📂Fluid Mechanics

Porous Media and Darcy's Law in Fluid Mechanics

Laws

Porous medium

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In particular, in fluid mechanics, a structure with many small holes or void spaces that allow a fluid to flow is called a porous medium.

Darcy’s law

Consider a pipe composed of a porous medium through which a fluid flows. Let the cross-sectional area of the pipe be $A$, its length be $L$, and the pressure difference between the ends be $\Delta p$. The degree to which the porous medium allows fluid to pass through is represented by the permeability $k$. The flow rate $Q$ through this pipe is given by the following expression, including the kinematic viscosity $\mu$, and this is known as Darcy’s law. $$ Q = \frac{k A}{\mu L} \Delta p $$

Explanation

An everyday example of a porous medium that we can readily encounter is SpongeBob².

Porous media play an important role in phenomena such as filtration and absorption, and are studied across many fields. Situations where porous media are of interest are diverse: groundwater or oil movement, transport of substances in biological tissues, breathability of building materials, and so on³.