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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 Darcy velocity is not the velocity of a fluid particle, but the volumetric flux (frequently represented by the symbol ) of the fluid stream. The fluid velocity in the pores v a {\displaystyle \mathbf {v} _{a}} (or short but inaccurately called pore velocity) is related to Darcy velocity by the relation
The SI unit for permeability is the square metre (m 2).A practical unit for permeability is the darcy (d), or more commonly the millidarcy (md) (1 d ≈ 10 −12 m 2). The name honors the French Engineer Henry Darcy who first described the flow of water through sand filters for potable water supply.
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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In this article, the following conventions and definitions are to be understood: The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density.
The method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid.Typically there are two surfaces (boundaries) which are at constant values of potential or hydraulic head (upstream and downstream ends), and the other surfaces are no-flow boundaries (i.e., impermeable; for example the bottom of the dam ...
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 .