Flow of suspensions in a rectangular channel
Daniel, Salomon M.
An explanation of some of the phenomena which occur in the now of solid liquid suspensionsis presented and theoretical relations which may be used for design purposes are developed. Special instrumentation, developed as part of this investigation, was used for the measurement of the solids transport concentration and mixture velocity distributions in the vertical plane of a rectangular channel. These measurements provided considerable insight into the fundamental mechanisms of suspension of solids. This in turn led to the developnent of theoretical expressions for the prediction of the concentration and velocity distribution in the now section as well as for the frictional energy losses of a system. The expressions obtained were tested for now in a rectangular channel for solid particles which varied in size from 0.0058 in. to 0.080 in. in diameter, in specific gravity from 2.64 to 10.87, and in settling velocity from 0.0723 f.p.s. to 2.52 f.p.s. A new approach to the problem of the flow of suspensions has been adopted and the behaviour of materials has been classified on the basis of the prevailing mechanism of suspension of the solid particles. In the case where suspension was considered to be due to fluid turbulenqe, the mixtures behaved as pseudo-fluids with Newtonian properties. For these suspensions the concentration and velocity distributions were used to determine eddy diffusivities. Although considerable scatter in the experimental values was observed, the data show fair agreement with values obtained by other experimentors for the flow of pure fluids in a circular pipe. Based on these values of eddy diffusivities fairly good predictions of the velocity and concentration distributions have been made. For the larger and heavier particles where the action of fiuid turbulence is insufficient to maintain the particles in suspension, Bagnold (1954, 1955, 1956) has shown that suspension can be due to a dispersive stress set up between the solid particles. This concept has been applied to the case of flow in a closed conduit, and an equation has been established for the prediction of the friction losses. This equation has been tested for flow in a rectangular channel and the empirical constant in the equation has been found to agree with that obtained by Bagnold for shear in an annulus. The theoretical equation shows qualitative agreement with an empirical equation obtained by previous workers for flow in a circular pipe.