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).
E.D. Solomentsev
CommentsThis 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. Birhoff,
"Hydrodynamics, a study in logic, fact and similitude"
, Princeton Univ. Press
(1960)
pp. Chapt. IV | | [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) |
This text originally appeared in Encyclopaedia of Mathematics
- ISBN 1402006098
|