LAW OF CONTINUITY 



53 



position hh, a distance equal to Vidt\ and the cross section fg to mn, 

 a distance equal to V2dt. 



The law of continuity may be applied in either of two ways. Con- 

 sidering the two cross sections hh and/g, Fig. 501 (a), there is less water 

 contained between these two cross sections at the end of the interval 

 dt, when the jump is at ke, than there was at the beginning of the 



(b) 



( V,-y^)dt W/// 



Fig. 501. Vertical Longitudinal Section through a Moving Hydraulic Jump. 

 (All velocities are toward the right.) 



interval, when the jump was at cd. Therefore, the amount of water 

 flowing out across the section /g, equal to D'^^di, is greater than the 

 amount flowing in across the section hh, equal to DiVidt; and greater 

 by an amount exactly equal to the reduction in storage between cross 

 section hh and fg. The reduction in storage is represented by the area 

 cdek, whose height is D2 — Di and whose length is VQdt. Therefore, 



D2V2 = i)iFi+ {D2-D,)Vq 



[501] 



