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Unformatted text preview: p / d x , where x is along the axis of the tubes. Show that the velocity profile at any radius r is u ( r ) = 1 4 μ ∞ d p d x b r 2a 2b 2a 2 ln( b / a ) ln r a B where a is the radius of the inner tube and b is the radius of the outer tube. Find the radius at which the maximum velocity is reached, the volume rate of flow, and the stress distribution. b a u ( r ) Problem 3 A long vertical cylinder of radius b rotates with angular velocity Ω concentrically outside a smaller stationary cylinder of radius a . The annular space is filled with fluid of viscosity μ ∞ . Show that the steady state velocity distribution is u θ = r 2a 2 b 2a 2 b 2 Ω r . Show that the torque exerted on either cylinder, per unit length, equals 4 πμ ∞ Ω a 2 b 2 / ( b 2a 2 ). b a u ( r ) Ω θ...
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 Fall '08
 Lee
 Fluid Dynamics, Thermodynamics, b2 − a2

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