Darcy's law

Darcy's Law is a phenomologically derived constituative equation that describes the flow of a fluid through a porous medium (typically water through an aquifer). The law was formulated by Henry Darcy based on the results of 1855 and 1856 experiments on the flow of water through beds of sand. It, along with the conservation of mass, comprises the groundwater flow equation, which is one the basic building relationships of hydrogeology.

Additional forms of Darcy's Law

For very short time scales, a time derivative of flux may be added to Darcy's law, which results in valid solutions at very small times (in heat transfer, this is called the modified form of Fourier's law),

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: au rac{partial q}{partial t}+q=-k abla h,

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where τ is a very small time constant which causes this equation to reduce to the normal form of Darcy's law at "normal" times (> nanoseconds). The main reason for doing this is that the regular groundwater flow equation (diffusion equation) leads to singularities at constant head boundaries at very small times. This form is more mathematically rigorous, but leads to a hyperbolic groundwater flow equation, which is more difficult to solve and is only useful at very small times, typically out of the realm of practical use.

Related Topics:
Nanosecond - Groundwater flow equation - Diffusion equation - Singularities - Hyperbolic

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Another extension to the traditional form of Darcy's Law is the Brinkman term, which is used to account for transitional flow between boundaries (introduced by Brinkman in 1947),

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: eta abla^{2}q +q =-k abla h,

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where β is an effective viscosity term. This correction term accounts for flow through medium where the grains of the media are porous themselves, but is difficult to use, and is typically neglected.

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