SMALL ORIFICES 



113 



i.e., the coefficient of contraction in the case of a Borda's mouthpiece, where 

 the effluent stream does not touch the sides of the mouthpiece, is one half. 



Borda's Mouthpiece running full. With a vertical Borda, where the 

 water in the vessel is initially quite steady, 

 the issuing jet after becoming parallel does 

 not again come into contact with the sides 

 of the mouthpiece. If, however, the water 

 in the vessel be agitated, the jet, after con- 

 tracting to form a vena contracta, again 

 expands to fill the mouthpiece (Fig. 62). 

 This is termed running full as opposed to 

 running freely as in the previous case. The 

 issuing motion is now turbulent, not steady 

 as is the case with a free Borda. It is 

 worthy of note that under no circumstances 



with a free Borda, or indeed with any jet having non-sinuous motion, is 

 any splash produced on meeting a solid surface. With sinuous motion 

 splashing always occurs. 



We now get a loss of head due to the expansion of the stream from a e 

 to a after contracting, so that 



PI _, ^i 2 , , ^o j_ t'o 2 

 n7 ~r o~^ ~t~ ^ 7?7 ~r Q " 



+ loss d |ie to expansion. 



The loss due to expansion (Art. 33) = =-- (m I) 2 , 



M 



where m = 



But pi = and r x = 0. Also Zi ZQ =h . 



(1) 



Now equating the momentum passing the section at per second, to 

 the force producing it, we get 



Ji7 7 W 2 



W a tin PQ a = a VQ* 



1t - ^ = 



. 2 



But /< - fr= <f- [ (m - I) 2 + 1] from (1) 



i; 



2 



Equating these values we get - =1 



H.A. 



