...contd...Analysis of Potential Flows through Complex Variables

Now consider another situation, where the complex potential is given by

(22.18)

and

and

entailing     and

and

Therefore     signifies uniform flow. The flow was earlier represented via Figure 20.2(a)

We may choose yet another complex potential, given by

(22.19)

or,

or,

(22.20)

This signifies

(22.21)

(22.22)

The flow is basically elementary uniform flow at an angle as represented by Figure 20.2 (b).

Consider another complex potential given by

where

(22.23)

We obtain   and   

If A is positive, is in the outward direction and it is a source flow (Figure 20.3). If A is negative, is in the inward direction and it is sink flow.

The radial and tangential component of velocities are given by

,    where   is the mass flux

The quantity K is,

and    is the volume flow rate