(2)
so that, with u = q cos θ, v = q sin θ, the function
| ζ = −Q | dz | = | Q | = | Q | (u + vi) = | Q | (cos θ + i sin θ), |
| dw | (u − vi) | q2 | q |
(3)
gives ζ as a vector representing the reciprocal of the velocity q in direction and magnitude, in terms of some standard velocity Q.
To determine the motion of a jet which issues from a vessel with plane walls, the vector ζ must be Constructed so as to have a constant direction θ along a plane boundary, and to give a constant skin velocity over the surface of a jet, where the pressure is constant.
It is convenient to introduce the function
Ω = log ζ = log (Q/q) + θi
(4)
| Fig. 4. |