# 5_21 - casing can be neglected the angular velocity of the...

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Problem 5.21 Radial outflow spinning up The sketch shows an impeller with radial vanes in a flat-sided casing of radius R and height h . The impeller is mounted on bearings and is free to rotate without friction, but the casing is held stationary. Fluid of density enters the impeller via a pipe which has a radius small compared with R . The velocity in the pipe is purely axial, and the volume flow rate is steady at a value Q . (a) Show that if a torque T is applied to the impeller shaft, and frictional forces on the
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Unformatted text preview: casing can be neglected, the angular velocity of the impeller obeys the equation I d dt + R 2 Q = T where I = 2 R 4 h . (b) If the impeller is stationary at t = 0, and a constant torque T is applied at t ≥ 0, obtain (t) . Sketch (t) and compare with the corresponding solution for Problem 5.20. Why is a final steady state reached in this problem, and not in Problem 5.20? ANSWER...
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