...contd...Analysis of Potential Flows through Complex Variables
Now consider another situation, where the complex potential is given by
|
 |
(22.18) |
and |
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
Let
|
, where is the mass flux |
|
The quantity K is,
|
and is the volume flow rate |
|
|