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Problem 4.37 - Problem 4.37[Difficulty 3 Given Velocity...

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Problem 4.37 [Difficulty: 3] Given: Velocity distribution in annulus Find: Volume flow rate; average velocity; maximum velocity; plot velocity distribution Solution: Governing equation For the flow rate (Eq. 4.14a) and average velocity (Eq. 4.14b) Q A V d = V av Q A = The given data is R o 5 mm = R i 1 mm = p L 10 kPa m = μ 0.1 N s m 2 = (From Fig. A.2) u r ( ) p 4 μ L R o 2 r 2 R o 2 R i 2 ln R i R o ln R o r + = The flow rate is Q R i R o r u r ( ) 2 π r d = Considerable mathematical manipulation leads to Q p π 8 μ L R o 2 R i 2 R o 2 R i 2 ln R o R i R i 2 R o 2 + = Substituting values Q π 8 10 10 3 ( ) N m 2 m m 2 0.1 N s 5 2 1 2 ( ) m 1000 2 5 2 1 2 ln 5 1
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