Validation of Bagnold’s Approximation of Critical Near-Bed Flow Velocity for Incipient Sediment Motion as Particle Settling Velocity

Abstract

In the derivation of his bedload formula, Bagnold approximated the critical near-bed flow velocity for incipient sediment motion as the particle settling velocity. However, this approximation has not yet been validated since Bagnold’s bedload formula was proposed in 1973. By comparing the drag coefficient defined based on the critical near-bed flow velocity and that defined based on the particle settling velocity, this note shows that the difference between the two velocities is negligible, which substantiates Bagnold’s approximation.