CHAPTER V 

 THE MOVING HYDRAULIC JUMP 



The moving hydraulic jump is a transitory phenomenon closely related 

 to the stationary hydraulic jump. The bore, which occurs in some 

 tidal rivers and estuaries, is a moving hydraulic jump. The surge is a 

 special case of the moving hydraulic jump. The action of the ocean 

 surf on smooth beaches provides a ceaseless natural example of the 

 moving hydraulic jump. As the height of a jump moving in still water 

 approaches zero, the water surface does not break, and the jump 

 becomes indistinguishable from the small "solitary positive wave" 

 observed by J. Scott Russell. 



By experimental means, Russell determined the correct formula for 

 the velocity of the wave in still water. ^ Later Bazin determined its 

 velocity in moving water. Bazin also experimented with surges and 

 moving jumps of appreciable height.^ 



The equations for the moving hydraulic jump may be derived from 

 those for the stationary jump by careful application of the principle of 

 relative velocities, or they may be derived by direct application of the 

 fundamental laws of continuity and change of momentum. Figure 

 501(a) represents a vertical longitudinal section through a hydraulic 

 jump moving to the right with velocity Vq. The channel is rectangular, 

 with horizontal bottom, and friction is to be neglected. It is conven- 

 ient to consider a unit width. The velocity distribution, at sections 

 before and after the jump, is assumed to be uniform, and the positive 

 direction for all velocities is toward the right. If Di, D2, Vi, and V2 

 are constant, then Vq will also be constant. 



In Fig. 501(a) at a particular instant the jump is supposed to be at 

 cd. Consider the mass of water acdfgja, including the jump and con- 

 tained between the vertical cross sections aj and fg. This is shown as 

 the shaded area in Fig. 501(6). After a brief interval of time dt all 

 this water will have moved towards the right, to the position bkemnhb, 

 shown by the shaded area in Fig. 501(c). The jump will have moved 

 from cd to ke, a distance equal to Vodt] the cross section aj to the 



^ Report of the fourteenth meeting of the British Association for the advance- 

 ment of science. London, 1845. 



^ " Recherches Hydrauliques," Darcy and Bazin, Paris, 1865. 



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