A Darcy Velocity Field is a mathematical field corresponding to fluid seepage through a porous medium, specifically if it is following Darcy's Law.
Darcy's Law applies to non-compressible fluids passing through a porous medium if the seepage is sufficiently slow that inertia and Turbulence are insignificant. It describes a Darcy Velocity, an overall throughput rate per unit cross-section, slower than the mean velocity of the fluid because of the porous material through which it is passing. It relates this to the pressure difference, Gravity, and length of the porous medium through which it is passing.
κAΔp Q = - ———— μL
Navier-Stokes Equations (NS Equations) are more general, and Darcy's Law can be derived from them.