{"id":1647,"date":"2026-02-14T04:22:59","date_gmt":"2026-02-14T04:22:59","guid":{"rendered":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/ch038-xhtml\/"},"modified":"2026-08-01T08:59:34","modified_gmt":"2026-08-01T08:59:34","slug":"using-the-theis-equation-to-predict-drawdowns-in-totally-confined-aquifers","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/using-the-theis-equation-to-predict-drawdowns-in-totally-confined-aquifers\/","title":{"raw":"8.2 Using the Theis Equation to Predict Drawdowns in Totally Confined Aquifers","rendered":"8.2 Using the Theis Equation to Predict Drawdowns in Totally Confined Aquifers"},"content":{"raw":"
\r\n
\r\n
\r\n\r\nWhen the properties of a fully confined aquifer are known, T<\/em> and S<\/em> can be inserted into the Theis equation (Equation\u00a0(26)<\/a>) and the drawdown for any time since pumping began can be computed at any radial distance from the pumping well.\r\n\r\n<\/div>\r\n
\r\n\r\nExample<\/strong>\r\n\r\n<\/div>\r\n
\r\n\r\nCompute the drawdown at an observation well located 300 m from a well that is pumped at a constant rate of 4000 L\/min (4 m3<\/sup>\/min = 5,760 m3<\/sup>\/d) for 8 hours (0.33 d) when the confined formation T<\/em> is estimated at 800 m2<\/sup>\/d and S<\/em>=0.00008.\r\n\r\n<\/div>\r\n
\r\n\r\nFirst u<\/em> is calculated, then the corresponding Theis well function value is derived.\r\n\r\n<\/div>\r\n
\r\n
\r\n\r\n[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(300\\ m)}^{2}0.00008}{4\\ \\left( 800\\ \\frac{m^{2}}{d} \\right)\\ 0.33\\ d} = u = \\ 0.0068\\ or\\ {6.8x10}^{- 3}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n\r\nAgain, it is important to use consistent units such that u<\/em> has no units because it is a dimensionless value. Using the well function table in Figure 26<\/a>, W(u<\/em>) = 4.4204. So, the drawdown 300 m from the pumping well would be calculated as follows.\r\n\r\n<\/div>\r\n
\r\n
\r\n\r\n[latex]s = \\frac{5760\\ \\frac{m^{3}}{d}\\ 4.4204}{4\\ (3.14)\\ 800\\ \\frac{m^{2}}{d}} = \\ 2.53\\ m[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n\r\nAs a check on the table value of W(u<\/em>), substituting values of u<\/em> into the infinite series shown in Equation\u00a0(27)<\/a> and only extending the calculation to the first two terms that contain u<\/em> results in W(u<\/em>) = 4.4204. This correlates with the table value.\r\n\r\n<\/div>\r\n
\r\n\r\nAgain, this analytical solution is for a fully confined, isotropic and homogeneous system using the general simplifying assumptions and the additional Theis assumptions. The values used in Equation\u00a0(26)<\/a> must have compatible units so that drawdown is reported in length units (e.g., ft, m).\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n
\n

When the properties of a fully confined aquifer are known, T<\/em> and S<\/em> can be inserted into the Theis equation (Equation\u00a0(26)<\/a>) and the drawdown for any time since pumping began can be computed at any radial distance from the pumping well.<\/p>\n<\/div>\n

\n

Example<\/strong><\/p>\n<\/div>\n

\n

Compute the drawdown at an observation well located 300 m from a well that is pumped at a constant rate of 4000 L\/min (4 m3<\/sup>\/min = 5,760 m3<\/sup>\/d) for 8 hours (0.33 d) when the confined formation T<\/em> is estimated at 800 m2<\/sup>\/d and S<\/em>=0.00008.<\/p>\n<\/div>\n

\n

First u<\/em> is calculated, then the corresponding Theis well function value is derived.<\/p>\n<\/div>\n

\n
\n

[latex]u = \\frac{r^{2}S}{4Tt} = \\frac{{(300\\ m)}^{2}0.00008}{4\\ \\left( 800\\ \\frac{m^{2}}{d} \\right)\\ 0.33\\ d} = u = \\ 0.0068\\ or\\ {6.8x10}^{- 3}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n

Again, it is important to use consistent units such that u<\/em> has no units because it is a dimensionless value. Using the well function table in Figure 26<\/a>, W(u<\/em>) = 4.4204. So, the drawdown 300 m from the pumping well would be calculated as follows.<\/p>\n<\/div>\n

\n
\n

[latex]s = \\frac{5760\\ \\frac{m^{3}}{d}\\ 4.4204}{4\\ (3.14)\\ 800\\ \\frac{m^{2}}{d}} = \\ 2.53\\ m[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n

As a check on the table value of W(u<\/em>), substituting values of u<\/em> into the infinite series shown in Equation\u00a0(27)<\/a> and only extending the calculation to the first two terms that contain u<\/em> results in W(u<\/em>) = 4.4204. This correlates with the table value.<\/p>\n<\/div>\n

\n

Again, this analytical solution is for a fully confined, isotropic and homogeneous system using the general simplifying assumptions and the additional Theis assumptions. The values used in Equation\u00a0(26)<\/a> must have compatible units so that drawdown is reported in length units (e.g., ft, m).<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":31,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1647","chapter","type-chapter","status-publish","hentry"],"part":574,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1647","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":3,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1647\/revisions"}],"predecessor-version":[{"id":2970,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1647\/revisions\/2970"}],"part":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/parts\/574"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1647\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/media?parent=1647"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapter-type?post=1647"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/contributor?post=1647"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/license?post=1647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}