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{{short description|Measure of the ability of a porous material to allow fluids to pass through it}}{{distinguish|Permeability (electromagnetism)}}{{Multiple issues|
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'''Permeability''' in [[fluid mechanics]], and[[materials thescience]] and [[Earth science]]s (commonly symbolized as ''k'') is a measure of the ability of a [[porous media|porous material]] (often, a [[Rock (geology)|rock]] or an unconsolidated material) to allow fluids to pass through it.[[File:In situ permeameter test.svg|thumb|100px|Symbol used to represent ''in situ'' permeability tests in geotechnical drawings]]
 
==Permeability==
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== Units ==
The [[International System of Units|SI]] unit for permeability is the [[square metre]] (m<sup>2</sup>). A practical unit for permeability is the ''[[darcy (unit)|Darcydarcy]]'' (d), or more commonly the ''millidarcy'' (md) (1&nbsp;Darcyd <math>\approx</math> 10<sup>−12</sup> m<sup>2</sup>). The name honors the French Engineer [[Henry Darcy]] who first described the flow of water through sand filters for potable water supply. Permeability values for most materials commonly range typically from a fraction to several thousand millidarciesmillidarcys. The unit of square centimetre (cm<sup>2</sup>) is also sometimes used (1&nbsp;cm<sup>2</sup> = 10<sup>−4</sup> m<sup>2</sup> <math>\approx</math> 10<sup>8</sup> d).
 
 
== Applications ==
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== Description ==
{{also|Fick's laws of diffusion}}
 
Permeability is part of the proportionality constant in [[Darcy's law]] which relates discharge (flow rate) and fluid physical properties (e.g. [[viscosity]]), to a pressure gradient applied to the porous media:<ref>[https://imechanica.org/files/JCIS-2019-Tailoring%20porous%20media%20for%20controllable%20capillary%20flow_0.pdf Controlling Capillary Flow], an application of Darcy's law, at iMechanica</ref>
 
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* <math>\boldsymbol \kappa </math> is the hydraulic permeability [[tensor]], <math>[\text{L}]^2</math>
* <math>\nabla </math> is the [[Del|gradient operator]], <math>[\text{L}]^{-1}</math>
* <math>P</math> is the [[pressure]] field in the fluid, <math>[\text{M}][\text{L}]^{-1}[\text{T}]^{-12}</math>
 
Connecting this expression to the isotropic case, <math>\boldsymbol \kappa = k\mathbb 1</math>, where k is the scalar hydraulic permeability, and 1 is the [[Identity matrix|identity tensor]].
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