$6\mathrm{.}9\mathrm{.}27$ WP A viscous fluid is contained between two infinitely long, vertical, concentric cylinders. The outer cylinder has a radius $\backslash ($ r$\_\{$o$\}\backslash )$ and rotates with an angular velocity $\backslash (\backslash$omega $\backslash ).$ The inner cylinder is fixed and has a radius $\backslash ($ r$\_\{$i$\}\backslash ).$ Make use of the Navier$-$Stokes equations to obtain an exact solution for the velocity distribution in the gap. Assume that the flow in the gap is axisymmetric $($neither velocity nor pressure are functions of angular position $\backslash (\backslash$theta $\backslash )$ within the gap$)$ and that there are no velocity components other than the tangential component. The only body force is the weight.