Kutta–Joukowski theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Kutta%E2%80%93Joukowski_theorem


00:02:30 1 Lift force formula
00:06:14 2 Circulation and the Kutta condition
00:08:47 3 Derivation
00:09:15 3.1 Heuristic argument
00:14:16 3.2 Formal derivation
00:14:26 4 Lift forces for more complex situations
00:23:01 5 See also



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SUMMARY
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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. It is named after Martin Kutta and Nikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. 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. However,  the circulation here is not induced by rotation of the airfoil. 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 a 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.