T = ½ρ ∫ φ dψ = −½ρ ∫ ψ dφ.

(14)

With the Stokes’ function ψ for motion symmetrical about an axis.

T = ½ρ ∫ φ dψ2πy ds = πρ ∫ φ dψ.
y ds

(15)

37. Flow, Circulation, and Vortex Motion.—The line integral of the tangential velocity along a curve from one point to another, defined by

∫ ( u dx+ v dy+ w dz) ds = ∫ (u dx + v dy + z dz),
ds dsds

(1)

is called the “flux” along the curve from the first to the second point; and if the curve closes in on itself the line integral round the curve is called the “circulation” in the curve.

With a velocity function φ, the flow