PS_4 - calculations use an approximation of the supertanker...

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ChBE421 Problem Set #4 Fall 2009 1. Consider the problem of laminar, unidirectional flow in a pipe of radius a that we worked through in class (remember to include viscosity!). Solve for the velocity profile, u(r) , in the pipe (in terms of Δ p ) Calculate the maximum and bulk velocity ( u max , u b ) for this flow What is the pressure drop ( Δ p ) along a length of this pipe, L , in terms of some easily quantifiable values ( μ , a , u b )? Show your work. From these viscous flow solutions, calculate the lost work ( lw ): frictional loss for laminar pipe flow. Consider the same pipe of radius a and length L. HINT: consider the full mechanical energy balance to determine lw in terms of other variables we know/have solved for 2. Consider two-dimensional, laminar, unidirectional flow between two parallel plates as shown. Calculate the velocity profile. 3. Consider a supertanker cruising at U = 17 knots. For all
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Unformatted text preview: calculations use an approximation of the supertanker as shown in the figure. • Calculate the force required to keep the tanker moving at U • Confirm you used the correct approximation for drag coefficient (HINT: use Reynolds No.) • Determine the power required to overcome the skin friction drag 4. Determine the bulk velocity ( u b ) and pressure drop ( Δ p ) in a non-Newtonian fluid flow (unidirectional, viscous) in a pipe of radius a . The velocity profile for a non-Newtonian fluid is: ? = ? ±²³ ∙ 1 − ´ µ ² ¶ · +1 · ¸ with: ? ±²³ = · · +1 ∙ ´− 1 2 ∙ ∆¹ º» ¶ 1 · ∙ ² · +1 · NOTE: n > 1 for shear thickening; n < 1 for shear thinning; n = 1 for Newtonian. K is a constant used to help describe the apparent viscosity of the liquid at any particular shear rate....
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This note was uploaded on 03/18/2010 for the course CHBE 421 taught by Professor 1` during the Spring '10 term at University of Illinois, Urbana Champaign.

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