Engineering >> Civil & Environmental EngineeringVolumetric Flow Rate of Water through a Ceramic Water Filterby Ileana Wald
Submitted : Fall 2011 How fast can a ceramic water filter (CWF) process water while still effectively improving water quality? This calculus project uses this question as a starting point to evaluate how the flow rate is dependent upon the size and shape of the filter and how calculus can be used to determine ideal specifications for these types of ceramic filters. The volumetric flow rate is dependent upon the pore size of the filter and the amount of surface area. Using the theory of conservation of mass, which states that the rate of mass into the vessel minus the rate of mass out of the vessel equals the rate of accumulation of mass, equations are derived using differential and integral calculus to determine the flow rate of water through a vessel in respect to time. The CWFs used in the study have a flowerpot shape. For simplification purposes this project models flow rate using a right cylinder shape. The equations also relate to research conducted in Dr. James R. Mihelcic’s lab (USF Civil and Environmental Engineering Lab) by using the manufacturer’s ideal flow rate for the filters to model the velocity of water flow out of a horizontal “slice” of the filter and calculate a volumetric flow rate coefficient. By integrating the function of flow rate through a “slice” of filter from initial height of water to final height (zero), the flow rate of water out of the sides and bottom of the filter with respect to time can be determined. Related Links:
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