[omega] = U(z + a²/z), (1)
so that
/ a²\ / a² \
[phi] = U ( r + -- ) cos [theta] = U ( 1 + -- )x, (2)
\ r / \ r² /
/ a²\ / a² \
[psi] = U ( r - -- ) sin [theta] = U ( 1 - -- )y.
\ r / \ r² /
Then [psi] = 0 over the cylinder r = a, which may be considered a
fixed post; and a stream line past it along which [psi] = Uc, a
constant, is the curve
/ a²\
( r - -- ) sin [theta] = c, (x² + y²)(y - c) - a²y = 0 (3)
\ r /
a cubic curve (C3).
Over a concentric cylinder, external or internal, of radius r = b,
/ a²\
[psi]´ = [psi] + U1y = [U ( 1 - --- ) + U1] y, (4)
\ b²/
and [psi]´ is zero if