112 MOTION OF A LIQUID IN TWO DIMENSIONS. [CHAP. IV 



79. An interesting variation of the problem of Art. 77 has 

 been discussed by Bobyleff*. A stream is supposed to impinge 

 symmetrically on a bent lamina whose section consists of two 

 equal straight lines forming an angle. 



If 2a be the angle, measured on the down-stream side, the boundaries of 

 the plane of can be transformed, so as to have the same shape as in the 

 Art. cited, by the assumption 



<T=cr, 



provided C and n be determined so as to make ^ = 1 when =eT Mi7r ~ a) , and 

 ('= - I when = e -*+ a >. This gives 



The problem is thus reduced to the former case, viz. we have 



<=' 



Hence for \^ = 0, and 0>$> - 1, we have, putting 0= -0' as before, 



The subsequent integrations are facilitated by putting g = t- n , whence 



<t>' = ,i . ,NS- 



We have here used the formulae 



where 



Since q = d<f>'/ds, where 8s is an element of a stream -line, the breadth of 

 either half of the lamina is given by (iii), viz. it is 



2a 4a 2 P t~^ v , 

 H h 5- I ^ (v). 



^ 7T ^ 7T 2 Jo 1+^ 



* Journal of the Russian Physico-Chemical Society, t. xiii. (1881); Wiedemann's 

 BeibUitter, t. vi., p. 163. 



