Solution_HW4 - Solutions for homework set #4 Problem # 1:...

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1 Solutions for homework set #4 Problem # 1: Newtonian fluid inside tube R z cylinder wall moves upward with velocity V a. The last equation you could use is equation 3.6-7 in the example problem, or equation 2.3-16 in Chapter 2. Note that everything is identical up to the point where the last boundary condition (u z = V at r = R in this case). b. Velocity distribution From equation 3.6-7 2 2 4 z P ur C L μ Δ =− + BC: At r = R, u z = V 2 2 2 2 4 4 P VR C L P CR V L Δ + Δ =+ Inputting the constant: 2 2 22 1 44 4 z PP P R r R V V LL L R μμ ⎛⎞ ΔΔ Δ + + = + ⎜⎟ ⎝⎠ c. Volume flow rate To find the volumetric flow rate, Q, integrate the velocity function with respect to radius (0 to R) and angle (0 to 2 π ).
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2 2 2 2 2 0 22 2 4 0 1 4 = 2 1 4 2 42 1 6 2 z AA R R PR r Q v rdrd V rdrd LR PR r Vr d r PR r P r rV LL θ μ π μμ ⎛⎞ Δ == + ⎜⎟ ⎝⎠ Δ −+ ΔΔ =− + ∫∫ Evaluating from 0 to R 2 4 2 4 1 6 2 1 6 2 8 PR R P R PR R PR QR V V V R L L ππ Δ Δ + = + = + Problem # 2: a. From Table B.5 in BSL book, the equation of motion in terms of z-momentum may be reduced
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This note was uploaded on 11/18/2010 for the course PGE 322K taught by Professor Dicarlo during the Spring '08 term at University of Texas.

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Solution_HW4 - Solutions for homework set #4 Problem # 1:...

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