(1)

so that

ψ = U ( r + a2) cos θ = U ( 1 + a2) x,
r r2

(2)

φ = U ( r + a2) sin θ = U ( 1 + a2) y.
r r2

(2)

Then ψ = 0 over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which ψ = Uc, a constant, is the curve

( r − a2) sin θ = c, (x2 + y2) (y − c) − a2y = 0
r

(3)

a cubic curve (C3).