A 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 with inner radius $R_o($the $z-$axis is out of the page$).$ The inner cylinder rotates at angular velocity ${}_i.$ The flow is steady, laminar, and two$-$dimensional in the $r-$plane.

The flow is also rotationally symmetric, meaning that nothing is a function of $($i$.$e$.,v_{}$ and pressure are functions of only the radius$).$ The flow is only circular, meaning that $v_r=0.$ Generate an exact expression for the velocity component, $v,$ as a function of the radius, $r,$ and the other parameters in the problem. You may ignore gravity. $(5$ pts$)$

HINT: The dimensions of velocity $($e$.$g$.,v,v_r)$ are in length per time $($e$.$g$.,$ m$/$s$).$ Make sure your final expression has these dimensions. Consider the dimensions of angular velocity.