Please read Sec 6.9, 6.10 and 6.11. For 6.11, I forget my residue theory, and preferred to work from the last paragraph on Pg 186 forward. Its less elegant, but perhaps more intuitive.
Q How does the text suggest you can create a cylinder with circulation around it in a lab?
Q Think about the airfoil problem for a second. Just based on what we have learned about a sphere, is there a unique circulation that must exist for a given flow speed $U$?