Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/103

of symmetry. The conditions require that it should be constituted of radial straight line flow equally distributed circumferentially in space. The field, in the case of motion in two dimensions, being shown plotted in Fig. 35 for a series of equal increments of flux, each line of flow will represent some definite value of the function $\psi ,$ any one of the lines being arbitrarily chosen as datum.

Fig. 35.

The equipotentials, $\phi =$ constant, will be a series of concentric circles whose radii form a geometrical progression.

If the functions $\psi$ and $\phi$ be interchanged, the diagram represents a cyclic motion round a filament, the radial lines becoming the equipotentials.

In the case of the source or sink, the velocity of the fluid at the origin is infinite, the whole flux having to pass through a region having no magnitude. In order to keep the problem within the range of physical conception it is customary in