with λ′ = 0 over the surface of the paraboloid; and then
ψ′ = ½ U [ y2 − p √ (x2 + y2) + px ];
(9)
ψ = −½ Up [ √ (x2 + y2) − x ];
(10)
φ = −½ Up log [ √ (x2 + y2) + x ].
(11)
The relative path of a liquid particle is along a stream line
ψ′ = ½ Uc2, a constant,
(12)