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== Background ==
Darcy's law was first determined experimentally by Darcy, but has since been derived from the [[Navier–Stokes equations]] via [[Homogenization (mathematics)|homogenization]] methods.<ref>{{cite journal |last = Whitaker |first = S. |title = Flow in porous media I: A theoretical derivation of Darcy's law |journal = Transport in Porous Media |volume = 1 |pages = 3–25 |doi = 10.1007/BF01036523 |year = 1986|bibcode = 1986TPMed...1....3W |s2cid = 121904058 }}</ref><ref>{{Cite journal |last=Brown |first=G. O. |date=2002 |title=Henry Darcy and the making of a law |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2001WR000727 |journal=Water Resources Research |language=en |volume=38 |issue=7 |doi=10.1029/2001WR000727 |issn=0043-1397}}</ref> It is analogous to [[Fourier's law]] in the field of [[heat conduction]], [[Ohm's law]] in the field of [[electrical networks]], and [[Fick's law]] in [[diffusion]] theory.
One application of Darcy's law is in the analysis of water flow through an [[aquifer]]; Darcy's law along with the equation of [[conservation of mass]] simplifies to the [[groundwater flow equation]], one of the basic relationships of [[hydrogeology]].
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In the integral form, Darcy's law, as refined by [[Morris Muskat]], in the absence of [[Gravity|gravitational forces]] and in a homogeneously permeable medium, is given by a simple proportionality relationship between the [[volumetric flow rate]] <math>Q</math>, and the [[pressure drop]] <math>\Delta p</math> through a [[porous medium]]. The proportionality constant is linked to the [[Permeability (Earth sciences)|permeability]] <math>k</math> of the medium, the dynamic [[viscosity]] of the fluid <math>\mu</math>, the given distance <math>L</math> over which the pressure drop is computed, and the cross-sectional area <math>A</math>, in the form:
<math display="block"> Q =
Note that the ratio:
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<math display="block"> R = \frac {\mu L}{k A}</math>
can be defined as the Darcy's law [[Hydraulic conductivity#Resistance|hydraulic resistance]].
The Darcy's law can be generalised to a local form:
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