= Solution
The flow is steady and irrotational, so the <Bernoulli equation> has the same constant throughout the connected exterior. Far from the sphere it equals $v^2/2+p_\infty/\rho$. On the surface the speed is $3v|\sin\theta|/2$, giving
$$
\boxed{p(R,\theta)=p_\infty+\frac{\rho v^2}{2}\left(1-\frac94\sin^2\theta\right).}
$$
The maximum stagnation <pressure> is $p_\infty+\rho v^2/2$ at both poles. At the equator, where the flow is fastest, the <pressure> is $p_\infty-5\rho v^2/8$. The fore-aft symmetry gives zero integrated <pressure> drag in this inviscid model, the content of <D'Alembert's paradox>; it does not predict zero drag for a real viscous separated flow.
\Image[/past-exam-of-the-flows-fluctuations-and-complexity-course-of-the-university-of-oxford/2016-sphere-potential-flow.png]
{title=Original streamlines around a sphere in its rest frame and the associated surface-pressure coefficient; the far flow is downward along negative z}
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