NOZZLES 283 



The discharge per second without the nozzle is given by 



/ 2 q H 

 VA x A = V -T71 X A cub> ft " 



1 L L * 



V 8 



and the kinetic energy by ^. A X 62'4 ft. Ibs. 

 2 a 7f ^ 62-4 



D 



With the nozzle, the quantity per second is 



/ 2 g H 



a = V 4^ 4 X * 



"* 1 + 



D 5 



with nozzle 



/ D& _ { ^L 



I (D 5 + 4/^ 4 )i 16 



\ D ( 7T 2 > 4 



V /'D 4- 4 / n 1 Ifi 



without nozzle 



16 ) 



/ d* 



-V / 



or the quantity passing the pipe is always less with, than without the 

 nozzle. 



Since the kinetic energy varies as the product of two factors (the 

 quantity and the (velocity) 2 ), one of which increases, while the other 

 diminishes as the nozzle area is increased, a maximum amount of kinetic 

 energy will be delivered at the nozzle with some definite ratio of pipe 

 and nozzle areas. 



To obtain this ratio we have 



v 3 

 K.E. with nozzle = ~ X 62'4 a ft. Ibs. per sec. 



j 1 + 4//^^ X 6 



2^X4 



H )f 

 = 395 d a -! I , 4 /' I d* [ ft. Ibs. per sec. (6) 



H 



= 395-^ D 2 4// ^ [ ft Ibs. per sec, (7) 



-^ I 1 I i^~ * 75 



