The flow is steady and irrotational, so the Bernoulli equation has the same constant throughout the connected exterior. Far from the sphere it equals . On the surface the speed is , giving
(1)
The maximum stagnation pressure is at both poles. At the equator, where the flow is fastest, the pressure is . 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.
Figure 1.
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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