Katabatic winds are gravity driven flows of a layer of cool air down a slope. They arise in the evening, after sunset, when the ground temperature decreases due to radiative cooling, and an air layer adjacent to the slope becomes colder than air at the same altitude further away from the slope. These flows are similar to gravity currents on an incline, which can be due to an inflow of cold, saline or turbid water into a water body, and they entrain warmer air at their upper boundary due to turbulent shear. The concept of entrainment is due to Morton, Taylor and Turner, who proposed a depth-averaged model for jets and plumes, which was later extended to gravity currents in deep water by Ellison and Turner [ET]. In a first part of this study the entrainment concept for gravity currents is compared with a diffusion model by Prandtl. The structure of ET’s shallow water equations for gravity currents is consistent with the Bresse equations for open channel flows, but their flow scales are not. This limitation of ET’s approach is addressed in a second part of the study, and mass-based flow scales are outlined which are consistent with those for open channel flows. Finally, results of field experiments on katabatic winds are reanalyzed to provide data for the diffusion rates of gravity driven flows in terms of both ET’s and mass-based flow scales.