SMALL OKIFICES 117 



x (m I) 2 , where in = , 



*/ 6 



.2 2 



we have 7i=^+| 2 -=^-(l + ( l) a } (2) 



Writing r = C v V 2 /* we get ^T= * 2 - 2 wi + 2 (3) 



v/U 



Giving C v its mean observed value, '825, this makes m = 1*685 



= -^7 7 while giving the value "62, as observed for a similar orifice 

 594 3 m 



without the external tube, it makes C v = *852. The difference between 

 this value and *852 is probably due to the loss due to expansion being 

 somewhat greater than indicated above. Assuming this loss to be given 



A 



by k~{ m 1 } 2 , cf. Art. 33, and introducing this into equation (2), 

 equation (3) becomes 



_!_ C* = m 2 - 2 m + 1 + -1 



while giving C v and the values *825, and *620, this makes k = 1*25. 



If, in equation (1), we substitute m C v V 2 g h = m VQ for r 2 this 

 becomes -j^- = h (1 m* C v z ), 



and giving C v and m the values '825 and -^- we have -rrr= '763 h. 



This agrees very closely with the observed value of ^L, which is 



approximately *75 h. 



If then an orifice be made in the mouthpiece, at the vena contracta 

 (Fig. 63 b), a tube coupled to this and having its lower end open and in 

 water will support a column of height approximately '75 h. Theoretically, 

 this will hold until '75 h = height of the water barometer = 34 feet, i.e., 



until h = T^T = 45'4 feet. The effect then of adding the external mouth- 

 piece is to reduce the pressure on the discharge side of the orifice, and so 

 to increase the effective head, and therefore the velocity of discharge. 

 For continuity of flow it is essential that the pressure at the vena contracta 

 should be greater than absolute zero ( 34 feet of water), so that a short 

 outlet tube will not run full under a head greater than about 40 feet. 

 If a diverging tube be placed at the discharge end of the mouthpiece 



