{"id":486,"date":"2022-12-11T23:09:08","date_gmt":"2022-12-11T23:09:08","guid":{"rendered":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/exercise-11-solution\/"},"modified":"2023-01-14T20:13:50","modified_gmt":"2023-01-14T20:13:50","slug":"exercise-11-solution","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/exercise-11-solution\/","title":{"raw":"Exercise 11 Solution","rendered":"Exercise 11 Solution"},"content":{"raw":"<div class=\"exercise-11-solution\">\r\n<ol type=\"a\">\r\n \t<li class=\"import-Normal\">The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe.<\/li>\r\n \t<li class=\"import-Normal\">If <em>\u00b5<\/em> increases, then the gradient increases in order to drive the same mean volumetric flow rate of a more viscous fluid through the same opening. That is, is the more viscous fluid presents more resistance to flow. This makes sense because a more viscous fluid is \u201cthicker\u201d like syrup compared to water, so the fluid does not flow as easily thus requiring more pressure to push the fluid through the pipe.<\/li>\r\n \t<li class=\"import-Normal\">The specific velocity is linearly proportional to the pressure gradient if the viscosity of the fluid is constant.<\/li>\r\n<\/ol>\r\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/exercise-11\/\"><span class=\"import-Hyperlink\">Return to Exercise <\/span><span class=\"import-Hyperlink\">11<\/span><\/a><\/p>\r\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/fluid-mechanics-of-pipes-and-open-channels\/#text-link-to-exercise-11\">Return to where text linked to Exercise 11<\/a><\/p>\r\n\r\n<\/div>","rendered":"<div class=\"exercise-11-solution\">\n<ol type=\"a\">\n<li class=\"import-Normal\">The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe.<\/li>\n<li class=\"import-Normal\">If <em>\u00b5<\/em> increases, then the gradient increases in order to drive the same mean volumetric flow rate of a more viscous fluid through the same opening. That is, is the more viscous fluid presents more resistance to flow. This makes sense because a more viscous fluid is \u201cthicker\u201d like syrup compared to water, so the fluid does not flow as easily thus requiring more pressure to push the fluid through the pipe.<\/li>\n<li class=\"import-Normal\">The specific velocity is linearly proportional to the pressure gradient if the viscosity of the fluid is constant.<\/li>\n<\/ol>\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/exercise-11\/\"><span class=\"import-Hyperlink\">Return to Exercise <\/span><span class=\"import-Hyperlink\">11<\/span><\/a><\/p>\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/chapter\/fluid-mechanics-of-pipes-and-open-channels\/#text-link-to-exercise-11\">Return to where text linked to Exercise 11<\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":58,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-486","chapter","type-chapter","status-publish","hentry"],"part":580,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapters\/486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":3,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapters\/486\/revisions"}],"predecessor-version":[{"id":888,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapters\/486\/revisions\/888"}],"part":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/parts\/580"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapters\/486\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/wp\/v2\/media?parent=486"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/pressbooks\/v2\/chapter-type?post=486"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/wp\/v2\/contributor?post=486"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-karst-aquifers\/wp-json\/wp\/v2\/license?post=486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}