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Solution: radial velocity $V_{r}$, the tangential velocity $V_{\theta}$ and the vorticity $\omega_{z}$.


\begin{displaymath}V_r = \frac{\partial \phi }{\partial r} = 0, V_\theta = \frac... ...t( {rV_\theta } \right) = 0 \mbox{\ except at \ } r = 0 \notag \end{displaymath}