Solution Found!
Consider the same two concentric cylinders of Prob. 4?45.
Chapter 4, Problem 45P(choose chapter or problem)
Consider the same two concentric cylinders of Prob. 4‒45. This time, however, the inner cylinder is rotating, but the outer cylinder is stationary. In the limit, as the outer cylinder is very large compared to the inner cylinder (imagine the inner cylinder spinning very fast while its radius gets very small), what kind of flow does this approximate? Explain. After a long time has passed, generate an expression for the tangential velocity profile, namely u θ as a function of (at most) r,ωi, R i, R o, ρ, and µ. Hint: Your answer may contain an (unknown) constant, which can be obtained by specifying a boundary condition at the inner cylinder surface.
Questions & Answers
QUESTION: Problem 45P
Consider the same two concentric cylinders of Prob. 4‒45. This time, however, the inner cylinder is rotating, but the outer cylinder is stationary. In the limit, as the outer cylinder is very large compared to the inner cylinder (imagine the inner cylinder spinning very fast while its radius gets very small), what kind of flow does this approximate? Explain. After a long time has passed, generate an expression for the tangential velocity profile, namely u θ as a function of (at most) r,ωi, R i, R o, ρ, and µ. Hint: Your answer may contain an (unknown) constant, which can be obtained by specifying a boundary condition at the inner cylinder surface.
ANSWER:
Step 1
The arrangement consists of two concentric cylinders. The outer cylinder is very large compared two inner cylinder and inner cylinder is rotating very fast and outer cylinder is stationary or it's not moving or at rest. When the inner cylinder is moving very fast, tangential velocity to be measured after some time.when the flow has been running long time so it is steady.