Abstract
The concentration distribution in a pipe transporting solids is considered the most important parameter in distinguishing flow patterns which can be associated with the prediction of pressure dorp.
The diffusion equation for suspended solid particles could be solved analytically, leading to transcendental equations, which would be dependent on the value of the index of the Richardson-Zaki equation for the hindered settling velocity of the solids. Although these equations, based on a diffusion model, have an advantage of simple calculation for relative concentration, we cannot calculate absolute in-situ concentrations without precise reference concentrations. Therefore an application technique of the Einsten equation for river mechanics to the slurry flow in a pipe were developed and discussed with calculated results.
Furthermore, using a composition method for integrating the transcendental equations, a numerical method was proposed in determining the reference concentrations and then computing the concentration distributions. This method revealed the influence of transport conditions such as the diameters of pipe and solid particles, delivered concentration, and the mean velocity of slurry flow on the concentration distribution. Finally, the parameter related to the degree of homogeneity of the suspended solids and the dimensionless parameter introduced by Batchelor into the diffusion equation were correlated.
