Groundwater Flow Equation

Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields.

The groundwater flow equation is often derived for a small representative elemental volume (REV), where the properties of the medium are assumed to be effectively constant. A mass balance is done on the water flowing in and out of this small volume, the flux terms in the relationship being expressed in terms of head by using the constituitive equation called Darcy's law, which requires that the flow is slow.

Read more about Groundwater Flow EquationMass Balance, Diffusion Equation (transient Flow), Laplace Equation (steady-state Flow), Two-dimensional Groundwater Flow

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MODFLOW - Groundwater Flow Equation - Limitations
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... The above groundwater flow equations are valid for three dimensional flow ... In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition in ... An alternative formulation of the groundwater flow equation may be obtained by invoking the Dupuit assumption (or Dupuit-Forcheimer assumption), where it is assumed that heads do not vary in the ...
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Hydrogeology - Calculation of Groundwater Flow
... To use the groundwater flow equation to estimate the distribution of hydraulic heads, or the direction and rate of groundwater flow, this partial differential equation (PDE) must be solved ... The most common means of analytically solving the diffusion equation in the hydrogeology literature are Laplace, Hankel and Fourier transforms (to reduce the ... No matter which method we use to solve the groundwater flow equation, we need both initial conditions (heads at time (t) = 0) and boundary conditions (representing ...
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