Darcys law was first determined experimentally by Darcy, but has since been derived from the Navier–Stokes equations via homogenization methods. It is analogous to Fouriers law in the field of heat conduction, Ohms law in the field of electrical networks, and Ficks law in diffusion theory.
One application of Darcys law is in the analysis of water flow through an aquifer; Darcys law along with the equation of conservation of mass simplifies to the groundwater flow equation, one of the basic relationships of hydrogeology.
Morris Muskat first refined Darcys equation for a single-phase flow by including viscosity in the single (fluid) phase equation of Darcy. It can be understood that viscous fluids have more difficulty permeating through a porous medium than less viscous fluids. This change made it suitable for researchers in the petroleum industry. Based on experimental results by his colleagues Wyckoff and Botset, Muskat and Meres also generalized Darcys law to cover a multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized multiphase flow equations by Muskat and others provide the analytical foundation for reservoir engineering that exists to this day.