WATERHAMMER AND SURGE TANKS 139 



flexibility of the penstock walls, however, the velocity is reduced 

 and may be computed from the following formula: 



a = 



Where 



a = velocity of pressure wave or vibration in feet per second ; 



g = acceleration of gravity = 32. 16; 



y = specific weight of water = 62.4 pounds per cu. ft.; 



A- = elasticity of water in compression =42,000,000 pounds per 



sq. ft. 



d = inside diameter of penstock in inches; 

 t = thickness of plate in inches; 

 K = elasticity of penstock material in tension : 

 For steel plate = 4,032,000,000 Ibs. per sq. ft. = 



(28,000,000 Ibs. per sq. in.); 

 For cast iron =2,160,000,000 Ibs. per sq. ft.= 



(15,000,000 Ibs. per sq. in.) 



The value of a varies from 2500 to 4000 feet per second as the 

 size of pipe decreases, and the time required for the pressure wave 

 to reach the top of the penstock and return is evidently equal to 



r,-=. 



a 

 Where 



Ti = time required for round trip of pressure wave in seconds; 

 L = Length of penstock in feet. 



If now the gate is closed instantaneously, or, in a time T, which 



or 

 is equal to or less than , i.e., before the reflected pressure wave 



has had time to return to the gate and reduce the pressure there, 

 we obtain a maximum excess pressure head which is equal to 



, av 



*-_, 



while the total pressure will be equal to the above plus that caused 

 by the static head, or 



at; 



