{"id":1536,"date":"2026-05-13T02:54:11","date_gmt":"2026-05-13T02:54:11","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/?post_type=part&#038;p=1536"},"modified":"2026-05-13T03:00:18","modified_gmt":"2026-05-13T03:00:18","slug":"notations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/part\/notations\/","title":{"raw":"24. Notations","rendered":"24. Notations"},"content":{"raw":"<div id=\"notations\" class=\"level1\">\r\n<table style=\"width: 85%;\" data-custom-style=\"Table\"><colgroup> <col style=\"width: 12%;\" \/> <col style=\"width: 3%;\" \/> <col style=\"width: 69%;\" \/> <\/colgroup>\r\n<thead>\r\n<tr>\r\n<th style=\"text-align: right;\"><em>Alpha<\/em>[latex]\\ A[\/latex]<\/th>\r\n<th style=\"text-align: center;\">=<\/th>\r\n<th>cross\u2011sectional area (L<sup>2<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]\\alpha[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>compressibility of the aquifer matrix (LT<sup>2<\/sup>M<sup>-1<\/sup>) , with the exception in the following row<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]\\alpha[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>in section 9.2.4, angle of refraction, also defined in the row above this row<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]b[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>saturated thickness of the aquifer (L), with the exception in the following row<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]b[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>in Sections 16 and 17, aperture (distance between walls of fracture) (L), also defined in the row above this row<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Beta<\/em> [latex]\\beta[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>compressibility of water (LT<sup>2<\/sup>M<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>d<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>number of flow tubes, areas bounded by adjacent pairs of flow lines (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Delta<\/em> [latex]\\mathrm{\\Delta}\\sigma[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>change in effective stress (MLT<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Delta<\/em> [latex]\\mathrm{\\Delta}L\/L[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>change in length (thickness) over the total length (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]\\mathrm{\\Delta}Storage[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>change in storage over time in a system that balances input and output<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]dh\/dl[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic gradient or change in hydraulic head (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]\\partial h\/\\partial x[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic gradient with respect to x (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>e<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>void ratio (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]f[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>number of equipotential drops across a flow net (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]g[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>gravitational acceleration (LT<sup>- 2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>h<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic head (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>head of the backwater above the weir crest in ft<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H_{a}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>heat energy added (L) expressed as height of column of water<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]{\\ H}_{L}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>mechanical energy lost (L) expressed as height of column of water<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H_{E}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>heat energy extracted (L) expressed as height of column of water<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>i<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic gradient (<em>dh\/dl<\/em>) (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Iota I(t)<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>input to a system over time<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>k<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>intrinsic permeability (L<sup>2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>K<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic conductivity (LT<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>L<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>length of the weir crest in ft<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Mu<\/em> [latex]\\mu_{fluid}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>viscosity of the fluid (ML<sup>-1<\/sup>T<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Mu \u03bc<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>viscosity (ML<sup>-1<\/sup>T<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>n<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>porosity ([latex]:[\/latex]), with the exception in the following row<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>n<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>in section 13.5.2, Manning roughness coefficient (:), also defined in the row above<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>\u03c9<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>gravimetric moisture content (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>O(t)<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>output from a system over time<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>p<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]P_{f}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>pore fluid pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]P_{h}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydrostatic pressure; hydrostatic pore fluid pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Phi \u03c6<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>porosity (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Phi<\/em> [latex]\\varphi_{eff}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>effective porosity (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Psi \u03c8<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>matric potential (or negative pressure head) (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Q<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>volumetric discharge (L<sup>3<\/sup>T<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>q<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>specific discharge of groundwater flow (LT<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>q\u2019<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>flow per unit width of aquifer (L<sup>2<\/sup>T<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>r<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>radius (distance from pumping well) (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>R<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>hydraulic radius (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Rho<\/em>[latex]\\ \\rho_{bulk}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>bulk density (ML<sup>-3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Rho<\/em>[latex]\\ \\rho_{fluid}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>density of the fluid (ML<sup>-3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Rho<\/em> [latex]\\ \\rho_{f}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>fluid density (ML<sup>-3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>s<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>drawdown (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>S<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>storativity, [latex]S = S_{s}b[\/latex] (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>S<sub>d<\/sub><\/em>[latex]S_{d}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>degree of saturation (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Sigma<\/em> [latex]\\sigma[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>total vertical stress; also called the normal stress (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Sigma \u03c3\u2019<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>effective stress, or \u201cgrain to grain\u201d stress in the rock (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>Sigma<\/em> [latex]\\sigma_{v}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>vertical stress (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]S_{r}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>specific retention (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]S_{s}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>specific storage (L<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]S_{y}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>specific yield (:)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>\u03b8<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>volumetric moisture content (L<sup>3<\/sup>L<sup>-3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>T<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>aquifer transmissivity, [latex]T\\ = \\ Kb[\/latex] (L<sup>2<\/sup>T<sup>-1<\/sup> )<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>t<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>time (T)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>u<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>excess fluid pressure<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>v<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>velocity (LT<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]v_{avg}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>average linear velocity (LT<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]V_{solids}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>volume of the solids (L<sup>3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]V_{total}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>total volume of the sample ((L<sup>3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\">[latex]V_{voids}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>volume of the voids (L<sup>3<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>w<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>rate of vertical leakage or recharge to the aquifer (LT<sup>-1<\/sup>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>x<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>some distance from [latex]h_{1}\\ ([\/latex]L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>x, y<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>Cartesian coordinates (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>x, y, z<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>lengths in the principal directions in our coordinate systems<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>elevation head (L) , with the exceptions in the two following rows<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>in section 15.3, equation 97, thickness of the layer of material (L), also defined in the row above and below<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\r\n<td style=\"text-align: center;\">=<\/td>\r\n<td>in section 15.3, equations 99 and 100, thickness of the overlying layer of water (L), also defined in the two rows above<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>","rendered":"<div id=\"notations\" class=\"level1\">\n<table style=\"width: 85%;\" data-custom-style=\"Table\">\n<colgroup>\n<col style=\"width: 12%;\" \/>\n<col style=\"width: 3%;\" \/>\n<col style=\"width: 69%;\" \/> <\/colgroup>\n<thead>\n<tr>\n<th style=\"text-align: right;\"><em>Alpha<\/em>[latex]\\ A[\/latex]<\/th>\n<th style=\"text-align: center;\">=<\/th>\n<th>cross\u2011sectional area (L<sup>2<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">[latex]\\alpha[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>compressibility of the aquifer matrix (LT<sup>2<\/sup>M<sup>-1<\/sup>) , with the exception in the following row<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]\\alpha[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>in section 9.2.4, angle of refraction, also defined in the row above this row<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]b[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>saturated thickness of the aquifer (L), with the exception in the following row<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]b[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>in Sections 16 and 17, aperture (distance between walls of fracture) (L), also defined in the row above this row<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Beta<\/em> [latex]\\beta[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>compressibility of water (LT<sup>2<\/sup>M<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>d<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>number of flow tubes, areas bounded by adjacent pairs of flow lines (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Delta<\/em> [latex]\\mathrm{\\Delta}\\sigma[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>change in effective stress (MLT<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Delta<\/em> [latex]\\mathrm{\\Delta}L\/L[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>change in length (thickness) over the total length (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]\\mathrm{\\Delta}Storage[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>change in storage over time in a system that balances input and output<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]dh\/dl[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic gradient or change in hydraulic head (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]\\partial h\/\\partial x[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic gradient with respect to x (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>e<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>void ratio (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]f[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>number of equipotential drops across a flow net (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]g[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>gravitational acceleration (LT<sup>&#8211; 2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>h<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic head (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>head of the backwater above the weir crest in ft<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H_{a}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>heat energy added (L) expressed as height of column of water<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]{\\ H}_{L}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>mechanical energy lost (L) expressed as height of column of water<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Eta<\/em> [latex]H_{E}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>heat energy extracted (L) expressed as height of column of water<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>i<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic gradient (<em>dh\/dl<\/em>) (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Iota I(t)<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>input to a system over time<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>k<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>intrinsic permeability (L<sup>2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>K<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic conductivity (LT<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>L<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>length of the weir crest in ft<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Mu<\/em> [latex]\\mu_{fluid}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>viscosity of the fluid (ML<sup>-1<\/sup>T<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Mu \u03bc<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>viscosity (ML<sup>-1<\/sup>T<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>n<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>porosity ([latex]:[\/latex]), with the exception in the following row<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>n<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>in section 13.5.2, Manning roughness coefficient (:), also defined in the row above<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>\u03c9<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>gravimetric moisture content (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>O(t)<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>output from a system over time<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>p<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]P_{f}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>pore fluid pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]P_{h}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydrostatic pressure; hydrostatic pore fluid pressure (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Phi \u03c6<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>porosity (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Phi<\/em> [latex]\\varphi_{eff}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>effective porosity (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Psi \u03c8<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>matric potential (or negative pressure head) (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Q<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>volumetric discharge (L<sup>3<\/sup>T<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>q<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>specific discharge of groundwater flow (LT<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>q\u2019<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>flow per unit width of aquifer (L<sup>2<\/sup>T<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>r<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>radius (distance from pumping well) (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>R<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>hydraulic radius (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Rho<\/em>[latex]\\ \\rho_{bulk}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>bulk density (ML<sup>-3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Rho<\/em>[latex]\\ \\rho_{fluid}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>density of the fluid (ML<sup>-3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Rho<\/em> [latex]\\ \\rho_{f}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>fluid density (ML<sup>-3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>s<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>drawdown (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>S<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>storativity, [latex]S = S_{s}b[\/latex] (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>S<sub>d<\/sub><\/em>[latex]S_{d}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>degree of saturation (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Sigma<\/em> [latex]\\sigma[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>total vertical stress; also called the normal stress (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Sigma \u03c3\u2019<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>effective stress, or \u201cgrain to grain\u201d stress in the rock (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>Sigma<\/em> [latex]\\sigma_{v}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>vertical stress (ML<sup>-1<\/sup>T<sup>-2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]S_{r}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>specific retention (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]S_{s}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>specific storage (L<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]S_{y}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>specific yield (:)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>\u03b8<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>volumetric moisture content (L<sup>3<\/sup>L<sup>-3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>T<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>aquifer transmissivity, [latex]T\\ = \\ Kb[\/latex] (L<sup>2<\/sup>T<sup>-1<\/sup> )<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>t<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>time (T)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>u<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>excess fluid pressure<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>v<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>velocity (LT<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]v_{avg}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>average linear velocity (LT<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]V_{solids}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>volume of the solids (L<sup>3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]V_{total}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>total volume of the sample ((L<sup>3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">[latex]V_{voids}[\/latex]<\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>volume of the voids (L<sup>3<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>w<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>rate of vertical leakage or recharge to the aquifer (LT<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>x<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>some distance from [latex]h_{1}\\ ([\/latex]L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>x, y<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>Cartesian coordinates (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>x, y, z<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>lengths in the principal directions in our coordinate systems<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>elevation head (L) , with the exceptions in the two following rows<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>in section 15.3, equation 97, thickness of the layer of material (L), also defined in the row above and below<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><em>z<\/em><\/td>\n<td style=\"text-align: center;\">=<\/td>\n<td>in section 15.3, equations 99 and 100, thickness of the overlying layer of water (L), also defined in the two rows above<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"parent":0,"menu_order":24,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1536","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1536","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1536\/revisions"}],"predecessor-version":[{"id":1567,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1536\/revisions\/1567"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1536"}],"wp:term":[{"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=1536"},{"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=1536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}