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Problem 4.192

# Problem 4.192 - Problem 4.192[Difficulty 4 Given Data on...

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Problem 4.192 [Difficulty: 4] Given: Data on rotating spray system Find: Torque required to hold stationary; steady-state speed Solution: Governing equation: Rotating CV The given data is ρ 999 kg m 3 = δ 2.5 mm = r o 300 mm = r i 300 250 () m m = Q in 3 L s = For no rotation ( ω = 0) this equation reduces to a single scalar equation T shaft A r V xyz ⎯⎯ × ρ V xyz ⎯⎯ d = or T shaft 2 δ r i r o r rV ρ V d = where V is the exit velocity with respect to the CV. We need to find V ( r ). To do this we use mass conservation, and the fact that the distribution is linear Vr V max rr i r o r i = and 2 1 2 V max r o r i δ Q in = so Q in δ i r o r i 2 = Hence T shaft 2 ρ δ r i r o r 2 d = 2 ρ Q in 2 δ r i r o r r i r o r i 2 2 d = T shaft ρ Q in 2 r i 3r o + 6 δ r o r i = T shaft 1

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Problem 4.192 - Problem 4.192[Difficulty 4 Given Data on...

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