(8)
is the time-rate of change of φ at a point fixed in space, which is left behind with velocity components u − u′, v − v′, w − w′.
In the case of a steady motion of homogeneous liquid symmetrical about Ox, where O is advancing with velocity U, the equation (5) of § 34
p/ρ + V + ½q′2 − ƒ (ψ′) = constant
(9)
becomes transformed into
| p | + V + ½q2 − | U | dψ | + ½U2 − ƒ (ψ + ½Uy2) = constant, | |
| ρ | y | dy |
(10)
ψ′ = ψ + ¼U y2,
(11)