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hw7 -S09 - Problem 8.2 a and b in Process Fluid Mechanics...

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Chemical Engineering 150A Spring Semester, 2009 Homework 7: Microscopic Balances Problem 1 A polymeric liquid is coated onto a surface by flowing the liquid down an inclined plate making an angle α with the vertical. Assume that the polymeric liquid behaves as a power-law fluid with a viscosity given by: " = K 1 2 II ( n # 1)/ 2 where K and n are constants. a) Obtain an expression for the velocity distribution in the film and for the thickness of the film given that the flow rate per unit width is q. Use the coordinate system indicated in the sketch. Indicate your assumptions and show your work. b) Show what your velocity field and film thickness expressions reduce to in the limit that the fluid behaves as a Newtonian fluid. Do not re-solve the entire problem for a Newtonian fluid. Note that this problem is related to Problem 8.3 from HW 6 (although the coordinate system and the constitutive equation are different). gravity polymeric liquid x y α air δ
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Unformatted text preview: Problem 8.2 a and b in Process Fluid Mechanics. Problem 3 Problem 8.7 in Process Fluid Mechanics. Problem 4 One type of compact heat exchanger is shown in Figure 4A below. In order to analyze the performance of such an apparatus, it is necessary to understand the flow in a duct whose cross section is an equilateral triangle. This is done most easily by installing a coordinate system as shown in Figure 4B. (a) Simplify the Navier-Stokes equations to get a partial differential equation for v z . How many boundary conditions are needed in order to solve this equation? (b) Verify that the velocity distribution for the laminar flow of a Newtonian fluid in a duct of this type is given by v z = P " P L ( ) 4 # LH y " H ( ) 3 x 2 " y 2 ( ) where the equivalent pressure changes by an amount (P L-P ) over a distance L in the flow direction. (c) Find the mass flow rate, average velocity, and maximum velocity. Figure 4A Figure 4B...
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hw7 -S09 - Problem 8.2 a and b in Process Fluid Mechanics...

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