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Q: Repeat Prob. 996, but let the inner cylinder be stationary and the outer cylinder rotate at angular velocity o . Generate an exact solution

Repeat Prob. 9–96, but let the inner cylinder be stationary and the outer cylinder rotate at angular velocity ωo. Generate an exact solution for uθ(r) using the step-by-step procedure discussed in this chapter.


Data from Problem 96

An incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite length— a solid inner cylinder of radius Ri and a hollow, stationary outer cylinder of radius Ro (Fig. P9–96; the z-axis is out of the page). The inner cylinder rotates at angular velocity ωi. The flow is steady, laminar, and two-dimensional in the rθ-plane. The flow is also rotationally symmetric, meaning that nothing is a function of coordinate θ (uθ and P are functions of radius r only). The flow is also circular, meaning that velocity component ur = 0 everywhere. Generate an exact expression for velocity component uθ as a function of radius r and the other parameters in the problem. You may ignore gravity.


FIGURE P9–96


Liquid: p. p. Ro Wi Rotating inner cylinder Stationary outer cylinder

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