It is a simple potential function which models a source of fluid at a given point $(x_{0},y_{0})$ for the 2D case and a point $(x_{0},y_{0},z_{0})$ for the 3D case. The volume flux of a source is its strength and denoted as $m$. The potential function $\phi$ representing a source is


\begin{displaymath}\phi(x,y) = \frac{m}{2\pi}\ln r \notag
\end{displaymath}  

for the 2D case with $r=\sqrt{(x-x_{0})^{2}+(y-y_{0})^{2}}$, and for the 3D case we have


\begin{displaymath}\phi(x,y) = -\frac{m}{4\pi r} \notag
\end{displaymath}  

where $r = \sqrt{(x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}}$.

Timothy S Choe
2003-03-15