Problem 4.188 - Problem 4.188 [Difficulty: 3] Given: Data...

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Problem 4.188 [Difficulty: 3] Given: Data on rotating spray system Find: Torque required to hold stationary; steady-state speed Solution: Basic equation: Rotating CV Assumptions: 1) No surface force; 2) Body torques cancel; 3) Sprinkler stationary; 4) Steady flow; 5) Uniform flow; 6) L<<r The given data is Q1 5 L min = R 225 mm = d5 m m = ρ 999 kg m 3 = For each branch V 1 2 Q π 4 d 2 = V 6.37 m s = The basic equation reduces to a single scalar equation (FOR EACH BRANCH) T shaft V r α r × () × ρ d A r V xyz ⎯⎯ × ρ V xyz ⎯⎯ d = where α is the angular acceleration But r α r × × r 2 α = (r and α perpendicular); the volume integral is V r α r × × ρ dV r 2 α ρ d = R 3 3 α
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