For stationary, creeping, incompressible flow, i.e. , the Navier–Stokes equation simplifies to the Stokes equation, which by neglecting the bulk term is:
where  is the viscosity,  is the velocity in the  direction, and  is the pressure. Assuming the viscous resisting force is linear with the velocity we may write:
where  is the porosity, and  is the second order permeability tensor. This gives the velocity in the  direction,
which gives Darcy's law for the volumetric flux density in the  direction,
In isotropic porous media the off-diagonal elements in the permeability tensor are zero,  for  and the diagonal elements are identical, , and the common form is obtained as below, which enables the determination of the liquid flow velocity by solving a set of equations in a given region.
The above equation is a governing equation for single-phase fluid flow in a porous medium.