ECH141-HW7-2010

ECH141-HW7-2010 - #2) A steady flow is two dimensional, but...

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Winter 2010 University of California at Davis Department of Chemical Engineering and Materials Science ECH 141 HW # 7 #1) (20 points) Consider steady flow in a horizontal pipe. Use dimensional analysis to generate a non-dimensional relationship for shear stress and other parameters. Let’s decide that the other parameters are velocity v, pipe diameter D, fluid density ρ, fluid viscosity μ and the roughness of the pipe wall ε (it is like a roughness height so it has units of length).
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Unformatted text preview: #2) A steady flow is two dimensional, but its inertial effects are very small. Using the definition of the stream function, show that the Navier-Stokes equations give rise to a biharmonic equation. The form of the biharmonic equation is given in problem 5-19. #3) The time-averaged Navier-Stokes equations are given by Eq. 6.2-24. Using dimensional analysis and the equation, generate a non-dimensional relationship for velocity. #4) Problem 6-5 Whitaker #5) Problem 3-5 Whitaker...
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