242 HYDRAULICS AND ITS APPLICATIONS 



than in the preceding case, and under such circumstances the wave 

 motion dies out very quickly. As the valve opening becomes greater, the 

 efficiency of the valve as a reflecting surface becomes less, so that with a 

 moderate opening the pressure may never even attain the pressure due to 

 the statical head. 



This is shown in Fig. 109, which is a diagram obtained by the author 

 from the experimental pipe line when the outlet valve was opened 

 suddenly (time <C'13 seconds) through half a complete turn. 



Neglecting the effect of elasticity of the water column, the velocity of 

 efflux accompanying a sudden valve opening may be obtained as follows : 



Imagine the effective valve opening to assume instantaneously a 



value a and to remain of this value, so that' C -~ = ~ ~. Equa- 



dt a dt 



tion (6), (p. 225), now becomes 



P i v * 1 ( x dv j f f * 2 7 



- + s h z ~ -- ~u ( ^ x ~ (T~ v <to + c (6 ) 



w 2 g g) gdt 2 gm J 



while equation (9) becomes 



or k = c s - 



where 



fl Cl(? 



., , f dv 1 f . 



so that I o % + D dt. 

 J c 2 r 2 /, J 



From this we get 



while since v = when t = 0, we have D = 0. 



1-ef * 



P er second 1 (12") 



1 + eT ' t ] 



giving the velocity of efflux at an instant t seconds after the valve 

 opens. 



" Water Hammer" ante cit., p. 51. This formula receives close experimental confirmation 

 from the results of experiments on the velocity of flow down the drive pipe of a hydraulic 

 ram, published in the Bulletin of the University of Wisconsin. No. 205, 11)08, p. ] 43. 



