# Analyze and discuss a limiting case of Prob. 999 in which there is no inner cylinder (R i =

## Question:

Analyze and discuss a limiting case of Prob. 9–99 in which there is no inner cylinder (R_{i} = ω_{i} = 0). Generate an expression for u_{θ} as a function of r. What kind of flow is this? Describe how this flow could be set up experimentally.

**Data from Problem 99**

Repeat Prob. 9–96 for the more general case. Namely, let the inner cylinder rotate at angular velocity ω_{i} and let the outer cylinder rotate at angular velocity ω_{o}. All else is the same as Prob. 9–96. Generate an exact expression for velocity component u_{θ} as a function of radius r and the other parameters in the problem. Verify that when ω_{o} = 0 your result simplifies to that of Prob. 9–96.

**Data from Problem 96**

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

**FIGURE P9–96**

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**Related Book For**

## Fluid Mechanics Fundamentals And Applications

**ISBN:** 9780073380322

3rd Edition

**Authors:** Yunus Cengel, John Cimbala

**Question Details**

**9**- DIFFERENTIAL ANALYSIS OF FLUID FLOW

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