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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 Darcy-Weisbach equation, combined with the Moody chart for calculating head losses in pipes, is traditionally attributed to Henry Darcy, Julius Weisbach, and Lewis Ferry Moody. However, the development of these formulas and charts also involved other scientists and engineers over its historical development.
The above form for Darcy's law is sometimes also called Darcy's extended law, formulated for horizontal, one-dimensional, immiscible multiphase flow in homogeneous and isotropic porous media. The interactions between the fluids are neglected, so this model assumes that the solid porous media and the other fluids form a new porous matrix through ...
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 ...
Darcy's Law does not seem to hold at high hydraulic gradients, and both the coefficients of permeability and volume compressibility decrease during consolidation. This is due to the non-linearity of the relationship between void ratio and effective stress, although for small stress increments assumption 7 is reasonable.
The Theis solution is based on the following assumptions: The flow in the aquifer is adequately described by Darcy's law (i.e. Re<10). homogeneous, isotropic, confined aquifer, well is fully penetrating (open to the entire thickness (b) of aquifer),
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]