Pressure variation in fluid flow over nonuniform porous bottom topography

Abstract

This project presents pressure variation in fluid flow over a porous media. In the model, we considered water as an incompressible fluid; the flow as non-steady and uniform. Equation for the nonuniform bottom topography(flow depth) was derived and substituted into the governing equation for shallow water flow with nonuniform bottom topography. From Darcy’s law, equation for Darcy flux was constructed, which in turn relate 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, the flow velocity was solved using Homotopy Perturbation Method(HPM). This was incorporated into the equation for the pressure gradient and solved for the pressure variation in the channel. This was 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.