whereas,- along the median plane or the a;-axis, q = - u and 



1+q 1-q 

 + in 



2q 



[112h] 



To trace the upper free streamline, to which the lower is symmetrical, introduce again 

 the angle d, which is here negative. Then 



^1/2 ^ ^'17/2 ^ pQg ^ J gjjj ^ pQg 



- , cos - =- (^1/2+ ^-1/2) = _i 



2 2 2 s / 5 



dz = dx + idy = - tdw = c I cos — + i sin — tan , 



* 2 9( / 9 9 



a; = — sin — - In sec — w = {0 - sin 0) + a, 



* 2 2 / 277 ^ ^ 



[112i,j] 



after integrating and using Equation [112d]. As 0->-77, a:-*-"^ and y ^ a/2. Thus the entire 

 jet is ultimately only 2a - a or a wide, and the ratio of contraction is a/2a = 1/2. The volume 

 of fluid issuing per second and per unit length is a. 

 One side of the jet is plotted in Figure 182. 



Figure 182 — Borda's mouthpiece: one side 

 of the jet. (Copied from Reference 1.) 



Line of Symmetry 



The same remarks hold here as in the last section in regard to the terminal form of the 

 free streamlines, the pressure, the velocity and the effect of gravity. 



(For notation and method see Section 34; Reference 1, Article 74, where b = a/2; 

 Reference 2, Section 11.51.) 



280 



