114 



HYDRAULICS AND ITS APPLICATIONS 



(ni I)' 2 = 1 or m 2, 



i.e., the coefficient of contraction at the neck in a Borda's mouthpiece 

 running full is one half. 



If the jet discharges into the atmosphere so that p = we have 



?- 2 = g 1i , so that v = ** .?._ (approximately), 

 v 2 



i.e., the velocity of discharge is /== times the velocity when flowing 



v ^ 

 free, and since the area of full jet = 2 (area of free jet). 



.'. Quantity flowing per) , 



second from full Borda I == V 2 (quantity from free Borda). 



The coefficient of discharge from such an orifice is thus equal to V 2 

 times the coefficient for a free Borda mouthpiece and therefore to 



7=f . Taking C v = '975 this would make C = '745. 

 C vV & 



Experiments by H. J. Bilton 1 on such mouthpieces, 2| diameters in 

 length, gave the following values for C, no variation of C with head being 

 noted for heads as low as 6 inches : 



The difference between the calculated and experimental values of C is 

 due to the fact that the area at the vena contracta is actually greater than 

 5 a because of the effect of viscosity in modifying the equation of 

 momentum. Eddy loss at the re-expansion of the stream is consequently 

 reduced with a corresponding increase in discharge. 



Denoting the contracted section by the suffix ( 2 ) we have 



t-'O i 



2~# 



2 



W'+Tj-i = fl 



But loss due to expansion = ^- (2 I) 2 = ~ 



2i O i Q 



Also i' 2 = 2 v > 



loss due to expansion. 



(Art. 33) 



1 "Victorian Inst. of Engineers," April 1, 1908. 



