Potential flow around a circular cylinder
= Potential flow around a circular cylinder
Uniform irrotational flow of speed $U$ past a circular cylinder of radius $a$, with zero circulation, has <velocity potential>
$$
\phi=U\left(r+\frac{a^2}{r}\right)\cos\theta.
$$
On the cylinder, the tangential speed is $-2U\sin\theta$, so the <Bernoulli equation> gives
$$
p(a,\theta)=p_\infty+\frac12\rho U^2(1-4\sin^2\theta).
$$