Zhukovsky's theorem, a theorem on the lift acting on a body in a plane-parallel flow of a liquid or a gas. It was formulated by N. E. Zhukovsky in 1904. According to this theorem, the lift is due to the vortices associated with the body in the flow (the so-called bound vortices), which arise because the liquid is viscous. The presence of these vortices means that the flow past the wing has a non-zero circulation of the velocity.
If a steady plane-parallel potential flow (see Potential flow) of an incompressible liquid meets an infinitely long cylinder at right angles to its generators, then a portion of the cylinder of unit length along the generator experiences a lift Y equal to the product of the density ρ of the medium, the velocity v of the flow at infinity and the circulation Γ of the velocity round any closed contour enclosing the cylinder, that is Y=ρvΓ. The direction of the lift is obtained by turning the velocity vector at infinity through a right angle against the direction of the circulation. Zhukovsky's theorem also holds for subsonic flow of a compressible liquid (gas) past an aerofoil. For sonic and supersonic flow speeds Zhukovsky's theorem cannot be proved in a general form. Zhukovsky's theorem became the basis of the modern theory of the wing and of the screw propeller. Zhukovsky's theorem can be used to calculate the lift of a wing of finite span, the thrust of a screw propeller, the pressure force on a turbine or compressor blade and others.
If a steady plane-parallel potential flow (see Potential flow) of an incompressible liquid meets an infinitely long cylinder at right angles to its generators, then a portion of the cylinder of unit length along the generator experiences a lift Y equal to the product of the density ρ of the medium, the velocity v of the flow at infinity and the circulation Γ of the velocity round any closed contour enclosing the cylinder, that is Y=ρvΓ. The direction of the lift is obtained by turning the velocity vector at infinity through a right angle against the direction of the circulation. Zhukovsky's theorem also holds for subsonic flow of a compressible liquid (gas) past an aerofoil. For sonic and supersonic flow speeds Zhukovsky's theorem cannot be proved in a general form. Zhukovsky's theorem became the basis of the modern theory of the wing and of the screw propeller. Zhukovsky's theorem can be used to calculate the lift of a wing of finite span, the thrust of a screw propeller, the pressure force on a turbine or compressor blade and others.