{"id":95,"date":"2022-12-30T18:15:39","date_gmt":"2022-12-30T18:15:39","guid":{"rendered":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/exercise-7\/"},"modified":"2023-01-08T01:04:23","modified_gmt":"2023-01-08T01:04:23","slug":"exercise-7","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/exercise-7\/","title":{"raw":"Exercise 7","rendered":"Exercise 7"},"content":{"raw":"<div class=\"exercise-7\">\r\n<p class=\"import-Normal\">Calculate the Rayleigh number for the unstable case shown in <a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/stable-and-unstable-density-configurations\/#figure-9\">Figure\u00a09b<\/a>. Assume that <em>\u03bc<\/em>\u00a0=\u00a01\u00a0\u00d7\u00a010<sup>\u22123<\/sup>\u00a0kg m<sup>\u22121<\/sup> s<sup>\u22121<\/sup>, <em>k<\/em>\u00a0=\u00a01\u00a0\u00d7\u00a010<sup>\u221210<\/sup> m<sup>2<\/sup><em>,<\/em><em> D<\/em><sub><em>T<\/em><\/sub> =\u00a01\u00a0\u00d7\u00a010<sup>\u22126<\/sup>\u00a0m<sup>2<\/sup> s<sup>\u22121<\/sup> and <em>\u2206<\/em><em>\u03c1<\/em>\u00a0=\u00a03\u00a0kg m<sup>\u22123<\/sup>. This value of <em>\u2206<\/em><em>\u03c1<\/em> is the approximate density difference at the moment when the boundary layer becomes unstable after about 2400\u00a0years. Compare your evaluation with the <a href=\"https:\/\/youtu.be\/9Ctn9Vm6psc\" target=\"_blank\" rel=\"noopener\">animated version<\/a> of this problem.<\/p>\r\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-7\/\"><span class=\"import-Hyperlink\">Click for solution to <\/span><span class=\"import-Hyperlink\">Exercise <\/span><span class=\"import-Hyperlink\">7<\/span><\/a><\/p>\r\n<p class=\"import-Normal\"><\/p>\r\n\r\n<\/div>","rendered":"<div class=\"exercise-7\">\n<p class=\"import-Normal\">Calculate the Rayleigh number for the unstable case shown in <a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/stable-and-unstable-density-configurations\/#figure-9\">Figure\u00a09b<\/a>. Assume that <em>\u03bc<\/em>\u00a0=\u00a01\u00a0\u00d7\u00a010<sup>\u22123<\/sup>\u00a0kg m<sup>\u22121<\/sup> s<sup>\u22121<\/sup>, <em>k<\/em>\u00a0=\u00a01\u00a0\u00d7\u00a010<sup>\u221210<\/sup> m<sup>2<\/sup><em>,<\/em><em> D<\/em><sub><em>T<\/em><\/sub> =\u00a01\u00a0\u00d7\u00a010<sup>\u22126<\/sup>\u00a0m<sup>2<\/sup> s<sup>\u22121<\/sup> and <em>\u2206<\/em><em>\u03c1<\/em>\u00a0=\u00a03\u00a0kg m<sup>\u22123<\/sup>. This value of <em>\u2206<\/em><em>\u03c1<\/em> is the approximate density difference at the moment when the boundary layer becomes unstable after about 2400\u00a0years. Compare your evaluation with the <a href=\"https:\/\/youtu.be\/9Ctn9Vm6psc\" target=\"_blank\" rel=\"noopener\">animated version<\/a> of this problem.<\/p>\n<p class=\"import-Normal\" style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-7\/\"><span class=\"import-Hyperlink\">Click for solution to <\/span><span class=\"import-Hyperlink\">Exercise <\/span><span class=\"import-Hyperlink\">7<\/span><\/a><\/p>\n<p class=\"import-Normal\">\n<\/div>\n","protected":false},"author":1,"menu_order":23,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-95","chapter","type-chapter","status-publish","hentry"],"part":143,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/95","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\/95\/revisions"}],"predecessor-version":[{"id":325,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/95\/revisions\/325"}],"part":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/143"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/95\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/media?parent=95"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=95"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=95"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/license?post=95"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}