140 WATER CONDUCTORS AND ACCESSORIES 



where 



corresponding to maximum pressure; 

 v = velocity of water in penstock in feet per second, cor- 



responding to the normal water flow; 

 ho = static head in feet. 



It is impossible for the pressure to rise above this value, H mM . 



2L 



The time , therefore, represents the critical time in which the 

 a 



turbine gates may be closed, and it is evident that the time of 



or 



closure should always be greater than , in which case the water- 



a 



hammer can never reach a maximum value. 



2L 



When the time is greater than , the excess pressure head 



a 



may be calculated from the following formula by Warren: 1 



, Lv 



and the total pressure head becomes: 



Haw* = ho -f 



The above pressure will also be obtained if the gate is only 

 closed partially, as long as the closing is at such a rate that T is 

 the time which it would require to completely close it. 



Example: Assume a steel pipe line having a length of 1000 feet, 

 a diameter of 4 feet and a plate thickness of J inch. The water 

 velocity is 6 feet per second and the net head 100 feet. What is 

 the minimum time in which the turbine gates may be closed, in 

 order that the excess pressure due to waterhammer shall not exceed 

 50 per cent of the normal pressure due to the net head? 



The first thing is to ascertain the velocity of the pressure wave 

 which is computed as follows : 



T 32.2 



/ i 48' x 



V \ 62 ' 1 42,000,000 + iX4,032,000,000/ 



1 For derivation of formula see Transactions Am. Soc. Civil Engrs., 

 Vol. 79, 1915, page 238. 



