Consider a viscous flow inside an annular pipe. The inner surface of the pipe is located at r = R₁ and is stationary. The outer surface is located at r = R₁ and moves to the right with speed Upipe. The pressure inside the pipe is constant. The fluid inside the pipe has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, axisymmetric, non-rotating, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity inside the pipe in terms of Upipe, R₁, Ro, and r. b. Determine the average velocity inside the pipe in terms of Upipe, Ri, and Ro. C. Determine the shear stress acting on the inner annulus in terms of Upipe, R₁, Ro, and μ.

Consider a viscous flow inside an annular pipe. The inner surface of the pipe is located at r = R₁ and is stationary. The outer surface is located at r = R₁ and moves to the right with speed Upipe. The pressure inside the pipe is constant. The fluid inside the pipe has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, axisymmetric, non-rotating, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity inside the pipe in terms of Upipe, R₁, Ro, and r. b. Determine the average velocity inside the pipe in terms of Upipe, Ri, and Ro. C. Determine the shear stress acting on the inner annulus in terms of Upipe, R₁, Ro, and μ.

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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