Modeling Flow Rate to Estimate Hydraulic Conductivity in a Parabolic Ceramic Water Filter

In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research conducted in Dr. James R. Mihelcic's Civil and Environmental Engineering Lab at USF.