Kutta-Joukowski Theorem

The Kutta-Joukowski theorem is a fundamental result in aerodynamics that relates the lift generated by an airfoil moving through a fluid at constant speed to the circulation of the fluid velocity field around it. It applies to an airfoil or any two dimensional body, including a circular cylinder, moving steadily through a uniform fluid, and it expresses the lift per unit span in terms of the fluid density, the airfoil speed, and the circulation, defined as a specific line integral of the fluid velocity around a loop enclosing the body. The theorem is named for Martin Kutta and Nikolai Zhukovsky, who independently developed its key ideas in the early twentieth century. Although it assumes an idealized, non viscous fluid, the theorem gives a good approximation of lift in real, viscous airflow for typical aerodynamic applications, and it is most often proved by mapping the airfoil onto a circular cylinder.