(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 = − = − 1 ,  v = − = 1 ,
dx ydy dyy dx