{"id":115,"date":"2021-01-02T12:27:37","date_gmt":"2021-01-02T12:27:37","guid":{"rendered":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/chapter\/exercise-4-solution\/"},"modified":"2021-01-09T18:08:55","modified_gmt":"2021-01-09T18:08:55","slug":"exercise-4-solution","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/chapter\/exercise-4-solution\/","title":{"raw":"Exercise 4 - Solution","rendered":"Exercise 4 – Solution"},"content":{"raw":"

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

    \r\n \t
  1. Original system<\/li>\r\n \t
  2. The system can be stretched by a factor of 5 in the y<\/em> direction to account for the anisotropy because 2250.5<\/sup>\/90.5<\/sup> = 15 \/ 3 = 5<\/li>\r\n \t
  3. A flow net is sketched in the transformed image as if the system is isotropic<\/li>\r\n \t
  4. The system is transformed back to 1\/5 the width to reveal the flow lines in the anisotropic system<\/li>\r\n<\/ol>\r\n

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

    Contour interval = (200 m) \/ (8 head drops) = 25 m<\/p>\r\n

    [latex]\\displaystyle Q_{total}=KHw\\frac{n_{f}}{n_{d}}a_{r}[\/latex]<\/span><\/p>\r\n

    The aspect ratio is one, so a<\/em>r<\/em><\/sub> = 1<\/p>\r\n

    K<\/em>equivalent<\/em><\/sub> for an anisotropic flow net<\/em><\/sub> = (K<\/em>x<\/em><\/sub>K<\/em>y<\/em><\/sub>)0.5 <\/sup>= ((225 m\/d)(9 m\/d))0.5 <\/sup>= 45 m\/d<\/p>\r\n

    Q<\/em>total<\/em><\/sub> =<\/em> (45 m\/d) (200 m) (100 m) (12 flow tubes) \/ (8 head drops) = 1,350,000 m3<\/sup>\/d<\/p>\r\n

    Return<\/span> to Exercise 4<\/span><\/a><\/p>","rendered":"

    \"Figure<\/p>\n

      \n
    1. Original system<\/li>\n
    2. The system can be stretched by a factor of 5 in the y<\/em> direction to account for the anisotropy because 2250.5<\/sup>\/90.5<\/sup> = 15 \/ 3 = 5<\/li>\n
    3. A flow net is sketched in the transformed image as if the system is isotropic<\/li>\n
    4. The system is transformed back to 1\/5 the width to reveal the flow lines in the anisotropic system<\/li>\n<\/ol>\n

      \"solution<\/p>\n

      Contour interval = (200 m) \/ (8 head drops) = 25 m<\/p>\n

      \"\displaystyle Q_{total}=KHw\frac{n_{f}}{n_{d}}a_{r}\"<\/span><\/p>\n

      The aspect ratio is one, so a<\/em>r<\/em><\/sub> = 1<\/p>\n

      K<\/em>equivalent<\/em><\/sub> for an anisotropic flow net<\/em><\/sub> = (K<\/em>x<\/em><\/sub>K<\/em>y<\/em><\/sub>)0.5 <\/sup>= ((225 m\/d)(9 m\/d))0.5 <\/sup>= 45 m\/d<\/p>\n

      Q<\/em>total<\/em><\/sub> =<\/em> (45 m\/d) (200 m) (100 m) (12 flow tubes) \/ (8 head drops) = 1,350,000 m3<\/sup>\/d<\/p>\n

      Return<\/span> to Exercise 4<\/span><\/a><\/p>\n","protected":false},"author":1,"menu_order":27,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-115","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\/115","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":6,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/115\/revisions"}],"predecessor-version":[{"id":382,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/pressbooks\/v2\/chapters\/115\/revisions\/382"}],"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\/115\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/media?parent=115"}],"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=115"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/contributor?post=115"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-json\/wp\/v2\/license?post=115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}