Гидродинамика

А MODIFICATION OF KIRCHHOFF'S METHOD OF REPRESENTING A TWO-DIMENSIONAI MOTION OF A FLUID, GIVEN Л CONSTANT VELOCITY ALONG AN UNKNOWN STREAM-LINE The modification introduced in to Kirchhoff's method by- Prof. Joukowsky is formulated by him in par. 1 of this work in the following words: „In the proposed modification of Kirchhoff's method we afford the means to proceed to the solution of a particular problem without a preliminary conformal transformation of the regions of the corresponding contours, and thus eliminate a superfluous operation which was necessary in the original Kirch­ hoff's method. The problem is not restricted either by the num­ ber of points of zero velocity nor by the number of currents. Owing to this our method has enabled the solution of many new problems that did not lend themselves to the treatment by Kirchhoff's method". Joukowsky's method is as follows: Let the region of the problem be the region of a complex variable z ~ x - \ - i g . Then, as is known, the characteristic stream-function will be (1) '•p being the velocity potential and i the stream-function. Differentiating and denoting by С the reciprocal of , wo r (z) have; С = -=jy r —— (cos 0 i - i sin ')) ~ ^ e"' r {z) V V where v is the velocity and 0 the angle of the velocity with the jc-axis. The value is at the base of Kirchhoff's method-