Darcy's law

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.

Although Darcy's law (an expression of Newton's second law) was determined experimentally by Darcy, it has since been derived from the Navier-Stokes equations via homogenization. It is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, or Fick's law in diffusion theory.

One application of Darcy's law is to analyze water flow through an aquifer; Darcy's law along with the equation of conservation of mass are equivalent to the groundwater flow equation, one of the basic relationships of hydrogeology.

Morris Muskat first refined Darcy's equation for single phase flow by including viscosity in the single (fluid) phase equation of Darcy, and this change made it suitable for the petroleum industry. Based on experimental results worked out by his colleagues Wyckoff and Botset, Muskat and Meres also generalized Darcy's law to cover multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized multiphase flow equations of Muskat et alios provide the analytical foundation for reservoir engineering that exists to this day.

...
Wikipedia