Velocity and Concentration Fields in Uniform Flow with Coarse Sands

Abstract

The vertical distributions of velocity and concentration for an open-channel flow mixed with coarse sands are investigated by using a mathematical model, taking account of the momentum transfer by the turbulent motion and the sediment mass balance by the diffusion and settling in a two-dimensional steady-state condition. An attempt is made here to obtain the horizontal time-mean velocity component and the sediment concentration quantitatively at a certain depth. An examination of measured velocity profiles plotted on semilogarithmic paper leads to the conclusion that the general characteristic of the flow is greatly affected by the increasing sediment load. The vertical distribution of the time-mean velocity is calculated by following the velocity gradient equation previously proposed. The concentration field is divided into the outer region and the inner region, since in each region the fall velocity varies according to the grain Reynolds number. For computing the concentration of suspended sediment, therefore, the writer proposes two formulas derived from Fick's diffusion equation. The theoretical results obtained by the velocity and concentration equations are found to be in good agreement with a set of experimental data, for the mean diameters of the sands ranged from 940 to 1,300 μm.