(3)
so that
2ζ/y = −y−2∇2ψ = dH/dψ
(4)
is a function of ψ, say ƒ′(ψ), and constant along a stream line;
dH/dv = 2qζ, H − ƒ(ψ) = constant,
(5)
throughout the liquid.
When the motion is irrotational,
| ζ = 0, u = − | dφ | = − | 1 | dψ | , v = − | dφ | = | 1 | dψ | , | ||
| dx | y | dy | dy | y | dx |