A differential version of this theorem applies on each element of the plate and is the basis of thin-airfoil theory. Formal derivation Lift forces for more complex situations The lift predicted by the Kutta-Joukowski theorem within the framework of inviscid potential flow theory is quite accurate, even for real viscous flow, provided the flow is steady and unseparated. When there are free vortices outside of the body, as may be the case for a large number of unsteady flows, the flow is rotational. When the flow is rotational, more complicated theories should be used to derive the lift forces. Below are several important examples.

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Learn how and when to remove this template message The Kutta—Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil and any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated.

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 around the airfoil. The circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop.

Kutta—Joukowski theorem is an inviscid theory , but it is a good approximation for real viscous flow in typical aerodynamic applications. Kutta—Joukowski theorem relates lift to circulation much like the Magnus effect relates side force called Magnus force to rotation. The fluid flow in the presence of the airfoil can be considered to be the superposition of a translational flow and a rotating flow.

This rotating flow is induced by the effects of camber , angle of attack and the sharp trailing edge of the airfoil. It should not be confused with a vortex like a tornado encircling the airfoil.

At a large distance from the airfoil, the rotating flow may be regarded as induced by a line vortex with the rotating line perpendicular to the two-dimensional plane. In the derivation of the Kutta—Joukowski theorem the airfoil is usually mapped onto a circular cylinder. In many text books, the theorem is proved for a circular cylinder and the Joukowski airfoil , but it holds true for general airfoils.

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