240 HYDRAULICS AND ITS APPLICATIONS 



should be guarded against by a relief valve or ether similar device placed 

 as near as convenient to the main valve. In the case of a pipe line for a 

 power plant, where the head is not excessive it is usual to provide a stand 

 pipe, or simple vertical pipe capable of taking the whole discharge of the 

 main, and open at the top to the atmosphere. This should be coupled to 

 the supply main just before its entrance to the power-house, and the 

 height should be so arranged that when standing under the statical 

 pressure of the supply reservoir, the water level is within a short distance 

 of the top. Under these conditions, the maximum pressure which may 

 occur in the pipe line is that due to the statical pressure in the stand pipe, 

 together with that necessary to produce motion up this pipe. 



It is usual in practice to make some allowance for possible water 

 hammer by designing the pipes to withstand a pressure of 100 Ibs. per 

 square inch in excess of that due to the statical head, thus, in effect, 

 allowing for an instantaneous stoppage at a velocity of 1*6 feet per second. 



Sudden Opening of a Valve. 



If the valve at the lower end of a pipe line be suddenly opened, the 

 pressure behind the valve falls by an amount p Ibs. per square inch, and 



a wave of velocity v towards the valve \v = p^/^L (approx.) L and of 



pressure p below statical, is propagated towards the pipe inlet. 



The magnitude of p depends on the speed and amount of opening of 

 the valve, and if the latter could be thrown wide open instantaneously 

 the pressure would fall to that obtaining on the discharge side. In the 

 author's experiments, with the valve thrown open through *5 of a com- 

 plete turn the maximum drop in pressure was 40 Ibs. per square inch, 

 the statical pressure being 45 Ibs. per square inch. 



With the valve opened through "10 of a complete turn the maximum 

 drop was 20 Ibs. per square inch, and with ^ of a complete turn the 

 drop was 11 Ibs. per square inch. In each case the time of opening was 

 less than '13 seconds (l+V p ). 



In the case of a horizontal pipe, or one which is so situated that the 

 absolute statical pressure is everywhere greater than p, this pressure 

 wave reaches the pipe inlet with approximately its original amplitude, 

 and at this instant the whole column is moving towards the valve with 

 velocity v and pressure p below normal. 



The pressure at the inlet is, however, maintained normal, so that the 

 wave returns from this end with normal pressure and with velocity 2v. 



