(~) A 



(■»)A' 

 in i 



u 



/^ 



-^ 



\ 





1 J-\ 





■Wi 



/l'(<-) 





V 







\ 



/' 



•4H 



v^ 



> 



/ 









B /( 



J 



1 — 



\ — 





B' A- 





Figure 181 - The two-dimensional Borda's mouthpiece. See Section 112. 



where c is real. Hence, using Equations [Ilia] and [112a], 



1/2, 



dz^- idw = - c[2«2 - 1 + "itit^ - 1) ■ 1 c?i^A, 



o T 1/2 ^ , 1/2^. 



= -clr + i(r-i) - In i;- In [^ + (r - 1) ]l + ^. 



[112c] 



Here the amplitudes of the algebraic functions of t^ except t and t - 1, are confined to the 



Tge from to tt. At 6 or 3 = ia, il = - 1; at s = - za, t=\. Hence, 



a a 



c= — , k = ia. 



n TT 



The velocity of the fluid at any point, using Equation [112a], is given by 



_2 

 9 1/2 



= -\t+ it^ -1^ 



dz C 



dw 1 ^ 9 1/2, 



- u + iv= — ^ -—^ = -[t + {r -1) 



[112d,e] 



[112f] 



By proceeding as in the last section it is found that along the walls AB and A'B' q ^ u and 



[112g] 



1-5- \ + q 

 - In 



•zq 



2q J 



279 



