The relationship between the predicted mean flow velocity (or pressure drop), the fluid viscosity and media thickness expressed in Darcy's law is used to compute and output the material permeability.

where is the fluid flow velocity, is the permeability, is the fluid viscosity, is the pressure, and is a force density.

When using Darcy’s law, the user should be aware of the following:

1. Darcy’s law only applies to very slow (so-called creeping or Stokes) flows, with a Reynolds number close to zero.
   The Stokes equations, which are simplified from Navier-Stokes equations by dropping the inertial term, are used to describe the flow. In this regime, changing pressure drop or velocity by a factor, linearly changes the other by the same factor, so that Darcy’s law always predicts the same value for the permeability.

2. The second caveat lies in the definition of length () in Darcy’s law. This length is meant not to include the inlet and outlet (inflow and outflow regions) that some virtual flow experiments require. Under the assumptions of slow flow and void of inlet and outlet, choosing the Stokes flow option in FlowDict and using the computed permeability is valid.