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Darcy's law is an equation that describes the flow of a fluid flow trough 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 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.
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 ...
If more than one formula is applicable in the flow regime under consideration, the choice of formula may be influenced by one or more of the following: Required accuracy; Speed of computation required; Available computational technology: calculator (minimize keystrokes) spreadsheet (single-cell formula) programming/scripting language (subroutine).
Morris Muskat et al. [1] [2] developed the governing equations for multiphase flow (one vector equation for each fluid phase) in porous media as a generalisation of Darcy's equation (or Darcy's law) for water flow in porous media.
Permeability is typically determined in the lab by application of Darcy's law under steady state conditions or, more generally, by application of various solutions to the diffusion equation for unsteady flow conditions. [8] Permeability needs to be measured, either directly (using Darcy's law), or through estimation using empirically derived ...
The Darcy–Weisbach friction factor f D is 4 times larger than the Fanning friction factor f, so attention must be paid to note which one of these is meant in any "friction factor" chart or equation being used. Of the two, the Darcy–Weisbach factor f D is more commonly used by civil and mechanical engineers, and the Fanning factor f by ...
The governing equation of Hele-Shaw flows is identical to that of the inviscid potential flow and to the flow of fluid through a porous medium (Darcy's law). It thus permits visualization of this kind of flow in two dimensions. [3] [4] [5]