Groundwater discharge is the volumetric flow rate of groundwater through an aquifer.
Total groundwater discharge, as reported through a specified area, is similarly expressed as:
Q=
| dh | |
| dl |
KA
Q is the total groundwater discharge ([L<sup>3</sup>·T<sup>−1</sup>]; m3/s),
K is the hydraulic conductivity of the aquifer ([L·T<sup>−1</sup>]; m/s),
dh/dl is the hydraulic gradient ([L·L<sup>−1</sup>]; unitless), and
A is the area which the groundwater is flowing through ([L<sup>2</sup>]; m2)
For example, this can be used to determine the flow rate of water flowing along a plane with known geometry.
The discharge potential is a potential in groundwater mechanics which links the physical properties, hydraulic head, with a mathematical formulation for the energy as a function of position. The discharge potential, [L<sup>3</sup>·T<sup>−1</sup>], is defined in such way that its gradient equals the discharge vector.[1]
Qx=-
| \partial\Phi | |
| \partialx |
Qy=-
| \partial\Phi | |
| \partialy |
Thus the hydraulic head may be calculated in terms of the discharge potential, for confined flow as
\Phi=KH\phi
and for unconfined shallow flow as
\Phi=
| 1 | |
| 2 |
K\phi2+C
where
is the thickness of the aquifer [L],
is the hydraulic head [L], and
is an arbitrary constant [L<sup>3</sup>·T<sup>−1</sup>] given by the boundary conditions.
As mentioned the discharge potential may also be written in terms of position. The discharge potential is a function of the Laplace's equation
| \partial2\Phi | |
| \partialx2 |
+
| \partial2\Phi | |
| \partialy2 |
=0
which solution is a linear differential equation. Because the solution is a linear differential equation for which superposition principle holds, it may be combined with other solutions for the discharge potential, e.g. uniform flow, multiple wells, analytical elements (analytic element method).