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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 .
Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually clay , silt , sand , and gravel ) but soil may also contain organic solids ...
However, the use of Darcy's law alone does not produce accurate results for heterogeneous media like shale, and tight sandstones, where there is a huge proportion of nanopores. This necessitates the use of a flow model that considers the weighted proportion of various flow regimes like Darcy flow, transition flow, slip flow, and free molecular ...
The porous medium equation name originates from its use in describing the flow of an ideal gas in a homogeneous porous medium. [6] We require three equations to completely specify the medium's density , flow velocity field , and pressure : the continuity equation for conservation of mass; Darcy's law for flow in a porous medium; and the ideal gas equation of state.
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
Darcy's law is used when one has a saturated soil that is uniform to describe how fluid flows through that medium. [10] This type of work would fall under hydrogeology. Stokes' law measures how quickly different sized particles will settle out of a fluid. [10] This is used when doing pipette analysis of soils to find the percentage sand vs silt ...
Terzaghi's principle applies well to porous materials whose solid constituents are incompressible - soil, for example, is composed of grains of incompressible silica so that the volume change in soil during consolidation is due solely to the rearrangement of these constituents with respect to one another.
In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes this connection is Darcy's law, [9] particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media. [10]