Kutta–Joukowski theorem

<p>The Kutta–Joukowski theorem is a fundamental theorem in <a href="/facts/Aerodynamics/Cn6Lnl3H">aerodynamics</a> used for the calculation of <a href="/facts/Lift_(force)/ehQKKaWP">lift</a> of an <a href="/facts/Airfoil/2d3l6hKd">airfoil</a> (and any two-dimensional body including circular cylinders) translating in a uniform <a href="/facts/Fluid/tMQ46Tmz">fluid</a> at a constant speed so large that the flow seen in the body-fixed frame is steady and <a href="/facts/Flow_separation/Lnvdqo4p">unseparated</a>. The theorem relates the lift generated by  an airfoil to the speed of the airfoil through the fluid, the <a href="/facts/Density/92p6hh9I">density</a> of the fluid and the <a href="/facts/Circulation_(fluid_dynamics)/9SbB60N2">circulation</a> around the airfoil. The circulation is defined as the <a href="/facts/Line_integral/10s4B3Nn">line integral</a> around a closed loop enclosing the airfoil of the component of the velocity of the fluid <a href="/facts/Tangent/sF0jH3EI">tangent</a> to the loop. It is named after <a href="/facts/Martin_Kutta/VwJXlfUJ">Martin Kutta</a> and <a href="/facts/Nikolay_Zhukovsky_(scientist)/avfrPXSs">Nikolai Zhukovsky</a> (or Joukowski) who first developed its key ideas in the early 20th century. Kutta–Joukowski theorem is an <a href="/facts/Inviscid_flow/GRNloKQ6">inviscid theory</a>, but it is a good approximation for real <a href="/facts/Viscous/QLVfrdCz">viscous</a> flow in typical aerodynamic applications. 
</p><p>Kutta–Joukowski theorem relates lift to circulation much like the <a href="/facts/Magnus_effect/Sgolud8d">Magnus effect</a> 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 <a href="/facts/Superposition_principle/GKGs9C92">superposition</a> of a translational flow and a rotating flow. This rotating flow is induced by the effects of <a href="/facts/Camber_(aerodynamics)/nCqgfTqd">camber</a>, <a href="/facts/Angle_of_attack/v5NkMgqu">angle of attack</a> and the sharp <a href="/facts/Trailing_edge/ymBLLVBl">trailing edge</a> of the airfoil. It should not be confused with a vortex like a <a href="/facts/Tornado/HSGNQzHa">tornado</a> 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 <a href="/facts/Airfoil/2d3l6hKd">airfoil</a> is usually mapped onto a circular cylinder. In many textbooks, the theorem is proved for a circular cylinder and the <a href="/facts/Joukowski_airfoil/gwtd93m9">Joukowski airfoil</a>, but it holds true for general airfoils.
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Kutta–Joukowski theorem open-in-new

Kutta–Joukowski theorem