Bed-Load Transport Equation for Sheet Flow

When open-channel flows become sufficiently powerful, the mode of bed-load transport changes from saltation to sheet flow. Where there is no suspended sediment, sheet flow consists of a layer of colliding grains whose basal concentration approaches that of the stationary bed. These collisions give rise to a dispersive stress that acts normal to the bed and supports the bed load. An equation for predicting the rate of bed-load transport in sheet flow is developed from an analysis of 55 flume and closed conduit experiments. The equation is ib=ω where ib=immersed bed-load transport rate; and ω=flow power. That ib=ω implies that eb=tan α=ub/u, where eb=Bagnold’s bed-load transport efficiency; ub=mean grain velocity in the sheet-flow layer; and tan α=dynamic internal friction coefficient. Given that tan α≈0.6 for natural sand, ub≈0.6u, and eb≈0.6. This finding is confirmed by an independent analysis of the experimental data. The value of 0.60 for eb is much larger than the value of 0.12 calculated by Bagnold, indicating that sheet flow is a much more efficient mode of bed-load transport than previously thought.