{"id":1138,"date":"2026-05-12T21:46:21","date_gmt":"2026-05-12T21:46:21","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/introduction-4\/"},"modified":"2026-05-13T03:11:02","modified_gmt":"2026-05-13T03:11:02","slug":"introduction-4","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/introduction-4\/","title":{"raw":"5.1 Introduction","rendered":"5.1 Introduction"},"content":{"raw":"
\r\n
\r\n\r\nIn Section 4 we discuss equations in general and introduced the main groundwater flow equation, which is shown here as Equation\u00a0(37)<\/span><\/a>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]\\frac{{\\partial q}_{x}}{\\partial x} + \\frac{{\\partial q}_{y}}{\\partial y} + \\frac{{\\partial q}_{z}}{\\partial z} = S_{s}\\frac{\\partial h}{\\partial t}[\/latex]<\/th>\r\n(37)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere (parameter dimensions are dark green font with mass as M, length as L, time as T):\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]q[\/latex]<\/th>\r\n=<\/th>\r\nspecific discharge (i.e., groundwater flow) in the x, y, or z direction (LT-1<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]h[\/latex]<\/td>\r\n=<\/td>\r\nhydraulic head (L)<\/td>\r\n<\/tr>\r\n
[latex]t[\/latex]<\/td>\r\n=<\/td>\r\ntime (T)<\/td>\r\n<\/tr>\r\n
[latex]x[\/latex],<\/em> [latex]y[\/latex],<\/em> [latex]z[\/latex]<\/td>\r\n=<\/td>\r\nlengths in the principal directions in our coordinate systems<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\nWe also substituted Darcy\u2019s law, shown as Equation\u00a0(38)<\/span><\/a> for [latex]q[\/latex], and to get Equation\u00a0(39<\/span><\/a>).\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]q = - K\\frac{dh}{dl}[\/latex]<\/th>\r\n(38)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere (parameter dimensions are dark green font with mass as M, length as L, time as T):\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n
[latex]K[\/latex]<\/th>\r\n=<\/th>\r\nhydraulic conductivity (LT-1<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]\\frac{dh}{dl}[\/latex]<\/td>\r\n=<\/td>\r\nhydraulic gradient, or change in head with length (:)<\/td>\r\n<\/tr>\r\n
<\/td>\r\n[latex]\\frac{\\partial\\left( K_{x}\\frac{\\partial h}{\\partial x} \\right)}{\\partial x} + \\frac{\\partial\\left( K_{y}\\frac{\\partial h}{\\partial y} \\right)}{\\partial y} + \\frac{\\partial\\left( K_{z}\\frac{\\partial h}{\\partial z} \\right)}{\\partial z} = S_{s}\\frac{\\partial h}{\\partial t}[\/latex]<\/td>\r\n(39)<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n[latex]S_{s}[\/latex] is a storage parameter called the specific storage.<\/em> It is a coefficient that relates changes in head in an aquifer to the change in the amount of water stored in the aquifer at a certain point. In other words, it is a quantity that tells us how much water that a unit volume of aquifer can yield for a unit decline in head. The term to the right of the equal sign in Equation\u00a0(39)<\/span><\/a> is equivalent to [latex]\\mathrm{\\Delta}S\/\\mathrm{\\Delta}T[\/latex] of Equation\u00a0(1)<\/span><\/a>\u2014that is, it represents the change in storage with respect to time<\/em>. As stated in Section 5, Equation\u00a0(39)<\/span><\/a> is another way of expressing the continuity equation.\r\n\r\n<\/div>\r\n
\r\n\r\nIn this section, we discuss storage parameters in general and how they relate to confined versus unconfined aquifer conditions. We also discuss transient versus steady-state conditions in dynamic systems like aquifers.\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

In Section 4 we discuss equations in general and introduced the main groundwater flow equation, which is shown here as Equation\u00a0(37)<\/span><\/a>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]\\frac{{\\partial q}_{x}}{\\partial x} + \\frac{{\\partial q}_{y}}{\\partial y} + \\frac{{\\partial q}_{z}}{\\partial z} = S_{s}\\frac{\\partial h}{\\partial t}[\/latex]<\/th>\n(37)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where (parameter dimensions are dark green font with mass as M, length as L, time as T):<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n
[latex]q[\/latex]<\/th>\n=<\/th>\nspecific discharge (i.e., groundwater flow) in the x, y, or z direction (LT-1<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n
[latex]h[\/latex]<\/td>\n=<\/td>\nhydraulic head (L)<\/td>\n<\/tr>\n
[latex]t[\/latex]<\/td>\n=<\/td>\ntime (T)<\/td>\n<\/tr>\n
[latex]x[\/latex],<\/em> [latex]y[\/latex],<\/em> [latex]z[\/latex]<\/td>\n=<\/td>\nlengths in the principal directions in our coordinate systems<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

We also substituted Darcy\u2019s law, shown as Equation\u00a0(38)<\/span><\/a> for [latex]q[\/latex], and to get Equation\u00a0(39<\/span><\/a>).<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]q = - K\\frac{dh}{dl}[\/latex]<\/th>\n(38)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where (parameter dimensions are dark green font with mass as M, length as L, time as T):<\/p>\n<\/div>\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
[latex]K[\/latex]<\/th>\n=<\/th>\nhydraulic conductivity (LT-1<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n
[latex]\\frac{dh}{dl}[\/latex]<\/td>\n=<\/td>\nhydraulic gradient, or change in head with length (:)<\/td>\n<\/tr>\n
<\/td>\n[latex]\\frac{\\partial\\left( K_{x}\\frac{\\partial h}{\\partial x} \\right)}{\\partial x} + \\frac{\\partial\\left( K_{y}\\frac{\\partial h}{\\partial y} \\right)}{\\partial y} + \\frac{\\partial\\left( K_{z}\\frac{\\partial h}{\\partial z} \\right)}{\\partial z} = S_{s}\\frac{\\partial h}{\\partial t}[\/latex]<\/td>\n(39)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

[latex]S_{s}[\/latex] is a storage parameter called the specific storage.<\/em> It is a coefficient that relates changes in head in an aquifer to the change in the amount of water stored in the aquifer at a certain point. In other words, it is a quantity that tells us how much water that a unit volume of aquifer can yield for a unit decline in head. The term to the right of the equal sign in Equation\u00a0(39)<\/span><\/a> is equivalent to [latex]\\mathrm{\\Delta}S\/\\mathrm{\\Delta}T[\/latex] of Equation\u00a0(1)<\/span><\/a>\u2014that is, it represents the change in storage with respect to time<\/em>. As stated in Section 5, Equation\u00a0(39)<\/span><\/a> is another way of expressing the continuity equation.<\/p>\n<\/div>\n

\n

In this section, we discuss storage parameters in general and how they relate to confined versus unconfined aquifer conditions. We also discuss transient versus steady-state conditions in dynamic systems like aquifers.<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":14,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1138","chapter","type-chapter","status-publish","hentry"],"part":1480,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1138\/revisions"}],"predecessor-version":[{"id":1719,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1138\/revisions\/1719"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1480"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1138\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1138"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1138"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1138"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}