(19)
which leads to no simple relation.
The velocity past the surface of the sphere is
| 1 | dψ′ | = ½U ( 2r + | a3 | ) | sin2 θ | = 3⁄2 U sin θ, when r = a; | |
| r sin θ | dr | r2 | r sin θ |
(20)
so that the loss of head is
(9⁄4 sin2 θ − 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.
With n = 2, a state of motion is given by