Math 6720 • Applied Complex Variables and Asymptotic Methods

Consider a source at \(z=-a\) and a sink at \(z=a\) of equal strength \(k\).
\begin{enumerate}
\item
(12 points) Show that the associated complex potential is
\[
\Omega(z)=k\log\left[\frac{z+a}{z-a}\right].
\]
\item
(13 points) Show that the flow speed is
\[
\frac{2ka}{\sqrt{a^4-2a^2r^2\cos(2\theta)+r^4}},
\]
where \(z=re^{i\theta}\).
\end{enumerate}
\end{enumerate}