Data from flume studies are used to develop a model for predicting bed-load transport rates in rough turbulent two-dimensional open-channel flows moving well sorted non-cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed-load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed-load transport rates. The model is based on a revised version of Bagnold’s basic energy equation *ibsb *= *eb*ù, where *ib *is the immersed bed-load transport rate, ù is flow power per unit area, *eb *is the efficiency coefficient, and *sb *is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for *sb *and *eb *in terms of *G*, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed-load transport equation *ib *= ù *G *3·4. This equation applies regardless of the mode of bed-load transport (i.e. saltation or sheet flow) and reduces to *ib *= ù where *G *approaches 1 in the sheet-flow regime. That *ib *= ù does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that *ib *is a transport rate that must be multiplied by *sb *to become a work rate before it can be compared with ù. It follows that the proportion of ù that is dissipated in the transport of bed load is *ibsb*/ù, which is approximately 0·6 when *ib *= ù. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain-to-grain to grain-to-bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain-to-bed collision than in a grain-to-grain one. Copyright © 2006 John Wiley & Sons, Ltd.

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(b) = omega where i(b) = immersed bed-load transport rate; and omega = flow power. That i(b) = omega implies that e(b) = tan alpha = u(b)/u, where e(b) = Bagnold's bed-load transport efficiency; u(b) = Mean grain velocity in the sheet-flow layer; and tan alpha = dynamic internal friction coefficient. Given that tan alpha approximate to 0.6 for natural sand, u(b) approximate to 0.6u, and e(b)approximate to 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.

%B Journal of Hydrologic Engineering %V 129 %P 159-163 %8 2003 %@ 0733-9429/2003/2-159-163 %G eng %U files/bibliography/JRN00378.pdf %M JRN00378 %L 00883 %) In File (8/8/2006) %R 10.1061/(ASCE)0733-9429(2003)129:2(159) %F 1286