{"id":1626,"date":"2026-02-14T04:22:34","date_gmt":"2026-02-14T04:22:34","guid":{"rendered":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/ch029-xhtml\/"},"modified":"2026-08-01T14:38:30","modified_gmt":"2026-08-01T14:38:30","slug":"using-polar-coordinates","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/using-polar-coordinates\/","title":{"raw":"6.1 Using Polar Coordinates","rendered":"6.1 Using Polar Coordinates"},"content":{"raw":"<div id=\"using-polar-coordinates\" class=\"level1\">\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\nRadial flow can be described using a polar coordinate system, where r is the radial distance from an origin (a pumping well) to an observation point (<a href=\"\/an-introduction-to-hydraulic-testing-in-hydrogeology\/part\/6-mathematics-of-flow-to-a-pumping-well\/#Xc233975da451b57d727ad7588bedc2ea662d1c7\">Figure 17<\/a>). The position of the observation point is defined by <em>r<\/em> and an angle, <em>\u03b8<\/em>, measured from a horizontal axis (polar axis) in a counterclockwise direction (<a href=\"\/an-introduction-to-hydraulic-testing-in-hydrogeology\/part\/6-mathematics-of-flow-to-a-pumping-well\/#Xc233975da451b57d727ad7588bedc2ea662d1c7\">Figure 17<\/a>). When conditions are isotropic and homogeneous, the water bearing unit is horizontal, and the open area of the pumping well fully penetrates the unit, the angle \u03b8\u00a0becomes unimportant as all flow is horizontal and thus is the same on every radius (Fetter, 2001).\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div id=\"using-polar-coordinates\" class=\"level1\">\n<div data-custom-style=\"First Paragraph\">\n<p>Radial flow can be described using a polar coordinate system, where r is the radial distance from an origin (a pumping well) to an observation point (<a href=\"\/an-introduction-to-hydraulic-testing-in-hydrogeology\/part\/6-mathematics-of-flow-to-a-pumping-well\/#Xc233975da451b57d727ad7588bedc2ea662d1c7\">Figure 17<\/a>). The position of the observation point is defined by <em>r<\/em> and an angle, <em>\u03b8<\/em>, measured from a horizontal axis (polar axis) in a counterclockwise direction (<a href=\"\/an-introduction-to-hydraulic-testing-in-hydrogeology\/part\/6-mathematics-of-flow-to-a-pumping-well\/#Xc233975da451b57d727ad7588bedc2ea662d1c7\">Figure 17<\/a>). When conditions are isotropic and homogeneous, the water bearing unit is horizontal, and the open area of the pumping well fully penetrates the unit, the angle \u03b8\u00a0becomes unimportant as all flow is horizontal and thus is the same on every radius (Fetter, 2001).<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":22,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1626","chapter","type-chapter","status-publish","hentry"],"part":570,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1626","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":4,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1626\/revisions"}],"predecessor-version":[{"id":4165,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1626\/revisions\/4165"}],"part":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/parts\/570"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1626\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/media?parent=1626"}],"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=1626"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/contributor?post=1626"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/license?post=1626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}