{"id":889,"date":"2020-12-09T05:01:05","date_gmt":"2020-12-09T05:01:05","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/?post_type=chapter&p=889"},"modified":"2020-12-29T18:35:42","modified_gmt":"2020-12-29T18:35:42","slug":"solution-to-exercise-4","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/chapter\/solution-to-exercise-4\/","title":{"raw":"Solution to Exercise 4","rendered":"Solution to Exercise 4"},"content":{"raw":"4) A regional unconfined sand aquifer was developed during 1990. As a result of the extraction of water the water table dropped about 40 m over a 1 square km area. If the porosity is 34% and the specific retention is 12%, how much water (m3<\/sup>) was withdrawn from the impacted area? How might this volume differ if the aquifer were a 100 m thick confined sand with water at a temperature of 8\u00b0C?\r\n\r\nCalculate the volume by using Equation 48 of this book.\r\n\r\n\r\n\r\n
Volume of Unconfined Water Drained<\/em> = S<\/em>y<\/em><\/sub>A<\/em>\u2206h<\/em><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Volume<\/em><\/td>\r\n=<\/td>\r\nvolume drained from an unconfined aquifer over an area, A<\/em>, for a water table elevation change of \u2206h<\/em> (L3<\/sup>)<\/td>\r\n<\/tr>\r\n
S<\/em>y<\/em><\/sub><\/td>\r\n=<\/td>\r\nspecific yield (dimensionless)<\/td>\r\n<\/tr>\r\n
A<\/em><\/td>\r\n=<\/td>\r\narea over which the water table changes (L2<\/sup>)<\/td>\r\n<\/tr>\r\n
\u2206h<\/em><\/td>\r\n=<\/td>\r\nchange in water table elevation (L)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nS<\/em>y<\/em><\/sub> can be determined as n<\/em>e<\/em><\/sub> - S<\/em>r<\/em><\/sub> as shown by Equation 13 of this book.\r\n\r\n\r\n\r\n\r\n\r\n
[latex]\\displaystyle n_e=\\ S_y+\\ S_r[\/latex]<\/td>\r\n<\/tr>\r\n
Volume of Unconfined Water Drained = (0.34 - 0.12) 1000m 1000m 40m<\/td>\r\n<\/tr>\r\n
Volume from Unconfined Aquifer = 8,800,000 m3<\/sup> = 8.8 million m3<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIf the aquifer were a 100-meter thick confined sand\r\n\r\n\r\n\r\n
S<\/em>s<\/em><\/sub> = \u03c1g<\/em> (\u03b1<\/em> + n<\/em>e<\/em><\/sub>\u03b2<\/em>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n\r\n
S<\/em>s<\/em><\/sub><\/td>\r\n=<\/td>\r\nspecific storage (1\/L)<\/td>\r\n<\/tr>\r\n
\u03b1<\/em><\/td>\r\n=<\/td>\r\ncompressibility of the aquifer solid structure (T2<\/sup>L\/M)<\/td>\r\n<\/tr>\r\n
n<\/em>e<\/em><\/sub><\/td>\r\n=<\/td>\r\neffective porosity (dimensionless)<\/td>\r\n<\/tr>\r\n
\u03b2<\/em><\/td>\r\n=<\/td>\r\ncompressibility of water (T2<\/sup>L\/M)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nUse a compressibility value for sand found in Table 4<\/a> and a density for 8\u00b0C water from Figure 28<\/a> in this book.\r\n\r\n\r\n\r\n\r\n
[latex]\\displaystyle S_s=\\left(1000\\frac{\\textup{kg}}{\\textup{m}^3}\\right)\\left(9.8\\frac{\\textup{m}}{{\\textup{s}}^2}\\right)\\ \\left({1\\times 10}^{-8}\\frac{\\textup{m}^2}{\\frac{\\textup{kg}\\ \\textup{m}}{{\\textup{s}}^2}}\\ +\\left(0.34\\right)\\ \\left(4.4\\times 10^{-10}\\frac{\\textup{m}^2}{\\frac{\\textup{kg}\\ \\textup{m}}{{\\textup{s}}^2}}\\right)\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
[latex]\\displaystyle S_{s}=\\frac{1\\times 10^{-4}}{\\textup{m}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEquation 49 of this book is used to determine storativity:\r\n\r\n\r\n\r\n
[latex]\\displaystyle S_{confined}=S_sb=\\left(\\frac{{1\\times10}^{-4}}{\\textup{m}}\\right)\\ 40\\ \\textup{m}=\\ {4\\times10}^{-3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEquation 50 of this book determines the volume.\r\n\r\n\r\n\r\n\r\n\r\n
Volume of Confined Water Drained<\/em> = SA<\/em>\u0394h<\/em><\/td>\r\n<\/tr>\r\n
Volume of Confined Water Drained<\/em> = 4\u00d710-3<\/sup> 1000m 1000m 40m<\/td>\r\n<\/tr>\r\n
Volume of Confined Water Drained<\/em> = 160,000m3<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

4) A regional unconfined sand aquifer was developed during 1990. As a result of the extraction of water the water table dropped about 40 m over a 1 square km area. If the porosity is 34% and the specific retention is 12%, how much water (m3<\/sup>) was withdrawn from the impacted area? How might this volume differ if the aquifer were a 100 m thick confined sand with water at a temperature of 8\u00b0C?<\/p>\n

Calculate the volume by using Equation 48 of this book.<\/p>\n\n\n\n
Volume of Unconfined Water Drained<\/em> = S<\/em>y<\/em><\/sub>A<\/em>\u2206h<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n
Volume<\/em><\/td>\n=<\/td>\nvolume drained from an unconfined aquifer over an area, A<\/em>, for a water table elevation change of \u2206h<\/em> (L3<\/sup>)<\/td>\n<\/tr>\n
S<\/em>y<\/em><\/sub><\/td>\n=<\/td>\nspecific yield (dimensionless)<\/td>\n<\/tr>\n
A<\/em><\/td>\n=<\/td>\narea over which the water table changes (L2<\/sup>)<\/td>\n<\/tr>\n
\u2206h<\/em><\/td>\n=<\/td>\nchange in water table elevation (L)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

S<\/em>y<\/em><\/sub> can be determined as n<\/em>e<\/em><\/sub> – S<\/em>r<\/em><\/sub> as shown by Equation 13 of this book.<\/p>\n\n\n\n\n\n
\"\displaystyle n_e=\ S_y+\ S_r\"<\/td>\n<\/tr>\n
Volume of Unconfined Water Drained = (0.34 – 0.12) 1000m 1000m 40m<\/td>\n<\/tr>\n
Volume from Unconfined Aquifer = 8,800,000 m3<\/sup> = 8.8 million m3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

If the aquifer were a 100-meter thick confined sand<\/p>\n\n\n\n
S<\/em>s<\/em><\/sub> = \u03c1g<\/em> (\u03b1<\/em> + n<\/em>e<\/em><\/sub>\u03b2<\/em>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n
S<\/em>s<\/em><\/sub><\/td>\n=<\/td>\nspecific storage (1\/L)<\/td>\n<\/tr>\n
\u03b1<\/em><\/td>\n=<\/td>\ncompressibility of the aquifer solid structure (T2<\/sup>L\/M)<\/td>\n<\/tr>\n
n<\/em>e<\/em><\/sub><\/td>\n=<\/td>\neffective porosity (dimensionless)<\/td>\n<\/tr>\n
\u03b2<\/em><\/td>\n=<\/td>\ncompressibility of water (T2<\/sup>L\/M)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Use a compressibility value for sand found in Table 4<\/a> and a density for 8\u00b0C water from Figure 28<\/a> in this book.<\/p>\n\n\n\n\n
\"\displaystyle S_s=\left(1000\frac{\textup{kg}}{\textup{m}^3}\right)\left(9.8\frac{\textup{m}}{{\textup{s}}^2}\right)\ \left({1\times 10}^{-8}\frac{\textup{m}^2}{\frac{\textup{kg}\ \textup{m}}{{\textup{s}}^2}}\ +\left(0.34\right)\ \left(4.4\times 10^{-10}\frac{\textup{m}^2}{\frac{\textup{kg}\ \textup{m}}{{\textup{s}}^2}}\right)\right)\"<\/td>\n<\/tr>\n
\"\displaystyle S_{s}=\frac{1\times 10^{-4}}{\textup{m}}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Equation 49 of this book is used to determine storativity:<\/p>\n\n\n\n
\"\displaystyle S_{confined}=S_sb=\left(\frac{{1\times10}^{-4}}{\textup{m}}\right)\ 40\ \textup{m}=\ {4\times10}^{-3}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Equation 50 of this book determines the volume.<\/p>\n\n\n\n\n\n
Volume of Confined Water Drained<\/em> = SA<\/em>\u0394h<\/em><\/td>\n<\/tr>\n
Volume of Confined Water Drained<\/em> = 4\u00d710-3<\/sup> 1000m 1000m 40m<\/td>\n<\/tr>\n
Volume of Confined Water Drained<\/em> = 160,000m3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Return to Exercise 4<\/a><\/p>\n","protected":false},"author":1,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-889","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\/889","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":10,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/889\/revisions"}],"predecessor-version":[{"id":1197,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/889\/revisions\/1197"}],"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\/889\/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=889"}],"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=889"},{"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=889"},{"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=889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}