Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 77 / 2 / a / Solution

The Laplacian and the added drag term in the Brinkman equation must have the same dimensions. ThereforeThe length ${\alpha }^{-1}$ is a hydrodynamic screening length. When the viscous coefficients are identical in the two terms, the corresponding permeability is ${\alpha }^{-2}$.