Extra Example 2.  Use a Schwarz-Christoffel transformation to show that the conformal mapping  

            
            

will map the flow in the upper half-plane from a source at    onto the flow from a channel with    into a sector, as shown in Figure 11.106.
Hint: Set   and .  Use the change of variable    in the resulting integral. 

     

                 Figure 11.106  Flow from a channel into a sector in the first quadrant.

Explore Extra Solution 2.

Use Mathematica to graph conformal mapping  w = S(z).

We are done.

Aside.  We can extend the flow into the fourth quadrant using symmetry.

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