10_32_exam2 - 10.32 Spring 2005 EXAM 2 April 13, 2005 1....

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10.32 Spring 2005 EXAM 2 April 13, 2005 1. (50 points) In the reverse osmosis systems we considered in class and for homework (Problem Set 3), we assumed that some salt or solute leaked through the membrane so that the permeate had a low salt concentration The flow of water and salt through the membrane can be modeled as two transport processes in parallel. Pure water permeates through the membrane wall by reverse osmosis and very small amounts of salt water pass through tiny pores or imperfections in the membrane by bulk flow. The salt concentration, C . C P P , is a result of both the osmotic flow of pure water and the bulk flow of salt water through pores. At any location along the length of the membrane tubes these two fluxes P N and N are: ( os 0 m 2 3 P - P K s m m N ∆Π = ) (1) for pure water through the walls by reverse osmosis and ( 0 P 2 3 P P - P K s m m N = ) ( 2 ) for bulk flow of salt water through the pores where P N N >> . In these equations, P is the pressure inside the tube, is the pressure outside the tube, o P os ∆Π is the osmotic pressure, and m K and are experimentally-determined coefficients.
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10_32_exam2 - 10.32 Spring 2005 EXAM 2 April 13, 2005 1....

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