Radial source flow
= Radial source flow
{title2=$u_r=Q/(2\pi r)$}
A two-dimensional incompressible line source with area flux $Q$ has radial <velocity> $Q/(2\pi r)$, obtained from flux conservation around a circle. It is irrotational away from the source, with potential $(Q/(2\pi))\ln r$. For a circular expanding interface, $Q=2\pi aa_t$ and $u_r=aa_t/r$, whose radial strain is $-aa_t/r^2$. That strain supplies a normal viscous stress even though the <velocity> is a potential flow.