Math 6720 • Applied Complex Variables and Asymptotic Methods

\begin{enumerate}
\item
Discuss the flow pattern around a circular obstacle associated with the complex potential
\[
\Omega(z)=u_0\left(z+\frac{a^2}{z}\right)+\frac{i\gamma}{2\pi}\log z.
\]
\item
Show that \(r=a\) is a streamline.
\item
Determine the asymptotic velocity when \(z\to\infty\). Sketch the flow when \(\gamma=0\).
\item
Use the Blasius formula
\[
F_x-iF_y=\frac{1}{2}i\rho\int_C \left(\frac{d\Omega}{dz}\right)^2\,dz
\]
to determine the lift on the obstacle when \(\gamma\neq 0\).
\end{enumerate}