Theoretical Modeling of Pseudo Hydrostatic Force in Solid-Liquid Pipe Flow with Two Layers

In the moving layer of particles with variable concentration, the shear estimation is not directly predictable and there is no existing clear mathematical or empirical formula to achieve this objective. This paper presents a developed approach to estimate the shear forces in a flow having suspended and moving layers of solid particles in liquid flow. The two-layer approach was taken whereby the flow consisting of one upper suspended layer of particles in the liquid, and the bottom layer was the moving bed of particles. In the present work, the method of finding the force acting on the pipe wall by the particles in the layer, termed as the ‘dry force’, was presented using a “pseudo hydrostatic pressure” method. To attain the equation for the dry force, a mathematical approach is taken with the assumptions that the flow is horizontal, two-phase pipe flow (solid in Newtonian liquid), incompressible and it is at steady-state. The analysis was conducted considering various particles densities, various concentrations in the suspended layer and different thicknesses of the moving bed. Changing the concentration in the suspended layer from 0.00001 up to 0.001 didn’t showed significant changes in the dry force evaluation. The dry friction force is increasing with increasing moving bed thickness. The developed mathematical model can be applicable in solving for the shear force in horizontal solid liquid two-phase flows.