= Rankine oval
{c}
{title2=$w(z)=Uz+\frac m{2\pi}\log\frac z{z-1}$}
A uniform planar stream combined with an equal source and sink produces a closed dividing <streamline> enclosing them. Outside it the flow approaches the uniform stream; inside it streamlines connect the source and sink. For positive $U,m$ and separation one, the <complex velocity> is $U-m/[2\pi z(z-1)]$ and the stagnation points are $[1\pm\sqrt{1+2m/(\pi U)}]/2$. Both lie on the dividing streamline, which has zero streamfunction with consistent logarithm branches.
Back to article page
