Dilution methods of measuring transport of sand from a point source

The application of the steady-dilution and time-integration methods for the measurement of sand discharge by injection from a point source has been examined under conditions of uniform flow in a laboratory channel. Close to the point source, the lateral spread of the sand particles was found to increase in proportion to the square root of the distance downstream and to be greater than that of the water particles because the sand traveled closer to the bed ripples, where the sideways water movements were larger than the mean. Because the flow across the channel was substantially uniform, the steady-dilution and time-integration methods could be applied before complete lateral mixing was achieved by averaging the concentration across the section. Such a procedure is valid only if a sufficient distance is allowed for the particles to be completely mixed in depth. In the present experiments this distance was found to be about 20 ft for sand particles of about 0.17 mm mean size and was considerably greater than that derived from an analysis of dispersion in suspended flow in which the velocity and diffusion over the depth were assumed uniform. The discrepancy is thought to be due to the very low diffusion of particles traveling in bed creep. Tracer concentrations, whether measured on the bed or in suspension, resulted in transport values accurate to within 5% for positions beyond the mixing distance. Estimates of the width of the plume in larger depths suggest that the restriction of the method to conditions of uniform transport in width will not be prohibitive for some rivers.