The potential function $\phi$ for this velocity field is the superposition of an uniform stream with speed $U$ plus a source and a sink with the same strength $m$ and a distance $2a$ appart. For the 2D case we have


\begin{displaymath}\phi = Ux+\frac{m}{2\pi}\left(\ln\sqrt{(x+a)^{2}+y^{2}}-\ln\sqrt{(x-a)^{2}+y^{2}}\right), \notag
\end{displaymath}  

and for the 3D case we have


\begin{displaymath}\phi = Ux-\frac{\mu}{4\pi}\left[\frac{1}{\sqrt{(x+a)^{2}+y^{2}+z^{2}}}-
\frac{1}{\sqrt{(x-a)^{2}+y^{2}+z^{2}}}\right] \notag
\end{displaymath}  



Timothy S Choe
2003-03-15