Predictions of the Reynolds equation for flow between rough-walled surfaces have been compared to a more exact calculation of Navier-Stokes flow based on a lattice-gas automaton method. Two-dimensional channels were constructed with an idealized sinusoidal roughness on each wall. Flow in the channels was studied by both methods for various amplitude to wavelength ratios of the roughness, surface separations, relative alignment or phase of the sinusoids, and Reynolds numbers. The Reynolds equation overestimates fluid velocity as the surfaces are placed together or the amplitude of the roughness increases relative to its wavelength. ¿ American Geophysical Union 1995.