An Expression for Bed-Load Transportation

A formula for the calculation of bed-load transportation per unit time and per unit width of the flow is suggested. This formula is valid for steady and uniform turbulent flow and for bed material consisting of grains of equal size and shape. It is assumed that the laminar sublayer of the turbulent flow is smaller than the size of the grains, and that the bed material is cohesionless. The existence of a critical tractive force is accepted. The value of this force, depending on the thickness of the laminar sublayer, must be determined from the Shields curve. The influence of ripple formation is not considered. The theoretically derived formula indicates an appreciable agreement with the experiment for the range of grain-sizes 0.3 mm to 28.6 mm.