WATER HAMMER 225 



In an experiment carried out by Prof. I. P. Church, 1 on a pipe line 

 1 inch in diameter and 2,395 feet long, fitted with a nozzle 2 inches 

 diameter at its lower end and discharging into the atmosphere, the nozzle 

 was closed in 25 seconds, so as, ft is stated, to give uniform retardation in 

 the pipe. The statical head at tho valve was 302 feet (131 Ibs. per square 

 inch), and the pressure at the nozzle during steady flow was 108 Ibs. per 

 square inch. The maximum pressure attained was 143 Ibs. per square 

 inch, so that p v p s = 12 Ibs. per square inch. 



Here, assuming a coefficient of velocity of '985, the velocity of efflux 

 would be '985 V2 g X 108 X 2'31 = 125 feet per second, so that the 

 velocity in the pipe would be 7'81 feet per second. 



This makes a=*812 feet per sec., per sec., and makes 



w , 62-4 X '312 X 2395 



. a I = - oaTn ~ =: 1>455 Ibs. per square foot, 

 g OA& 



= 10*1 Ibs. per square inch, 

 as compared with the observed value 12 Ibs. per square inch. 



Uniform Closure of Valve. Where the outlet valve is closed uniformly, the 

 acceleration varies from instant to instant according to a complicated law. 



Let the pipe line, of uniform area a square feet, discharge at its lower 

 end through a valve into a chamber where the pressure is uniformly 

 PQ Ibs. per square foot. Let times be measured backward from the 

 instant the valve reaches its seat, so that, if the valve be closed uniformly 



in T seconds, using the same notation as before we have a = ai - r -~ as 



giving the valve opening at an instant t seconds before closure is complete. 

 Let v a be the velocity in the pipe line. Equation (3) now becomes 



w %g g Jo d t Zgmjo 



Bt being negative. 



p= 

 Also since, when jc = Q, 



) v = v p v 2 - 

 ' Va \ J v ~ dx - ' 



Again, when x=l, i.e., on the outlet side of the valve, neglecting losses 

 in the valve, we have 



dt 



1 Journal of Franklin Institute, April and May, 1890. 

 H.A. 



