Saturated, collisional flows of spheres over an inclined, erodible bed between vertical sidewalls

We consider a steady, uniform, dense, fully-saturated, gravity-driven, inclined flow of water and identical spherical grains over an erodible bed between parallel, vertical sidewalls. The grains are inelastic and the energy lost in their interaction is also influenced by the fluid viscosity. We use an extension of kinetic theory for dense flows and employ approximate integrations of the momentum and energy balances for the grains in order to obtain analytical expressions for the depth of flow and for the volume flow rate of the mixture as functions of inclination and average concentration. We also predict the range of slopes for which dense, fully-saturated flows are possible. The predictions are in reasonable agreement with already published experimental results.