Гидродинамика

366 а m o d i f i c a t i o no f k i r c h h o f f s m e t h o d The essential change introduced by Pro{". Joukowsky consists in the first place in that he considers not С itself, but the value log (wQ, where w is constant velocity on the contour of a free current Evidently = + ( 7 ) This logarithmic function of Prof. Joukowsky has the following very important property*, on the contours of free currents the real part of the function is zero, since г» is equal to w, and on rectilinear walls of vessels the imaginary part becomes constant, as the direction of velocity is unchanged. The complex variables (1) and (7) are the fundamental varia ­ bles in Joukowsky's method. There exists a relation connecting' these variables in view of С = „ /V, • This relation is defined / ' ( Z ) by Joukowsky as follows. He introduces an auxiliary variable and puts Separating the real and the imaginary parts of the function '/.(и) and making them equal to arbitrary constants, Prof Joukowsky obtains on the upper half-plane (;, vj) two families of mutually orthogonal isothermal lines a = const and ''j —- const. These two families are termed by Prof. Joukowsky the g e n e r a - t i n g s e t. Similarly, for the function 0(w) are obtained another two families of curves iV const and 0 " const, termed the d i r e c t i n g s e t . Both of the two sets are made by Prof. Joukowsky to satisfy the following fundamental conditions. In the" first place, both sets, are disposed, as has been mentioned, in the upper half-plane a " T -|- П| i) -j- гО = Ф (ii). (9)