1891.] 



Fluid Motions in two dimensions. 



191 



9. Peoblem (iii). Oblique impact of a jet upon a finite lamina. 



This problem includes Mr Michell's of the impact of a jet 

 against an infinite plane, and also the problem of the impact of an 

 infinite stream against a finite lamina worked out by Kirchhoff 

 and Lord Rayleigh. 



The ^-region is bounded by two free stream-lines, by the lamina, 

 and by the continuations of the stream-line that divides on the 

 lamina. 



We shall suppose that u = ± 1 correspond to the ends of the 

 lamina, and u = a to the point where the stream-line divides, u = b 

 and u = c to the points to which the two streams go. 



The w-region will be bounded by the two infinite lines yjr = 

 and yjr = tt say, making the breadth of the original jet ir, and by 

 the two sides of a line ty = (3 say, where it > (3 > ; thus 



a\Z 



-1 



and this region can be conformably represented upon the half- 

 plane u by means of the relation 



dw 

 du 



u — a 



(u — b) (u — c)' 



•(21), 



and then 



"dr = 



a—b 

 ~c~^b 



