Example 11.23.  Consider the complex potential    where A is a positive real number.  The velocity potential and stream function are given by

              

respectively.  

The streamlines    form a family of hyperbolas with asymptotes along the coordinate axes.  The velocity vector    indicates that in the upper half-plane , the fluid flows down along the streamlines and spreads out along the x axis, as against a wall, as depicted in Figure 11.50.

Figure 11.50  The fluid flow with complex potential  .  

Explore Solution 11.23.

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