The Dupuit–Forchheimer assumption holds that

groundwater Groundwater is the water present beneath Earth's surface in rock and Pore space in soil, soil pore spaces and in the fractures of stratum, rock formations. About 30 percent of all readily available fresh water in the world is groundwater. A unit ...

flows horizontally in an

unconfined aquifer An aquifer is an underground layer of water-bearing material, consisting of permeable or fractured rock, or of unconsolidated materials (gravel, sand, or silt). Aquifers vary greatly in their characteristics. The study of water flow in aquifers ...

and that the groundwater discharge is proportional to the saturated

aquifer An aquifer is an underground layer of water-bearing material, consisting of permeability (Earth sciences), permeable or fractured rock, or of unconsolidated materials (gravel, sand, or silt). Aquifers vary greatly in their characteristics. The s ...

thickness. It was formulated by Jules Dupuit and Philipp Forchheimer in the late 1800s to simplify

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 ...

s for

analytical solution In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. C ...

s. The Dupuit–Forchheimer assumption requires that the

water table The water table is the upper surface of the phreatic zone or zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with groundwater, which may be fresh, saline, or brackish, depending on the loc ...

be relatively flat and that the groundwater be

hydrostatic Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and o ...

(that is, that the

equipotential In mathematics and physics, an equipotential or isopotential refers to a region (mathematics), region in space where every point is at the same Electric potential, potential. This usually refers to a scalar potential (in that case it is a level ...

lines are vertical): :

\frac &= 0 \end

where

\partial P/\partial z

is the vertical pressure gradient,

\gamma

is the

specific weight Specific may refer to: * Specificity (disambiguation) * Specific, a cure or therapy for a specific illness Law * Specific deterrence, focussed on an individual * Specific finding, intermediate verdict used by a jury in determining the fin ...

\rho

is the density of water,

g

is the

standard gravity The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant ...

, and

\partial h/\partial z

is the vertical hydraulic gradient.

References

* * {{DEFAULTSORT:Dupuit-Forchheimer assumption Aquifers Hydraulic engineering Hydrology