A is the area which the groundwater is flowing through ([L^{2}]; m^{2})

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

The discharge potential

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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, ${\textstyle \Phi }$ [L^{3}·T^{−1}], is defined in such way that its gradient equals the discharge vector.^{[1]}

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

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

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

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

where

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

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

${\textstyle C}$ is an arbitrary constant [L^{3}·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

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).

^Strack, Otto D. L. (2017). Analytical Groundwater Mechanics. Cambridge: Cambridge University Press. doi:10.1017/9781316563144. ISBN 978-1-316-56314-4.

Freeze, R.A. & Cherry, J.A., 1979. Groundwater, Prentice-Hall. ISBN 0-13-365312-9