A simple numerical model is developed that successfully simulates observations of small-scale, laboratory, density currents flowing down inclines of constant slope. The model results suggest that laboratory determinatiions of the bulk Richardson number have been biased by molecular processes but that determinations of the entrainment coefficient are probably applicable to large-scale currents, and even to turbidity currents in which the gravitational driving force is provided by suspended sediment. The entrainment coefficient is a function of the gradient Richardson number Ri above the velocity maximum in both density and turbidity currents; Ri is itself a strong function of the bottom slope but not of the sediment settling velocity or the roughness of the bottom boundary. Therefore for a given bottom slope the entrainment coefficient is uniquely defined. The bulk Richardson number Ri0, on the other hand, is additionally a function of the drag coefficient, which depends on both the Reynolds number and the bottom roughness. However, Ri0 is not a strong function of the sediment settling velocity as long as the current is energetic enough to maintain sediment in suspension. ¿ American Geophysical Union 1988