Open Access Library Journal 2020, Volume 7, e6033 ISSN Online: 2333-9721 ISSN Print: 2333-9705 DOI: 10.4236/oalib.1106033 Feb. 28, 2020 1 Open Access Library Journal Pressure Variation in a Fluid Flow over Non-Uniform, Porous Bottom Topography Godwin Christopher Ezike Mbah, Emmanuel Oluwakorede Oshilim Department of Mathematics, University of Nigeria, Nsukka, Nigeria 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 non- steady and uniform. We derived an equation for the nonuniform bottom to- pography (flow depth) and substituted into the governing equation for shal- low water flow with nonuniform bottom topography. We made use of Dar- cy’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 Pertur- bation 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 pres- sure, 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. Subject Areas Fluid Mechanics Keywords Pressure Variation, Porous Media, Darcy’s Law, Porosity, Permeability 1. Introduction The modern understanding of fluid motion began several centuries ago, with the work of L. Euler, Isaac Newton, Bernoulli, Lagrange etc. [1]. The ocean and the atmosphere remain phenomenal and have been a wonder, source of curiosity over the years. It’s properties like buoyancy, wave and weather, transport of How to cite this paper: Mbah, G.C.E. and Oshilim, E.O. (2020) Pressure Variation in a Fluid Flow over Non-Uniform, Porous Bottom Topography. Open Access Library Journal, 7: e6033. https://doi.org/10.4236/oalib.1106033 Received: December 27, 2019 Accepted: February 25, 2020 Published: February 28, 2020 Copyright © 2020 by author(s) and Open Access Library Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access