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The Kutta-Joukowski Theorem is a fundamental theorem of aerodynamics. It is named after the German Martin Wilhelm Kutta and the Russian Nikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid, and the circulation. The circulation is the line integral of the velocity of the fluid, in a closed loop enclosing an airfoil. It can be understood as the total amount of "spinning" of the fluid around the airfoil.

The theorem refers to two-dimensional flow around an airfoil (or an airfoil of infinite span) and determines the lift generated by one unit of span. When the circulation Γ is known, the airfoil lift l per unit span can be calculated using the following equation:

l = ρVΓ

where ρ is the fluid density, V is the speed of the airfoil through the fluid, and Γ is the circulation.

Formal proof of the theorem is to be found in standard texts (see eg ref. 1, p 406). However as a plausibility argument, consider a thin airfoil of chord c and infinite span, moving through air of density ρ. Let the airfoil be inclined to the oncoming flow to produce an average air speed V on one side of the airfoil, and an average air speed V + ΔV on the other side. The circulation is then

Γ = (V + ΔV)c − (V)c = ΔV.c

The difference in pressure ΔP between the two sides of the airfoil can be found by applying Bernoulli's equation:

ΔP = ρ.V.ΔV (ignoring )

so the lift force per unit span is

l = ΔP.c = ρ.V.ΔV.c = ρVΓ

A differential version of this theorem applies on each element of the plate and is the basis of thin-airfoil theory.

Batchelor, G. K. (1967) An Introduction to Fluid Dynamics, Cambridge University Press

• Kutta condition
• Lift
• Lift coefficient
• Horseshoe vortex
• Wing

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