Groundwater Discharge

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:
:$Q = \fracKA$
where
:''Q'' is the total groundwater discharge ( ³Â·T^−1 m³/s),
:''K'' is the hydraulic conductivity of the aquifer ( ·T^−1 m/s),
:''dh/dl'' is the hydraulic gradient ( ·L^−1 unitless), and
:''A'' is the area which the groundwater is flowing through ( ² 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, $\Phi$ ³Â·T^−1 is defined in such way that its gradient equals the discharge vector.

$Q_x = -\frac$

$Q_y = -\frac$

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

$\Phi = \fracK\phi^2+C$

where

:$H$ is the thickness of the aquifer
:$\phi$ is the hydraulic head and
:$C$ is an arbitrary constant ³Â·T^−1given 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

$\frac + \frac = 0$

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).

See also

*Groundwater flow equation
*Groundwater energy balance
* Submarine groundwater discharge
*Discharge (hydrology)
*Flux (transport definition)
* Darcy's Law

References

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

Hydrology
Aquifers