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 i b5v where i b5immersed bed-load transport rate; and v5flow power. That i b5v implies that e b5tan a5ub /u, where e b 5Bagnold's bed-load transport efficiency; ub5mean grain velocity in the sheet-flow layer; and tan a5dynamic internal friction coeffi- cient. Given that tan a'0.6 for natural sand, ub'0.6u, and e b'0.6. This finding is confirmed by an independent analysis of the experimental data. The value of 0.60 for e b 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.