The Kutta condition is a principle in steady-flow fluid dynamics , especially aerodynamics , that is applicable to solid bodies with sharp corners, such as the trailing edges of airfoils. It is named for German mathematician and aerodynamicist Martin Kutta. In fluid flow around a body with a sharp corner, the Kutta condition refers to the flow pattern in which fluid approaches the corner from both directions, meets at the corner, and then flows away from the body. None of the fluid flows around the sharp corner. The Kutta condition is significant when using the Kutta—Joukowski theorem to calculate the lift created by an airfoil with a sharp trailing edge.
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Two early aerodynamicists, Kutta in Germany and Joukowski in Russia, worked to quantify the lift achieved by an airflow over a spinning cylinder. The lift relationship is.
The vortex strength is given by. Like all aerodynamic lift, this seems a bit mysterious, but it can be looked at in terms of a redirection of the air motion. If the cylinder traps some air in a boundary layer at the cylinder surface and carries it around with it, shedding it downward, then it has given some of the air a downward momentum.
That can act to give the cylinder an upward momentum in accordance with the principle of conservation of momentum. Another approach is to say that you have exerted a downward component of force on the air and by Newton's 3rd law there must be an upward force on the cylinder. Yet another approach is to say that the top of the cylinder is assisting the airstream, speeding up the flow on the top of the cylinder.
Then by the Bernoulli equation , the pressure on the top of the cylinder is diminished, giving an effective lift. Kutta-Joukowski Lift Theorem Two early aerodynamicists, Kutta in Germany and Joukowski in Russia, worked to quantify the lift achieved by an airflow over a spinning cylinder.
Kutta-Joukowski Lift Theorem
Wings to your curious mind! Kutta Joukowski Theorem. Background and Historical Note:. But now the question arises what is the reason for this pressure difference?
Kutta-Joukowski force expression for viscous flow
We'd like to understand how you use our websites in order to improve them. Register your interest. The Kutta Joukowski KJ theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. However, this theorem was only proved for inviscid flow and it is thus of academic importance to see whether there is a viscous equivalent of this theorem.
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.