Pressure Variation in a Fluid Flow over Non-Uniform, Porous Bottom Topography

Abstract

This paper presents pressure variation in fluid flow over a porous media. In the model, we considered water as an incompressible fluid: the flow as nonsteady and uniform. We derived an equation for the nonuniform bottom topography (flow depth) and substituted into the governing equation for shallow water flow with nonuniform bottom topography. We made use of Darcy’s law to construct equation for Darcy flux, which in turn related pressure gradient to the flow velocity, the porosity, and the permeability of the porous media. From the governing equation of shallow water flow with nonuniform bottom topography, we solved for the flow velocity using Homotopy Perturbation Method (HPM). We incorporated the flow velocity into the equation for the pressure gradient and solved for the pressure variation in the channel. We analyzed and found out that, the higher the permeability the lower the pressure within the flow and the lower the permeability the higher the pressure, because there is going to be a pressure build-up under this condition. We also found that the higher the flow height (H) the higher the pressure.