Modelling of Pseudo Hydrostatic Force in Two – Phase Flow with Different Layers

In the study of solid-in-liquid flow, shear stress is important in determining the force that is acting on the pipe wall. In case of homogenous suspension solid-in-liquid flow, the properties can be considered as mixture properties with constant concentration profile across the flow area. In the moving bed of particles with variable concentration, the shear estimation is not directly predictable and there is no existing clear mathematical formula to achieve this objective. In the present work, the method of finding the force acted on the pipe wall by the particles in the layer, which is termed the dry force will be presented using a method called the “pseudo hydrostatic pressure” method. To attain the equation for the dry force, a mathematical approach is taken with the assumptions that the flow is a horizontal, two-phase pipe flow (solid-liquid), incompressible and it is at steady-state. For initial study, only Newtonian fluid is to be considered in the case. The two-layer approach is taken whereby the flow will consist of one upper suspended layer of particles in the fluid, and the bottom layer which is the moving bed of particles. Thus, the developed mathematical model can be applicable in solving for the shear force in horizontal two-phase flows.