Exercise 1.   Consider the ideal fluid flow for the complex potential   ,   where  .             
1 (b).   Show that the velocity vector      is tangent to the unit circle      at all points except     and  .  

            Hint.  Show that   ,   where      and   .  

Solution 1 (b).

See text and/or instructor's solution manual.

Calculation will reveal that  

                       

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell