We study the vertical liquid profile of foam drainage using the threedimensional large- Q Potts model extended to include gravity. Forced drainage with constant-rate liquid input from the top of the foam produces a constant profile. In free drainage, without liquid input from the top, homogeneously distributed liquid drains to the bottom of the foam until capillary effects and gravity balance. For pulsed drainage, as liquid drains from the top of the foam into the dry foam, a sharp interface between the wet and dry foam develops. The fixed profile moves downwards at a constant velocity with a flat interface. The results of our simulations are suggested in both experiments and simplified meanfield analytical results.