= Two-dimensional point sink
{title2=$W(z)=-\frac Q{2\pi}\log(z-z_0)$}
A <two-dimensional point sink> of strength $Q>0$ removes <volume flux> $Q$ per unit depth at $z_0$. Its <complex potential of a two-dimensional potential flow> is the displayed expression, so $u-iv=-Q/[2\pi(z-z_0)]$. The radial <velocity> is $u_r=-Q/(2\pi r)$: integrating over a circle gives outward flux $2\pi r u_r=-Q$. This is the planar cross-section of a <line sink>. A passive particle satisfies $d(r^2)/dt=-Q/\pi$ and reaches the ideal point singularity in finite time. This is a flow singularity, distinct from a stable <sink equilibrium> of a regular dynamical system.
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