{"id":102,"date":"2022-12-30T18:15:40","date_gmt":"2022-12-30T18:15:40","guid":{"rendered":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-1\/"},"modified":"2023-01-08T01:10:55","modified_gmt":"2023-01-08T01:10:55","slug":"solution-exercise-1","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-1\/","title":{"raw":"Solution Exercise 1","rendered":"Solution Exercise 1"},"content":{"raw":"<div class=\"solution-exercise-1\">\r\n<p class=\"import-Normal\">For the fresh water: <span style=\"font-size: NaNpt; color: #; ; text-decoration: none;\"><em>p<\/em> = <em>\u03c1<\/em><sub><em>f<\/em><\/sub><em>g<\/em>(<em>y<\/em> + <em>h<\/em>)<\/span><\/p>\r\n<p class=\"import-Normal\">For the seawater:\u00a0<em>p<\/em> = <em>\u03c1<\/em><sub><em>s<\/em><\/sub><em>g<\/em><em>y<\/em><\/p>\r\n<p class=\"import-Normal\">Equating the pressures and rearranging gives: [latex]y=\\frac{\\rho _{f}}{\\rho _{s}-\\rho _{f}}h=40h[\/latex]<\/p>\r\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/exercise-1\/\"><span class=\"import-Hyperlink\">Return<\/span><span class=\"import-Hyperlink\"> to <\/span><span class=\"import-Hyperlink\">Exercise\u00a0<\/span><span class=\"import-Hyperlink\">1<\/span><\/a><\/p>\r\n\r\n<\/div>","rendered":"<div class=\"solution-exercise-1\">\n<p class=\"import-Normal\">For the fresh water: <span style=\"font-size: NaNpt; color: #; ; text-decoration: none;\"><em>p<\/em> = <em>\u03c1<\/em><sub><em>f<\/em><\/sub><em>g<\/em>(<em>y<\/em> + <em>h<\/em>)<\/span><\/p>\n<p class=\"import-Normal\">For the seawater:\u00a0<em>p<\/em> = <em>\u03c1<\/em><sub><em>s<\/em><\/sub><em>g<\/em><em>y<\/em><\/p>\n<p class=\"import-Normal\">Equating the pressures and rearranging gives: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-content\/ql-cache\/quicklatex.com-4a136142e976927843301b1658366532_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#114;&#104;&#111;&#32;&#95;&#123;&#102;&#125;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#95;&#123;&#115;&#125;&#45;&#92;&#114;&#104;&#111;&#32;&#95;&#123;&#102;&#125;&#125;&#104;&#61;&#52;&#48;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"138\" style=\"vertical-align: -10px;\" \/><\/p>\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/exercise-1\/\"><span class=\"import-Hyperlink\">Return<\/span><span class=\"import-Hyperlink\"> to <\/span><span class=\"import-Hyperlink\">Exercise\u00a0<\/span><span class=\"import-Hyperlink\">1<\/span><\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":26,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-102","chapter","type-chapter","status-publish","hentry"],"part":155,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":3,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/102\/revisions"}],"predecessor-version":[{"id":326,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/102\/revisions\/326"}],"part":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/155"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/102\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/media?parent=102"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=102"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=102"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/license?post=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}