Kutta-Joukowski theorem in fluid dynamics

In fluid dynamics, the lift per unit distance (L') acting on a body in a two-dimensional flow field is directly proportional to the circulation, that is, it can be expressed as the product of the circulation Γ on the body, the density of the fluid ρ, and the velocity of the body with respect to the free stream V:.

This is known as the Kutta-Joukowski theorem.[4]​.

This equation applies around aerodynamic surfaces, where circulation is generated by aerodynamic action; and around rotating objects experiencing the Magnus effect where circulation is mechanically induced. In aerodynamic action, the magnitude of the circulation is determined by the Kutta condition.[4]​.

The circulation in each closed curve around the airfoil has the same value, and is related to the lift generated by each unit of span length. As long as the closed curve encloses the airfoil, the choice of curve is arbitrary.[3]​.

Circulation is often used in computational fluid dynamics as an intermediate variable to calculate forces on an airfoil or other body.

Fundamental equations of electromagnetism

In electrodynamics, the Maxwell-Faraday Law of Induction can be stated in two equivalent ways:[5]​ that the curvature of the electric field is equal to the negative rate of change of the magnetic field.

or that the circulation of the electric field around a loop is equal to the negative rate of change of the magnetic field flux through any surface traversed by the loop, by Stokes' theorem.

The circulation of a static magnetic field is, by Ampère's law, proportional to the total current enclosed by the loop.

For systems with electric fields that change over time, the law must be modified to include a term known as Maxwell's correction.

• - Maxwell's equations.

• - Biot-Savart law.

• - Kelvin circulation theorem.

Kutta-Joukowski theorem in fluid dynamics

In fluid dynamics, the lift per unit distance (L') acting on a body in a two-dimensional flow field is directly proportional to the circulation, that is, it can be expressed as the product of the circulation Γ on the body, the density of the fluid ρ, and the velocity of the body with respect to the free stream V:.

This is known as the Kutta-Joukowski theorem.[4]​.

This equation applies around aerodynamic surfaces, where circulation is generated by aerodynamic action; and around rotating objects experiencing the Magnus effect where circulation is mechanically induced. In aerodynamic action, the magnitude of the circulation is determined by the Kutta condition.[4]​.

The circulation in each closed curve around the airfoil has the same value, and is related to the lift generated by each unit of span length. As long as the closed curve encloses the airfoil, the choice of curve is arbitrary.[3]​.

Circulation is often used in computational fluid dynamics as an intermediate variable to calculate forces on an airfoil or other body.

Fundamental equations of electromagnetism

In electrodynamics, the Maxwell-Faraday Law of Induction can be stated in two equivalent ways:[5]​ that the curvature of the electric field is equal to the negative rate of change of the magnetic field.

or that the circulation of the electric field around a loop is equal to the negative rate of change of the magnetic field flux through any surface traversed by the loop, by Stokes' theorem.

The circulation of a static magnetic field is, by Ampère's law, proportional to the total current enclosed by the loop.

For systems with electric fields that change over time, the law must be modified to include a term known as Maxwell's correction.

• - Maxwell's equations.

• - Biot-Savart law.

• - Kelvin circulation theorem.