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A cylindrical drum of length / and radius r can rotate inside a fixed concentric cylindrical casing, the clearance space c between the drum and the casing being very small and filled with liquid of dynamic viscosity u. To rotate the drum with angular velocity o requires the same power as to pump the liquid axially through the clearance space while the drum is stationary, and the pressure difference between the ends of the drum is p. The motion in both cases is laminar. Neglecting end effects, show that 2ulro/3

A cylindrical drum of length / and radius r can rotate inside a fixed concentric cylindrical casing, the clearance space c between the drum and the casing being very small and filled with liquid of dynamic viscosity u. To rotate the drum with angular velocity o requires the same power as to pump the liquid axially through the clearance space while the drum is stationary, and the pressure difference between the ends of the drum is p. The motion in both cases is laminar. Neglecting end effects, show that 2ulro/3

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please solve following problem. Especially I cannot understand how to get flow rate.

A cylindrical drum of length l and radius r can rotate inside a fixed concentric cylindrical casing, the clearance space c between the drum and the casing being very small and filled with liquid of dynamic viscosity µ. To rotate the drum with angular velocity o requires the same power as to pump the liquid axially through the clearance space while the drum is stationary, and the pressure difference between the ends of the drum is p. The motion in both cases is laminar. Neglecting end effects, show that 2µlro/3 p = c2
Transcribed Image Text:A cylindrical drum of length l and radius r can rotate inside a fixed concentric cylindrical casing, the clearance space c between the drum and the casing being very small and filled with liquid of dynamic viscosity µ. To rotate the drum with angular velocity o requires the same power as to pump the liquid axially through the clearance space while the drum is stationary, and the pressure difference between the ends of the drum is p. The motion in both cases is laminar. Neglecting end effects, show that 2µlro/3 p = c2
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