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Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
The above equation is a vector form of the most general equation for fluid flow in porous media, and it gives the reader a good overview of the terms and quantities involved. Before you go ahead and transform the differential equation into difference equations , to be used by the computers, you must write the flow equation in component form.
Henry Philibert Gaspard Darcy (French: [ɑ̃ʁi daʁsi]; 10 June 1803 – 3 January 1858) was a French engineer who made several important contributions to hydraulics, including Darcy’s law for flow in porous media.
In fluid dynamics through porous media, the Darcy number (Da) represents the relative effect of the permeability of the medium versus its cross-sectional area—commonly the diameter squared. The number is named after Henry Darcy and is found from nondimensionalizing the differential form of Darcy's Law .
Diagram showing definitions and directions for Darcy's law. Darcy's law states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess fluid pressure with distance. The constant of proportionality includes the viscosity of the fluid and the intrinsic permeability of the soil.
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It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.