{"id":926,"date":"2020-12-09T05:09:55","date_gmt":"2020-12-09T05:09:55","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/?post_type=chapter&#038;p=926"},"modified":"2020-12-10T19:06:02","modified_gmt":"2020-12-10T19:06:02","slug":"solution-to-exercise-16","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/chapter\/solution-to-exercise-16\/","title":{"raw":"Solution to Exercise 16","rendered":"Solution to Exercise 16"},"content":{"raw":"16) In the accompanying figure flow lines (black lines) form two flow tubes, A and B. If conditions are isotropic and homogeneous and flow is at steady state, create equipotential lines under the following conditions.\r\n\r\n<em>16a) For A, assume the aquifer thickness and hydraulic conductivities are constant.<\/em>\r\n\r\nThe volumetric flow rate in flow tube A must be constant, so the increasing distance between the flow lines (indicated by the black arrows) in a system where the aquifer thickness and hydraulic conductivity is constant indicates the gradient needs to decrease (equipotential lines space further apart).\r\n\r\n<em>b) For B, assume the thickness of the aquifer increases from left to right while all other conditions remain constant.<\/em>\r\n\r\nThe volumetric flow rate in flow tube B must be constant, if the thickness of the aquifer is increasing from left to right, the flow area is increasing to the right. As a result, the gradients must decrease to the right, requiring larger distance between equipotential lines.\r\n\r\n<img class=\"alignnone wp-image-1039 size-large\" src=\"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-1024x588.jpg\" alt=\"\" width=\"1024\" height=\"588\" \/>\r\n<p style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/part\/exercises\/#Exercise16\">Return to Exercise 16<\/a><\/p>","rendered":"<p>16) In the accompanying figure flow lines (black lines) form two flow tubes, A and B. If conditions are isotropic and homogeneous and flow is at steady state, create equipotential lines under the following conditions.<\/p>\n<p><em>16a) For A, assume the aquifer thickness and hydraulic conductivities are constant.<\/em><\/p>\n<p>The volumetric flow rate in flow tube A must be constant, so the increasing distance between the flow lines (indicated by the black arrows) in a system where the aquifer thickness and hydraulic conductivity is constant indicates the gradient needs to decrease (equipotential lines space further apart).<\/p>\n<p><em>b) For B, assume the thickness of the aquifer increases from left to right while all other conditions remain constant.<\/em><\/p>\n<p>The volumetric flow rate in flow tube B must be constant, if the thickness of the aquifer is increasing from left to right, the flow area is increasing to the right. As a result, the gradients must decrease to the right, requiring larger distance between equipotential lines.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1039 size-large\" src=\"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-1024x588.jpg\" alt=\"\" width=\"1024\" height=\"588\" srcset=\"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-1024x588.jpg 1024w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-300x172.jpg 300w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-768x441.jpg 768w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-65x37.jpg 65w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-225x129.jpg 225w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16-350x201.jpg 350w, https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-content\/uploads\/sites\/4\/2020\/12\/figEXsp16.jpg 1145w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p style=\"text-align: right;\"><a href=\"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/part\/exercises\/#Exercise16\">Return to Exercise 16<\/a><\/p>\n","protected":false},"author":1,"menu_order":16,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-926","chapter","type-chapter","status-publish","hentry"],"part":873,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/926","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":5,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/926\/revisions"}],"predecessor-version":[{"id":1040,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/926\/revisions\/1040"}],"part":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/873"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/926\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/media?parent=926"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=926"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=926"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/license?post=926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}