The aim of this paper is to present a turbulence model that allows turbulent flows between smooth and/or rough walls to be dealt with. After analyzing available literature data, an improvement of the Elrod, Ng, and Pan turbulence model is proposed, taking into account the effect of wall asperities. This model is then applied to a hydrostatic mechanical seal that is rough on one face, operating in nonlaminar flow. The roughness is due to particle deposits occurring during the seal operation. As expected, the wall roughness leads to a decrease in leakage rate.