Laplace's Equation

Laplace’s equation is fundamental to the analysis of many groundwater flow problems. It arises from the combination of Darcy’s law and the equation of continuity or conservation of mass for a homogeneous isotropic aquifer. 

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Dupuit-Forchheimer Assumptions

For some of the 2D flow problems, one component of the flow can be neglected with respect to the other. In particular, in some unconfined flows with a free surface, the vertical component of the flow can be neglected. This approximation pioneered by Dupuit (1863) and utilized later by Forchheimer (1930) is known as the Dupuit–Forchheimer assumption. It gives reasonable results when the depth of the unconfined flow is shallow and the slope of the free surface is small. These assumptions are summarized as follows:

Groundwater Movement

Movement occurs from higher hydraulic head in recharge areas (natural or artificial), where precipitation is generally higher, to discharge areas of lower hydraulic head (wells, springs, rivers, lakes, and wetlands). (dh in Figure.1.). The reason is Gravity. Gravity is driving force that moves groundwater. The quantity of groundwater movement through porous media is controlled by Darcy’s law.