WATERHAMMER AND SURGE TANKS 141 



The permissible excess pressure is equal to 



Cri 



X 100 = 50 feet; 



and thus 



1000X6 



50 = 



/ loooy 



V 2700/ 

 T=4.1 seconds. 



An extensively used formula for calculating waterhammer is 

 also the following one, derived by L. Allievi: 



where 



This formula is applicable for a slow closing of the valve when 



2L 



T is considerably greater than , but may be incorrect for a 



a 



2L 



quick closing as when the value of T 7 is close to . 



a 



Surge Tanks. In plants with long pipe lines under medium 

 and high heads it is often found that not only the pressure rise, 

 but also the pressure drop will be excessive, and in such cases 

 it may be necessary to provide both a relief valve and a surge 

 tank to equalize the pressure variation. Synchronous relief 

 valves (see page 258) are, of course, only of use against a pressure 

 rise when the load is going off and not when the load is coming on, 

 because they cannot supply to the moving water column the 

 kinetic energy which it has lost and which it must regain before it 

 can flow at the higher velocity required by an increase of load. 

 To accomplish this, surge tanks, or standpipes as they are also 

 commonly termed, must be used. 



There are two kinds of surge tanks, the simple and the differ- 

 ential. The former consists of an open standpipe or storage tank 

 placed at the downstream end of the pipe line (Fig. 68). When 

 the gates are closed the inertia of the water column in the penstock 

 causes a rise of the water in the standpipe, and the velocity is 

 thus gradually reduced. On the other hand, when the load comes 



