[(Hydro)(Geo)(Physics)(Science)]

Laplace's Equation

2009-12-09T13:51:00.001+02:00

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

2009-12-07T02:12:00.000+02:00

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:

1. The flow is horizontal at any vertical cross-section.
2. The velocity is constant over the depth.
3. The velocity is calculated using the slope of the free surface as the hydraulic gradient.
4. The slope of the water table is relatively small.

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Groundwater Movement

2009-11-29T22:50:00.001+02:00

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.

Figure.1.

Schematic of Darcy’s law showing change in head (dh) over the flow path length (dl) and the area perpendicular to flow (aquifer width times thickness (b) for horizontal flow).

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