Kutta–Joukowski theorem

The Kutta–Joukowski theorem states that lift per unit span on a body in steady two-dimensional flow equals fluid density times flow speed times circulation around the body.

Circulation (fluid dynamics): A scalar measure of fluid velocity’s tangential component integrated around a closed curve. It is the flow quantity that the theorem multiplies by density and speed to determine lift.
Two-dimensional flow: A flow whose velocity and relevant properties vary in two spatial dimensions, with no variation in the third. The theorem’s lift is defined per unit span under this geometric idealization.
Martin Kutta: A German mathematician who studied fluid flow and formulated the trailing-edge condition for airfoils. His work supplied the condition that selects circulation in practical airfoil flow.
Thin airfoil theory: A linear aerodynamic theory that predicts lift and moments for thin airfoils at small angles of attack. It uses circulation-based lift to derive airfoil lift coefficients.
Navier–Stokes equations: Partial differential equations describing viscous fluid motion and its momentum transport. Unlike the theorem’s ideal-flow setting, they account directly for viscosity.
Kutta condition: A condition selecting the physically realized circulation around a lifting body with a sharp trailing edge. It supplies the circulation value used to predict lift for an airfoil.
Incompressible flow: A flow in which fluid density is treated as constant along fluid motion. The standard theorem assumes density can be treated as uniform and constant.
Nikolay Zhukovsky: A Russian mathematician and aerodynamicist who developed foundational theories of lift and airfoil flow. His independent derivation helped establish the circulation–lift relation.
Finite wing: A wing of limited span whose flow includes three-dimensional effects and wingtip vortices. The two-dimensional theorem alone misses the induced effects of finite span.
Unsteady aerodynamics: The study of aerodynamic forces when flow or body motion changes with time. Time-dependent forces require extensions beyond the theorem’s steady-flow statement.

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Aerodynamic liftRelated: It gives a compact mathematical account of lift on a two-dimensional section.