268 HYDRAULICS AND ITS APPLICATIONS 



Discharge from two small pipes = I ^ l ^ 2 . ^- \ ^ 



PI 



5 5 



/. For same discharge D% = Z d 2 



.'. D = <$ d = 1-32 d. 



Thus, assuming the resistance to vary as v 2 , one pipe 15'84 inches 

 diameter would give the same discharge as two 12-inch pipes. 



Assuming more correctly the results of the experiments quoted on 

 p. 222, and taking 



we should have in the above example, D 2 ' 58 = 2 d 2 ' 58 



.-. D = 2 8 . d = 1-308 d. 



or one pipe 15'70 inches would now give the same discharge as the two 

 12 inch pipes. 



This duplication in parallel of supply pipes is very common in large 

 water supply systems, and is also of use where, in the case of a fire main, 

 the pressure at the nozzle is insufficient to give the required velocity of 

 flow. By coupling a second line of hose between the supply main and 

 the hydrant box, the fall in pressure at the nozzle is much reduced and 

 consequently a higher jet is obtained. 



ART. 80. MAIN OF UNIFORM DIAMETER IN WHICH THE DISCHARGE 

 DIMINISHES AS THE LENGTH INCREASES. 



In water mains for domestic supply, the main pipe is tapped at 

 intervals by service pipes, so that the volume carried gradually 

 diminishes. Let the rate of diminution be uniform and equal to q cubic 

 feet per second per foot run of the pipe. Let I be the total length ; H 

 the total loss of head in the pipe ; Q the initial supply ; V the initial 

 velocity of flow. Then the volume passing any point P distant x from 

 the entrance, will be Q qx c. f. s. Let h x be the loss of head up to 

 this point. 



Then since the loss of head in a length Bx at P 



