424 Sp07 Exam 1

424 Sp07 Exam 1 - ENCH 424 - Transport Processes II: Mass...

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ENCH 424 - Transport Processes II: Mass & Heat Transfer Exam No. 1 Open Book Tuesday, March 6, 2007 1. (36 Points) Steady Oxygen Consumption in a Stagnant Polluted Pond: A long, wide stagnant pond with surface area S and uniform depth h is polluted with sewage, which decomposes by consuming oxygen. Therefore, as oxygen from the air diffuses into the pond it can react away, so there is less available to aquatic life. We want to develop a model to predict the oxygen consumption rate, and how the oxygen concentration varies with depth in the pond. Oxygen is only slightly soluble in water. At equilibrium, the solubility of oxygen in water is given by P A = H x A , where P A is the partial pressure of oxygen in the air, x A is the mole fraction of oxygen in the water and H is the appropriately dimensioned Henry’s Law constant. Let P , be the partial pressure of oxygen in standard air. At the air-water interface (z = 0), there is a finite convective resistance to oxygen transfer across the air boundary layer, characterized by mass transfer coefficient, k C . The pond is stagnant and has no velocity. As it is consumed, oxygen diffuses toward the bottom of the pond with diffusivity D O2 . The bottom of the pond (z = h) is impermeable to oxygen. Since the sewage is always present in excess, the reaction with sewage is first order in oxygen
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424 Sp07 Exam 1 - ENCH 424 - Transport Processes II: Mass...

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