Potential of a translating sphere
= Potential of a translating sphere
{title2=$\Phi=-Ua^3\cos\theta/(2r^2)$}
For a sphere translating through an unbounded inviscid incompressible fluid at rest far away, the laboratory fluid <velocity> written in coordinates centred on the moving sphere is the gradient of the displayed dipole potential. Its radial <velocity> at the surface equals $U\cos\theta$. The sphere-rest-frame <velocity> instead needs the additional uniform potential $-Ur\cos\theta$.