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, [L3·T−1], is defined in such way that its gradient equals the discharge vector.[1]
Thus the hydraulic head may be calculated in terms of the discharge potential, for confined flow as
and for unconfined shallow flow as
where
is the thickness of the aquifer [L],
is the hydraulic head [L], and
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
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).