{"id":51,"date":"2020-10-14T23:36:55","date_gmt":"2020-10-14T23:36:55","guid":{"rendered":"https:\/\/books.gw-project.org\/groundwater-resource-development\/chapter\/water-balance\/"},"modified":"2020-12-14T19:00:07","modified_gmt":"2020-12-14T19:00:07","slug":"water-balance","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/groundwater-resource-development\/chapter\/water-balance\/","title":{"raw":"3.2 Water Balance","rendered":"3.2 Water Balance"},"content":{"raw":"Conservation of mass is a basic principle for understanding groundwater flow. Combining this principle (as a continuity equation) with Darcy\u2019s Law yields a partial differential equation describing changes in head and flux through a groundwater system in response to stresses and boundary conditions. This is discussed in another Groundwater Project book<\/a> that describes the principles of groundwater flow, including the groundwater flow equations. We can also present a simpler but useful algebraic equation that describes a water balance in an aquifer. A quantitative global water balance statement for a groundwater system can be expressed as Equation 1:\r\n\r\n\r\n\r\n
<\/td>\r\n\u2206V<\/em>\/\u2206t<\/em> = (R<\/em>0<\/sub> + \u2206R<\/em>t<\/em><\/sub>) \u2013 (D<\/em>0<\/sub> + \u2206D<\/em>t<\/em><\/sub>) \u2013 Q<\/em>t<\/em><\/sub><\/td>\r\n(1)<\/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\r\n\r\n\r\n\r\n
\u2206V<\/em><\/td>\r\n=<\/td>\r\nchange in the volume of water in storage in the aquifer (L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u2206t<\/em><\/td>\r\n=<\/td>\r\nlength of a time increment of interest (T)<\/td>\r\n<\/tr>\r\n
\u2206V<\/em>\/\u2206t<\/em><\/td>\r\n=<\/td>\r\nglobal (aquifer-wide) rate of change in storage (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
R<\/em>0<\/sub><\/td>\r\n=<\/td>\r\ntotal recharge rate into the undisturbed natural system (the virgin recharge) (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
\u0394R<\/em>t<\/em><\/sub><\/td>\r\n=<\/td>\r\nglobal change in recharge caused by the pumping (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
D<\/em>0<\/sub><\/td>\r\n=<\/td>\r\ntotal discharge rate from the undisturbed system (prior to development) (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
\u0394D<\/em>t<\/em><\/sub><\/td>\r\n=<\/td>\r\nglobal change in discharge caused by the pumping (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
Q<\/em>t<\/em><\/sub><\/td>\r\n=<\/td>\r\nglobal rate of pumping during the time period, t (L3<\/sup>\/T)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"

Conservation of mass is a basic principle for understanding groundwater flow. Combining this principle (as a continuity equation) with Darcy\u2019s Law yields a partial differential equation describing changes in head and flux through a groundwater system in response to stresses and boundary conditions. This is discussed in another Groundwater Project book<\/a> that describes the principles of groundwater flow, including the groundwater flow equations. We can also present a simpler but useful algebraic equation that describes a water balance in an aquifer. A quantitative global water balance statement for a groundwater system can be expressed as Equation 1:<\/p>\n\n\n\n
<\/td>\n\u2206V<\/em>\/\u2206t<\/em> = (R<\/em>0<\/sub> + \u2206R<\/em>t<\/em><\/sub>) \u2013 (D<\/em>0<\/sub> + \u2206D<\/em>t<\/em><\/sub>) \u2013 Q<\/em>t<\/em><\/sub><\/td>\n(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n\n\n\n\n
\u2206V<\/em><\/td>\n=<\/td>\nchange in the volume of water in storage in the aquifer (L3<\/sup>)<\/td>\n<\/tr>\n
\u2206t<\/em><\/td>\n=<\/td>\nlength of a time increment of interest (T)<\/td>\n<\/tr>\n
\u2206V<\/em>\/\u2206t<\/em><\/td>\n=<\/td>\nglobal (aquifer-wide) rate of change in storage (L3<\/sup>\/T)<\/td>\n<\/tr>\n
R<\/em>0<\/sub><\/td>\n=<\/td>\ntotal recharge rate into the undisturbed natural system (the virgin recharge) (L3<\/sup>\/T)<\/td>\n<\/tr>\n
\u0394R<\/em>t<\/em><\/sub><\/td>\n=<\/td>\nglobal change in recharge caused by the pumping (L3<\/sup>\/T)<\/td>\n<\/tr>\n
D<\/em>0<\/sub><\/td>\n=<\/td>\ntotal discharge rate from the undisturbed system (prior to development) (L3<\/sup>\/T)<\/td>\n<\/tr>\n
\u0394D<\/em>t<\/em><\/sub><\/td>\n=<\/td>\nglobal change in discharge caused by the pumping (L3<\/sup>\/T)<\/td>\n<\/tr>\n
Q<\/em>t<\/em><\/sub><\/td>\n=<\/td>\nglobal rate of pumping during the time period, t (L3<\/sup>\/T)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":1,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-51","chapter","type-chapter","status-publish","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapters\/51","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":13,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapters\/51\/revisions"}],"predecessor-version":[{"id":363,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapters\/51\/revisions\/363"}],"part":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/parts\/43"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapters\/51\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/wp\/v2\/media?parent=51"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/pressbooks\/v2\/chapter-type?post=51"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/wp\/v2\/contributor?post=51"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-resource-development\/wp-json\/wp\/v2\/license?post=51"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}