Consider steady, incompressible flow maintained between two concentric cylinders by steady angular velocity of both cylinders. Assume that there is no axial velocity and gravitational effect is negligible. a. Derive an expression for the tangential velocity profile of the fluid between two cylinders. State all the assumptions that are necessary to reduce the governing equations (continuity and Navier-Stokes equations) you choose. Indicate what assumptions are used to eliminate the terms in the equation. State appropriate boundary conditions. You need to show the detailed solution processes for the continuity and Navier-Stokes equations.
b. Determine the velocity profile in the limit as the outer cylinder becomes very large and remains fixed or not rotating.