SEDIMENTATION MOTION OF SAND PARTICLES IN MOVING WATER (Ⅱ)——SEDIMENTATION OF SAND PARTICLES IN LAMINAR FLOW

Abstract

In dealing with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully examined. In the previous paper, we gave the resistance acting on a sphere moving in a non-uniform flow field. In this paper, we assume the concentration of sand particles to be very small, and using the previously obtained formula for the resistance, we establish the general equations of motion of laminar flow of sand particles and water. Then, we discuss the sedimentation motion of sand particles for laminar flow in an open channel.Finally, we find that the component of relative velocity parallel to the main stream is not equal to zero. Thereby, we obtain the error in the position of sedimentation as calculated by means of the usual simplified assumption. This error in position is proportional to the depth of water, and is independent of the size of sand particles. In general, it is not a negligible quantity.