282 HYDRAULICS AND ITS APPLICATIONS 



With a ring nozzle the preceding formula becomes 



p g 



(4) 



V -.*-J 



where a c is now the area of the vena contracta of the issuing stream. 



In any case, when k and the coefficient of contraction for any given 

 nozzle are known, the value of v a can be directly determined in terms of 

 p. Then since the energy discharged at the nozzle per second 



we have the horse-power delivered at the nozzle given by 

 H p _ Wa c v* _ 62-4 a c v a 3 _ 8 



~2g X 550" 1,100 g ' "' V(l 



P 



EXAMPLE. 



With a uniformly converging nozzle, Ij inch diameter, taking k = *03, 

 and assuming a supply pipe of 3 inches diameter, we have a c = a = area 



2 -j 



of Ij inch pipe = '01227 square feet, while ^ -. Thus if the 



.A. 4 



pressure at the nozzle is 80 Ibs. per square inch, we have 

 H.P. at nozzle = 3*17 X '01227 | ^ I* 



= '0389 { 102-7 }i 

 = 40'5 H. P. 



If water is supplied at the pipe entrance under a constant pressure 

 P Ibs. per square foot, neglecting the difference in head between pipe 



p 



entrance and nozzle, we have =-.. = H, 



W 



.'. v a = V ' 





D 5 ) 

 Without the nozzle we should have a = A, v a = V A , 



I' ^ if H 

 and v 4 = V - -AT] fc - P er sec - 



so that the velocity with, is greater than without tht- nozzle. 



