= Solution
A <velocity potential> satisfying uniform flow at infinity and no radial flow through $r=a$ is
$$
\phi(r,\theta)
=U\left(r+\frac{a^2}{r}\right)\cos\theta.
$$
Therefore
$$
\boxed{
u_r=U\left(1-\frac{a^2}{r^2}\right)\cos\theta,
\qquad
u_\theta=-U\left(1+\frac{a^2}{r^2}\right)\sin\theta
}.
$$
On the cylinder, $u_r=0$ and $u_\theta=-2U\sin\theta$. The steady <Bernoulli equation>, compared with the uniform flow at infinity, gives
$$
p+\frac12\rho|\mathbf u|^2
=p_\infty+\frac12\rho U^2.
$$
Hence
$$
\boxed{
p(a,\theta)
=p_\infty+\frac12\rho U^2(1-4\sin^2\theta)
},
$$
the <pressure> in <potential flow around a circular cylinder>.
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