Exercises 4

Question 1

For the uniform two dimensional flow of an inviscid and incompressible fluid about a
body, what can you say about the drag. What does it take to obtain non-zero lift?

Answer 1

To obtain non-zero lift there has to be circulation. That means that a vortex must be shed in order to create a net fluid rotation. If taking inviscid incompressible flows this might (mistankely) show there is no drag which is impossible. This is due to the D’Alambert paradox, ehihc states that the net aero force on a rigid body is zero, no matter the shape.

Question 2

What does the Joukowski formula say?

Answer 2

It gives the lift force directly in terms of circulation. It greatly simplifies computing lift about the body that would require integrating pressure over the entire surface:
F=ρUeΓ