{"id":107,"date":"2021-01-02T12:27:34","date_gmt":"2021-01-02T12:27:34","guid":{"rendered":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/chapter\/exercise-1-solution\/"},"modified":"2021-01-04T19:00:19","modified_gmt":"2021-01-04T19:00:19","slug":"exercise-1-solution","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/chapter\/exercise-1-solution\/","title":{"raw":"Exercise 1 - Solution","rendered":"Exercise 1 – Solution"},"content":{"raw":"

\"\"<\/p>\r\n

\"calculation<\/p>\r\n

Comment: You might be wondering: what happens along the flow line that begins exactly at the midpoint of the inlet screen? The answer to this question addresses the relation between a mathematical characterization of a process and what happens in reality. From a mathematical standpoint, the flow line that begins exactly at the midpoint of the screen flows directly towards the pillar. When the flow line meets the pillar, mathematical analysis shows that there are two possible solutions. The flow line can either go around either side of the pillar. When both possibilities are drawn in the flow net, there is the appearance that the flow line splits at the pillar into two branches, one branch going around the left side of the pillar, and the other branch going around the right side. However, this is a misleading conceptualization. Instead, it is better to think of the flow line as representing two separate flow lines, one starting at a minute distance to the left, and the other starting at a minute distance to the right (Figure below). In this conceptualization, there is no notion of a flow line splitting. In reality, it is not possible to define a flow line starting at the midpoint of the inlet screen with mathematical exactness, because real objects do not possess exact geometric shapes. The most reasonable statement that can be made about a flow line that starts near the midpoint of the inlet screen is that it is equally likely to go around the left side of the pillar as around the right side.<\/p>\r\n\"\"\r\n

Return to Exercise 1<\/a><\/p>","rendered":"

\"\"<\/p>\n

\"calculation<\/p>\n

Comment: You might be wondering: what happens along the flow line that begins exactly at the midpoint of the inlet screen? The answer to this question addresses the relation between a mathematical characterization of a process and what happens in reality. From a mathematical standpoint, the flow line that begins exactly at the midpoint of the screen flows directly towards the pillar. When the flow line meets the pillar, mathematical analysis shows that there are two possible solutions. The flow line can either go around either side of the pillar. When both possibilities are drawn in the flow net, there is the appearance that the flow line splits at the pillar into two branches, one branch going around the left side of the pillar, and the other branch going around the right side. However, this is a misleading conceptualization. Instead, it is better to think of the flow line as representing two separate flow lines, one starting at a minute distance to the left, and the other starting at a minute distance to the right (Figure below). In this conceptualization, there is no notion of a flow line splitting. In reality, it is not possible to define a flow line starting at the midpoint of the inlet screen with mathematical exactness, because real objects do not possess exact geometric shapes. The most reasonable statement that can be made about a flow line that starts near the midpoint of the inlet screen is that it is equally likely to go around the left side of the pillar as around the right side.<\/p>\n

\"\"<\/p>\n

Return to Exercise 1<\/a><\/p>\n","protected":false},"author":1,"menu_order":24,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-107","chapter","type-chapter","status-publish","hentry"],"part":135,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/107","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":5,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/107\/revisions"}],"predecessor-version":[{"id":314,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/107\/revisions\/314"}],"part":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/parts\/135"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/107\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/media?parent=107"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapter-type?post=107"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/contributor?post=107"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/license?post=107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}