(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).