Example 11.24.  Find the complex potential for an ideal fluid flowing from left to right across the complex plane and around the unit circle  .  

Figure 11.51  Fluid flow around a circle.  

Explore Solution 11.24.

Consider the complex potential   where  A  is a positive real number.  The velocity potential and stream function are given by  
  
Enter the complex potential and determine the velocity potential and stream function.

Use Mathematica to make a plot of the stream function.

For illustration purposes, we choose A = 1.

The inverse of  .  

Use conformal mapping  z = g(w)  to make an image of the flow.

(c) 2006 John H. Mathews, Russell W. Howell