Chapter 4, Problem 44P

A very small circular cylinder of radius R_tis rotating angular velocity ${\omega }_i$ , inside a much larger concentric cylinder of radius R₀that is rotating at angular velocity ${\omega }_0$ . A liquid of density $\rho$ and viscosity $\mu$ is confined between the two cylinders, as in Fig. P4-41. Gravitational and end effects can be neglected (the flow is two-dimensional into the page). If ${\omega }_j={\omega }_0$ and a long time has passed. generate an expression for the tangential velocity profile. $u_{\theta }$ as a function of (at most) $r,\omega ,R_j,R_o,\rho$ . and $\mu$ . where $\omega ={\omega }_1={\omega }_0$. Also, calculate the torque exerted by the fluid on the inner cylinder and on the outer cylinder.