HE THEORY OF THIN BODIES

S. K. Betyaev

UDC 532.527

It is shown that, in accordance with the law of plane 
sections representing the basis of the theory of thin bodies, two 
analogies are true: a nonstationary analogy and a stationary one. 
Within the framework of the stationary analogy, a new-type expansion 
reducing a three-dimensional problem to a stationary two-dimensional 
one is introduced. The asymptotic conditions of validity of the stationary 
and nonstationary analogies were determined and the boundary-layer 
conceptions for both cases were compared. Solutions of the internal 
and external problems on a two-dimensional flow in a narrow zone were 
obtained in the closed form. An asymptotically correct mathematical 
model of a flow in a film is proposed. The stationary and nonstationary 
analogies for a swirling flow around a body and a flow around a rotating 
body were determined.

Prof. N. E. Zhukovskii Central Aerodynamics Institute, 
1 Zhukovskii Str., Zhukovskii, Moscow Obl., 140181, Russia; email: 
betyaevs@gmail.comanslated from Inzhenerno-Fizicheskii Zhurnal, 
Vol. 80, No. 5, pp. 45-54, September-October, 2007. Original 
article submitted February 22, 2006.