= Vortex-induced force on a plane wall
{title2=$F=\rho\Gamma^2/(4\pi d)$}
A vortex of circulation $\Gamma$ distance $d$ from a plane wall has an opposite-sign image across the wall. The wall velocity has magnitude $|\Gamma|d/[\pi(d^2+y^2)]$, giving a pressure reduction $\rho\Gamma^2d^2/[2\pi^2(d^2+y^2)^2]$ by the <Bernoulli equation>. Integrating this deficit gives the displayed force per unit width, directed from the wall toward the fluid and vortex. The uniform ambient pressure is subtracted to isolate the finite vortex-induced force.
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