30 HYDRAULIC JUMP IN RECTANGULAR CHANNELS 



quently that, under the theory of inelastic impact, the depth can change 

 abruptly from a value less than the critical depth to a particular related 

 value greater than the critical depth. The change in the jump from the 

 initial velocity to the final velocity, however, is very evidently not in- 

 stantaneous. At points between the cross sections where the initial and 

 final velocities occur, the average velocity must have intermediate values. 

 At first glance this would seem to contravene the theory of the jump, 

 which seems to preclude any value for the average velocity after the 

 initial value, except the calculated final one. 



A reason for this may be found if we examine conditions within the 

 jump. Except in very small jumps in which surface tension prevents 

 their entrance, the water is filled with thousands of minute bubbles. 

 These rise to the surface quickly, leaving clear water. They undoubtedly 

 assist in the dissipation of energy and in smoothing out the violent 

 velocity variations. On the steep forward surface of the jump, a roller 

 forms, tumbling in erratic manner against the rapidly flowing sheet 

 below. The admixture of air reduces the specific gravity of the liquid, 

 and this increases the static pressure on a vertical section. By finding 

 how much the static pressure needs to be increased in order that the 

 law of momentum may be satisfied at every intermediate section, a 

 hypothetical profile through the jump may be computed.^ Unfortu- 

 nately this profile does not fit observed data; it is too high. It should 

 not be expected to fit, for the assumption is made that the velocity 

 is uniform throughout each vertical section. Owing to the presence of 

 the roller, the velocity distribution is far from uniform. 



Another hypothetical profile may be computed by assuming that the 

 roller has no resultant downstream momentum, but that it supplies the 

 necessary pressure on top of the expanding jet to preserve continuity 

 in the pressure-plus-momentum relations.^ This profile does not fit the 

 observed data; it is too low. 



No mathematical analysis of conditions within the jump which will 

 give results that consistently agree with experiment is known to the 

 authors. Apparently the answer to this difficult problem must await 

 laboratory investigation. A few investigations have been made, es- 

 pecially directed toward determining the length of the jump. There is 

 a lack of agreement among the different investigators, and until this has 

 been resolved by further experimentation, it seems unwise to accept any 



^ Miami Conservancy District Technical Reports, Part III, p. 28 et seq. 



^ " The Hydraulic Jump and its Top Roll and the Discharge of Sluice Gates," 

 by Kazimierz Woycicki, Chapters III & IV, translated by I. B. Hosig, Bureau of 

 Reclamation, Technical Memorandum 435. 



