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:

${\displaystyle Q={\frac {dh}{dl))KA}$

where

Q is the total groundwater discharge ([L³·T⁻¹]; m³/s),

K is the hydraulic conductivity of the aquifer ([L·T⁻¹]; m/s),

dh/dl is the hydraulic gradient ([L·L⁻¹]; unitless), and

A is the area which the groundwater is flowing through ([L²]; m²)

For example, this can be used to determine the flow rate of water flowing along a plane with known geometry.

The discharge potential

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, ${\textstyle \Phi }$ [L³·T⁻¹], is defined in such way that its gradient equals the discharge vector.^[1]

${\displaystyle Q_{x}=-{\frac {\partial \Phi }{\partial x))}$

${\displaystyle Q_{y}=-{\frac {\partial \Phi }{\partial y))}$

Thus the hydraulic head may be calculated in terms of the discharge potential, for confined flow as

${\displaystyle \Phi =KH\phi }$

and for unconfined shallow flow as

${\displaystyle \Phi ={\frac {1}{2))K\phi ^{2}+C}$

where

${\textstyle H}$ is the thickness of the aquifer [L],

${\textstyle \phi }$ is the hydraulic head [L], and

${\textstyle C}$ is an arbitrary constant [L³·T⁻¹] 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

${\displaystyle {\frac {\partial ^{2}\Phi }{\partial x^{2))}+{\frac {\partial ^{2}\Phi }{\partial y^{2))}=0}$

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).