Zhukovskii theorem

One of the fundamental theorems in the hydromechanics of incompressible ideal fluids, obtained by N.E. Zhukovskii in 1906 using methods of the theory of functions of a complex variable: The lifting force of a wing (per unit length of the wing) in a stationary plane-parallel stream of a fluid (a gas) is orthogonal to the velocity of the stream at infinity and is equal in magnitude to the product of this velocity, the circulation velocity, and the density of the fluid. When applying Zhukovskii's theorem, it must be borne in mind that the magnitude of the circulation velocity is uniquely determined by the Zhukovskii condition for the finiteness of the velocity of the fluid at the rear sharp edge of the wing (see Zhukovskii function, Figure 2 and the literature cited).

Comments

This theorem is usually called the Kutta–Zhukovskii theorem in the Western literature. "Zhukovskii" is also spelled "Joukowski" in the Western literature.

References

[a1]	L.D. Landau, E.M. Lifshitz, "Fluid mechanics" , Addison-Wesley (1959) (Translated from Russian)
[a2]	G. Birkhoff, "Hydrodynamics, a study in logic, fact and similitude" , Princeton Univ. Press (1960) pp. Chapt. IV Zbl 0095.20303
[a3]	H. Lamb, "Hydrodynamics" , Cambridge Univ. Press (1932)
[a4]	L.M. Milne-Thompson, "Theoretical hydrodynamics" , Macmillan (1957)
[a5]	L. Prandtl, O.G. Tietjens, "Applied hydro- & aeromechanics" , Dover, reprint (1934)
[a6]	L. Prandtl, O.G. Tietjens, "Applied hydro- & aeromechanics" , Dover, reprint (1934)