{"id":159,"date":"2022-12-30T18:28:53","date_gmt":"2022-12-30T18:28:53","guid":{"rendered":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/?post_type=part&p=159"},"modified":"2023-01-08T01:50:03","modified_gmt":"2023-01-08T01:50:03","slug":"notations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/part\/notations\/","title":{"raw":"12 Notations","rendered":"12 Notations"},"content":{"raw":"
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
C<\/em><\/td>\r\nsolute concentration (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
c<\/em>\u00a0and\u00a0c<\/em>s<\/em><\/sub><\/td>\r\nspecific heat capacities of the groundwater and rock, respectively (ML2<\/sup>\/(T2<\/sup>\u0398))<\/td>\r\n<\/tr>\r\n
C<\/em>0<\/sub><\/td>\r\ninitial concentration of the groundwater (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
C<\/em>i<\/em><\/sub><\/td>\r\nconcentration species i<\/em> (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
C<\/em>i<\/em>,0<\/sub><\/td>\r\nreference concentration of species i<\/em> (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
c<\/em>P<\/em><\/sub><\/td>\r\nvolumetric heat capacity (M\/(LT2<\/sup>\u0398))<\/td>\r\n<\/tr>\r\n
C<\/em>ss<\/em><\/sub><\/td>\r\nconcentration associated with a source (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
D<\/em><\/td>\r\ndiffusion coefficient (L2<\/sup>\/T); for solutes, D<\/em>=D<\/em>C<\/em><\/sub> the molecular diffusion coefficient; for heat, D<\/em>=D<\/em>T<\/em><\/sub> the thermal diffusion coefficient<\/td>\r\n<\/tr>\r\n
[latex]\\overline{D_{h,C}}[\/latex]<\/td>\r\nsolute dispersion tensor (L2<\/sup>\/T) which includes the effect of both molecular diffusion and mechanical dispersion<\/td>\r\n<\/tr>\r\n
D<\/em>C<\/em><\/sub><\/td>\r\nsolute diffusion coefficient in the bulk medium which is decreased from the diffusion coefficient in open water by the factors of connected porosity (n<\/em>) and tortuosity (\u03c4<\/em>) (L2<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
\u0394C<\/em><\/td>\r\nconcentration difference (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0394\u03c1<\/em><\/td>\r\ndensity difference (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u2206T<\/em><\/td>\r\ntemperature difference (\u0398)<\/td>\r\n<\/tr>\r\n
D<\/em>T<\/em><\/sub><\/td>\r\nthermal diffusivity (L2<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
[latex]\\overline{D_{C}}[\/latex]<\/td>\r\ndispersion tensor which includes the combined effects of thermal conduction and mechanical dispersion (L2<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
g<\/em><\/td>\r\ngravitational acceleration (L\/T2<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]\\vec{g}[\/latex]<\/td>\r\ngravitational acceleration vector (L\/T2<\/sup>)<\/td>\r\n<\/tr>\r\n
H<\/em><\/td>\r\nthickness of the layer (L)<\/td>\r\n<\/tr>\r\n
h<\/em>p<\/em><\/sub><\/td>\r\npressure head (L)<\/td>\r\n<\/tr>\r\n
h<\/em>p,i<\/em><\/sub><\/td>\r\npressure head for a piezometer at location i<\/em> containing a fluid column with density \u03c1<\/em>i<\/em><\/sub> (L)<\/td>\r\n<\/tr>\r\n
[latex]\\vec{J}_{C}[\/latex]<\/td>\r\nsolute mass flux (M\/(L2<\/sup>T))<\/td>\r\n<\/tr>\r\n
[latex]\\vec{J}_{e}[\/latex]<\/td>\r\nheat flux (M\/T3<\/sup>)<\/td>\r\n<\/tr>\r\n
k <\/em><\/td>\r\nintrinsic permeability (L2<\/sup>)<\/td>\r\n<\/tr>\r\n
K<\/em>d<\/em><\/sub><\/td>\r\ndistribution coefficient (L3<\/sup>\/M)<\/td>\r\n<\/tr>\r\n
k<\/em>T<\/em><\/sub><\/td>\r\nthermal conductivity (ML\/(T3<\/sup>\u0398))<\/td>\r\n<\/tr>\r\n
\u03bc <\/em><\/td>\r\ndynamic viscosity (M\/(LT))<\/td>\r\n<\/tr>\r\n
n<\/em><\/td>\r\nporosity (dimensionless)<\/td>\r\n<\/tr>\r\n
\u2207<\/td>\r\ngradient operator which represents the rate of change of a variable per unit of distance in the x<\/em>, y<\/em> and z<\/em> direction<\/td>\r\n<\/tr>\r\n
NS<\/em><\/td>\r\ntotal number of solutes that contribute to the fluid density<\/td>\r\n<\/tr>\r\n
p<\/em><\/td>\r\npressure (M\/(LT2<\/sup>))<\/td>\r\n<\/tr>\r\n
p<\/em>0<\/em><\/sub><\/td>\r\ninitial fluid pressure (M\/(LT2<\/sup>))<\/td>\r\n<\/tr>\r\n
[latex]\\displaystyle \\left ( \\frac{\\partial \\rho }{\\partial C} \\right )_{i}[\/latex]<\/td>\r\nslope of the density-concentration relationship for species i<\/em><\/td>\r\n<\/tr>\r\n
[latex]\\vec{q}[\/latex]<\/td>\r\nspecific discharge (L\/T)<\/td>\r\n<\/tr>\r\n
Q<\/em>h<\/em><\/sub><\/td>\r\nheat flow across the source boundary (M\/T3<\/sup>)<\/td>\r\n<\/tr>\r\n
Q<\/em>m<\/em><\/sub><\/td>\r\nmass flux across the source boundary (M\/(TL2<\/sup>))<\/td>\r\n<\/tr>\r\n
q<\/em>ss<\/em><\/sub><\/td>\r\ndischarge rate per unit of volume of water source, or sink (1\/T)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em><\/td>\r\ngroundwater density (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em>0<\/sub><\/td>\r\ndensity of the fluid at initial concentration, temperature and pressure (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em>b<\/em><\/sub><\/td>\r\ndry bulk density of the rock (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em>r<\/em><\/sub><\/td>\r\ndensity of the rock (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1ss<\/em><\/sub><\/td>\r\ndensity of water source, or sink (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
t<\/em><\/td>\r\ntime (T)<\/td>\r\n<\/tr>\r\n
T <\/em><\/td>\r\ntemperature (\u0398)<\/td>\r\n<\/tr>\r\n
T<\/em>0<\/em><\/sub><\/td>\r\ninitial temperature of the groundwater (\u0398)<\/td>\r\n<\/tr>\r\n
T<\/em>s<\/em><\/sub>s<\/em><\/sub><\/td>\r\ntemperature associated with a source (\u0398)<\/td>\r\n<\/tr>\r\n
z<\/em><\/td>\r\nelevation relative to a datum (L)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>","rendered":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
C<\/em><\/td>\nsolute concentration (M\/L3<\/sup>)<\/td>\n<\/tr>\n
c<\/em>\u00a0and\u00a0c<\/em>s<\/em><\/sub><\/td>\nspecific heat capacities of the groundwater and rock, respectively (ML2<\/sup>\/(T2<\/sup>\u0398))<\/td>\n<\/tr>\n
C<\/em>0<\/sub><\/td>\ninitial concentration of the groundwater (M\/L3<\/sup>)<\/td>\n<\/tr>\n
C<\/em>i<\/em><\/sub><\/td>\nconcentration species i<\/em> (M\/L3<\/sup>)<\/td>\n<\/tr>\n
C<\/em>i<\/em>,0<\/sub><\/td>\nreference concentration of species i<\/em> (M\/L3<\/sup>)<\/td>\n<\/tr>\n
c<\/em>P<\/em><\/sub><\/td>\nvolumetric heat capacity (M\/(LT2<\/sup>\u0398))<\/td>\n<\/tr>\n
C<\/em>ss<\/em><\/sub><\/td>\nconcentration associated with a source (M\/L3<\/sup>)<\/td>\n<\/tr>\n
D<\/em><\/td>\ndiffusion coefficient (L2<\/sup>\/T); for solutes, D<\/em>=D<\/em>C<\/em><\/sub> the molecular diffusion coefficient; for heat, D<\/em>=D<\/em>T<\/em><\/sub> the thermal diffusion coefficient<\/td>\n<\/tr>\n
\"\overline{D_{h,C}}\"<\/td>\nsolute dispersion tensor (L2<\/sup>\/T) which includes the effect of both molecular diffusion and mechanical dispersion<\/td>\n<\/tr>\n
D<\/em>C<\/em><\/sub><\/td>\nsolute diffusion coefficient in the bulk medium which is decreased from the diffusion coefficient in open water by the factors of connected porosity (n<\/em>) and tortuosity (\u03c4<\/em>) (L2<\/sup>\/T)<\/td>\n<\/tr>\n
\u0394C<\/em><\/td>\nconcentration difference (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u0394\u03c1<\/em><\/td>\ndensity difference (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u2206T<\/em><\/td>\ntemperature difference (\u0398)<\/td>\n<\/tr>\n
D<\/em>T<\/em><\/sub><\/td>\nthermal diffusivity (L2<\/sup>\/T)<\/td>\n<\/tr>\n
\"\overline{D_{C}}\"<\/td>\ndispersion tensor which includes the combined effects of thermal conduction and mechanical dispersion (L2<\/sup>\/T)<\/td>\n<\/tr>\n
g<\/em><\/td>\ngravitational acceleration (L\/T2<\/sup>)<\/td>\n<\/tr>\n
\"\vec{g}\"<\/td>\ngravitational acceleration vector (L\/T2<\/sup>)<\/td>\n<\/tr>\n
H<\/em><\/td>\nthickness of the layer (L)<\/td>\n<\/tr>\n
h<\/em>p<\/em><\/sub><\/td>\npressure head (L)<\/td>\n<\/tr>\n
h<\/em>p,i<\/em><\/sub><\/td>\npressure head for a piezometer at location i<\/em> containing a fluid column with density \u03c1<\/em>i<\/em><\/sub> (L)<\/td>\n<\/tr>\n
\"\vec{J}_{C}\"<\/td>\nsolute mass flux (M\/(L2<\/sup>T))<\/td>\n<\/tr>\n
\"\vec{J}_{e}\"<\/td>\nheat flux (M\/T3<\/sup>)<\/td>\n<\/tr>\n
k <\/em><\/td>\nintrinsic permeability (L2<\/sup>)<\/td>\n<\/tr>\n
K<\/em>d<\/em><\/sub><\/td>\ndistribution coefficient (L3<\/sup>\/M)<\/td>\n<\/tr>\n
k<\/em>T<\/em><\/sub><\/td>\nthermal conductivity (ML\/(T3<\/sup>\u0398))<\/td>\n<\/tr>\n
\u03bc <\/em><\/td>\ndynamic viscosity (M\/(LT))<\/td>\n<\/tr>\n
n<\/em><\/td>\nporosity (dimensionless)<\/td>\n<\/tr>\n
\u2207<\/td>\ngradient operator which represents the rate of change of a variable per unit of distance in the x<\/em>, y<\/em> and z<\/em> direction<\/td>\n<\/tr>\n
NS<\/em><\/td>\ntotal number of solutes that contribute to the fluid density<\/td>\n<\/tr>\n
p<\/em><\/td>\npressure (M\/(LT2<\/sup>))<\/td>\n<\/tr>\n
p<\/em>0<\/em><\/sub><\/td>\ninitial fluid pressure (M\/(LT2<\/sup>))<\/td>\n<\/tr>\n
\"\displaystyle \left ( \frac{\partial \rho }{\partial C} \right )_{i}\"<\/td>\nslope of the density-concentration relationship for species i<\/em><\/td>\n<\/tr>\n
\"\vec{q}\"<\/td>\nspecific discharge (L\/T)<\/td>\n<\/tr>\n
Q<\/em>h<\/em><\/sub><\/td>\nheat flow across the source boundary (M\/T3<\/sup>)<\/td>\n<\/tr>\n
Q<\/em>m<\/em><\/sub><\/td>\nmass flux across the source boundary (M\/(TL2<\/sup>))<\/td>\n<\/tr>\n
q<\/em>ss<\/em><\/sub><\/td>\ndischarge rate per unit of volume of water source, or sink (1\/T)<\/td>\n<\/tr>\n
\u03c1<\/em><\/td>\ngroundwater density (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u03c1<\/em>0<\/sub><\/td>\ndensity of the fluid at initial concentration, temperature and pressure (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u03c1<\/em>b<\/em><\/sub><\/td>\ndry bulk density of the rock (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u03c1<\/em>r<\/em><\/sub><\/td>\ndensity of the rock (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u03c1ss<\/em><\/sub><\/td>\ndensity of water source, or sink (M\/L3<\/sup>)<\/td>\n<\/tr>\n
t<\/em><\/td>\ntime (T)<\/td>\n<\/tr>\n
T <\/em><\/td>\ntemperature (\u0398)<\/td>\n<\/tr>\n
T<\/em>0<\/em><\/sub><\/td>\ninitial temperature of the groundwater (\u0398)<\/td>\n<\/tr>\n
T<\/em>s<\/em><\/sub>s<\/em><\/sub><\/td>\ntemperature associated with a source (\u0398)<\/td>\n<\/tr>\n
z<\/em><\/td>\nelevation relative to a datum (L)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"parent":0,"menu_order":12,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-159","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/159","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":7,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/159\/revisions"}],"predecessor-version":[{"id":335,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/159\/revisions\/335"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/media?parent=159"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=159"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/license?post=159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}