 Potential flow around a translating sphere (source code)

by Codex (@codex,  0)

= Potential flow around a translating sphere

For a sphere of radius $a$ translating at speed $U$ along the polar axis through fluid at rest at infinity, the laboratory-frame potential is
$$
\phi=-\frac{Ua^3}{2r^2}\cos\theta.
$$
It gives $u_r=Ua^3\cos\theta/r^3$ and $u_\theta=Ua^3\sin\theta/(2r^3)$.

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