1 d[psi]´ / a³ \ sin² [theta]
------------ ------- = ½U ( 2r + -- ) ------------- = 3/2 U sin [theta], when r = a; (20)
r sin[theta] dr \ r² / r sin [theta]
so that the loss of head is
(9/4 sin² [theta] - 1) U²/2g, having a maximum 5/4 U²/2g, (21)
which must be less than the head at infinite distance to avoid
cavitation at the surface of the sphere.