Low Reynolds number flow in a Hele-Shaw cell
is described by the lubrication approximation, i.e. by
non-dimensionalizing Stokes equations
(where 
is the dynamic pressure, 
) using
the length scale L in 
, the co-ordinate directions parallel
to the plates and the length scale b in z, the co-ordinate
direction perpendicular to the plate, where 
. This yields
the result that the velocity is parallel to the plates, and the
pressure is independent of z, and
(where 
and we choose the coordinate z such that one
plate lies in the plane z=0 and the other lies in the plane z=b).
Solutions of the approximated equations averaged over the gap between
the fluids match Darcy's law with the permeability 
.