= Vortex ring
{wiki}
A <vortex ring> is a <vortex tube> bent into a closed loop, often approximately a <circle>. Its <vorticity> runs around the loop, while the induced <velocity field> passes through the centre and returns outside. For a thin ring of radius $r$ and <circulation (physics)> $\Gamma$, the <Biot-Savart law> for incompressible <vorticity> gives an axial <velocity> $u_z(z)=\Gamma r^2/[2(r^2+z^2)^{3/2}]$, measured relative to the ring centre, with its sign set by the <circulation> orientation. A <vortex ring> is not a loop of <fluid> whose <velocity> everywhere merely follows the circular <vortex line>.
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