Гидродинамика

SUMMARY 367 (E, •({). The $-axis must represent the boundaries of the flow con ­ sidered, i. e. the contours of free currents and of walls of vessels. Accordingly it must, firstly, consist of different branches of the curves ili — const and, secondly, of alternating • portions — const and 0 = const. Then the segments on which simulta ­ neously ij) = const and 0 = const will give the rectilinear walls of vessels, and the segments const and — const — the contours of the stream-lines. In order to satisfy the conditions imposed on the generating set ('-p, ij »), Prof. Joukowsky puts (w) к \ I к J where F(u) is a whole algebraic function of the order not above the second, with real coefficients, which may involve an additio ­ nal imaginary constant and which corresponds to a stream with an infinite volume of passing fluid; the values a,., p,., are real quantities. The points 0) are termed the p o l e s of t h e g e n e r a t i n g s e t . The number of poles corresponds to the number of currents of the problem in question. Since when a circle is described around one of the poles, the function /- (u) is increased by the quantity of fluid carried by each current will be As to the function ф(и), this function is written by Prof. Joukowsky, in accordance with the conditions previously stated, in the following form: ф{и) = т С , ( U ) J У (и —c^) (и — C . J (li —C a ) where m is unity, or i, and Cj, • Сд are real quantities. The points (c,,, 0) are termed the f o c i of t h e d i r e c t i n g s e t : they are the boundaries of the portions 0 = const, and i) = const, i. e. they correspond to the places of transition from the walls to the free currents. The function f(u) has the form: к " (12)