linked to Exercise 17<\/u><\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":128,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1409","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\/1409","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":3,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1409\/revisions"}],"predecessor-version":[{"id":1888,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1409\/revisions\/1888"}],"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\/1409\/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=1409"}],"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=1409"},{"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=1409"},{"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=1409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}