The potential function $\phi$ for this velocity field is a superposition of a stream function with speed $U$ and a source with strength $m$ located at the origin. In 2D we have


\begin{displaymath}\phi = Ux+\frac{m}{2\pi}\ln\sqrt{x^{2}+y^{2}}, \notag
\end{displaymath}  

and in 3D we have


\begin{displaymath}\phi = Ux-\frac{m}{4\pi}\frac{1}{\sqrt{x^{2}+y^{2}+z^{2}}}. \notag
\end{displaymath}  



Timothy S Choe
2003-03-15