= Corner sink in a semi-infinite channel
{title2=$\psi=-my-\frac{2m}{\pi}\sum_{n\ge1}\frac{e^{-n\pi x}\sin(n\pi y)}n$}
For unit channel width, <incompressible flow> towards a corner withdrawal point has $\psi=0$ on the lower wall and $\psi=-m$ on the upper and left walls, with $\psi\to-my$ far downstream. For <irrotational flow>, <separation of variables> gives the displayed harmonic correction: the Fourier sine coefficients of $-m(1-y)$ are $-2m/(n\pi)$. Near the corner, $\psi\sim-2m\theta/\pi$ and radial velocity is $-2m/(\pi r)$, whose integrated inward flux across a quarter-circle is $m$.
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