ProblemSet5_18.pdf - ECH 141 Problem Set#5 Due Wednesday 1...

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ECH 141 Problem Set #5 Due Wednesday 2/21/18 1. The generalized Newtonian fluid (GNF) model provides a simple way to describe non-Newtonian fluids in steady unidirectional flow, and the power-law model is the simplest example of a GNF. Here you will derive a generalized form of the Hagen-Poiseuille equation for fully developed flow of a power-law fluid through a long, cylindrical tube. As the flow is steady and fully developed, you may assume that v z = v z r ( ) only, v r = v θ = 0 and consequently that η = m dv z dr n 1 and τ rz = m dv z dr n 1 dv z dr a) If the dynamic pressure at z=0 is P 0 and at z=L is P L , derive an expression for the velocity profile v Z (r) of the fluid in the tube. b) Use your result from part (a) to derive an expression for the flow rate Q. Show that your result simplifies to the Newtonian, Hagen-Poiseuille equation in the limit n=1 and m= μ . R
2. A 13.5% by weight solution of polyisoprene in isopentane has the following power-law parameters at 323 K:

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