HYDRAULIC JUMP 



27 



of energy, whereas the change represented by equation (304) always 

 involves loss of energy. The loss of energy approaches zero as Di 

 approaches D2, or as the height of the jump becomes infinitesimal. The 

 depths before and after the jump approach the critical depth, which is 

 the depth at which small fluctuations in depth may occur freely. 



Consider the different possible depths at which a given quantity of 

 water can flow in a rectangular frictionless open channel with parallel 

 sides, for different values of the total head. The constant width of the 

 channel may be assumed to be unity, so that 



Q = VD 



Denoting the total head by H, 



H = D -{■ 



2g 



Eliminating V between the two equations, 



D^{H - D) = — == a constant 

 2g 



[305] 



This relation between the depth of flow and the total head is plotted in 

 Fig. 302, Values of abscissas and ordinates are plotted in terms of the 

 critical depth. This diagram shows (1 ) that the total head is a minimum 

 when it is two- thirds depth and one-third velocity head. When at this 



Total Head 



Fig. 302. Depths of Flow in a Rectangular Channel, for Constant Discharge. 



stage, the flow is critical, and the depth may change appreciably with 

 comparatively no change in total head. (2) When the flow is not 

 critical, two depths of flow are possible at any given total head, one 

 greater, and one less, than the critical depth. These are the alternate 

 depths illustrated by Fig. 201. When water is flowing freely at either 



