Ground Water Flow Equation

When the fluid mass flows through various porous medium it will follow the physical property and nature of media. With the combination of Darcy’s law and equation of continuity, we can describe the conservation of fluid mass during flow through porous medium

CONFINED AQUIFER

Steady State Flow

Here the flow is taking place in all the three directions. Hence the rate of inflow any elemental control volume is equal to the rate of out flow elementary control volume. Hence for the steady state flow through isotropic and homogeneous medium is given by following equation

This is also called as Laplace’s equation

Transient Flow

The main principle for the flow equation is the rate of flow into any elemental control volume is equal to the time rate of change of fluid mass storage within the element



In special case of horizontal confined aquifer of thickness b, S = Ss b and T = Kb, then the above equation simplified as



UNCONFINED AQUIFER

Transient flow in unconfined aquifer

Here the flow distributions govern by the water table shape. To find a solution Dupit’s given two assumptions

Flow line are horizontal, equi potential lines are vertical
The horizontal k is equal to the slope of the free surface and is invariant with depth



Solution for Ground Water Flow Equation

To solve the flow equation either analytical or numerical methods are used. In analytical methods the actual filed conditions are so complex, it becomes to obtain solution, whereas the numerical solutions are much more versatile and with widespread availability of computer, they are much easier to use than complex analytical methods

In general numerical methods, such as the finite element method (FEM) and Integrate finite difference method (IFDM) are most commonly used.

While solving the groundwater flow equation is more real time problem, boundary condition have to be considered. Basically three-boundary condition, such as variable head boundary, constant head and no flow boundary exists.