32 HYDRAULIC JUMP IN RECTANGULAR CHANNELS 



bend itself, the water being given an abnormal velocity distribution 

 which persists for some distance downstream before its energy is dissi- 

 pated. 



If the hydraulic jump is " drowned out," that is, if the tailwater is 

 raised so high that the jump no longer forms, the high velocity sheet 

 will continue in an erratic and fluctuating manner for a considerable 

 distance under and through the slower water. Conditions then are more 

 like those in the bend. The energy loss is not concentrated in a small 

 space, but is spread out through a large volume. 



The energy loss through a hydraulic jump which is functioning properly 

 may be evaluated theoretically. By Bernoulli's theorem the loss of head 

 (including that due to friction from the bottom and sides of the channel, 

 which is small) is 



Introducing equation (304) which was derived from the momentum 

 relation, and the law of continuity Q = Y\D\ = V2D2 which applies 

 because the flow is steady, the loss of head through the jump may be 

 expressed in terms of velocities 



. _ (Fi - V2)' 

 2g(Fi + V2) 



[306] 



or depths 



It is seen that the loss becomes greater as the height of the jump in- 

 creases, and approaches zero as the height of the jump approaches zero. 



Uses of the hydraulic jump. Perhaps the earliest practical use of the 

 hydraulic jump was as a " head increaser." Water to be discharged at 

 as low an elevation as possible is caused to flow into the passing stream 

 at a point where the velocity is high and the depth low, upstream from a 

 hydraulic jump.® 



The hydraulic jump frequently forms close to the toe of overflow dams. 

 If it forms at all stages, and remains close to the dam, it is a particularly 

 efficient means of destroying the excess energy of the overflowing water, 

 and preventing the dam from being undermined and washed out. 

 Unless the dam and apron have been carefully designed to insure the 



* Among the unpublished papers of the late D. L. Yarnell is found reference to 

 the use of the hydraulic jump in this manner, described, he said, in Del Moto E 

 Misura Dell ' Acqtia, by Leonardo da Vinci (Bologna, 1828). 



