(4)
is the relative stream-function, constant over a solid boundary moving with components U and V of velocity.
If the liquid is stirred up by the rotation R of a cylindrical body,
dψ/ds = normal velocity reversed
| = −Rx | dx | − Ry | dy | , |
| ds | ds |
(5)
ψ + ½R (x2 + y2) = ψ′,
(6)
a constant over the boundary; and ψ′ is the current-function of the relative motion past the cylinder, but now
V2ψ′ + 2R = 0,