Problem 4.191

# Problem 4.191 - Problem 4.191[Difficulty 4 Given Data on...

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Problem 4.191 [Difficulty: 4] Given: Data on rotating spray system Find: Torque required to hold stationary; steady-state speed Solution: Basic equation: Rotating CV The given data is ρ 999 kg m 3 = δ 2.5 mm = r o 300 mm = Q in 3 L s = r i 300 250 () m m = For no rotation ( ω = 0) the basic 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 = 2 ρ V 2 δ r i r o r r d = ρ V 2 δ r o 2 r i 2 = where V is the exit velocity with respect to the CV V Q in 2 δ r o r i = V 2.40 m s = Hence T shaft ρ Q in 2 δ r o r i 2 δ r o 2 r i 2 = T shaft ρ Q in 2 4 δ r o r i + r o r i = T shaft 1 4 3 L s 10 3 m 3 L × 2 × 999 kg m 3 × 1 0.0025 m × 0.3 0.05 + 0.3 0.05 × = T shaft 1.26 N m =

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Problem 4.191 - Problem 4.191[Difficulty 4 Given Data on...

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