Total groundwater discharge, as reported through a specified area, is similarly expressed as:
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, [L3·T−1], is defined in such way that its gradient equals the discharge vector.
Thus the hydraulic head may be calculated in terms of the discharge potential, for confined flow as
and for unconfined shallow flow as
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).