28 HYDRAULIC JUMP IN RECTANGULAR CHANNELS 



of these depths, a small change of depth cannot occur without a corre- 

 sponding change in total head. (Flow as in Figs. 201, 202, or 203 is 

 excluded from consideration, for Fig. 302 represents flow in a parallel- 

 sided, horizontal, rectangular channel, with free surface.) 



The dotted lines on Fig. 302 connect values of Di and D2 before and 

 after a hydraulic jump. The horizontal distance between the ends of 

 one of the dotted lines represents the loss of total head in passing through 

 the jump. 



The alternate depths, for which the total head is the same, should 

 not be confused with the depths before and after a jump, for which the 

 total head is not the same, except for very low jumps. Depths before 

 and after a jump have been called conjugate depths, to distinguish them 

 from alternate depths, but the writers prefer a term suggested by M. F. 

 Thorne, sequent depths. The word conjugate is almost synonymous with 

 alternate, and implies reversibility. Sequent, on the other hand, carries 

 the idea of a definite, irreversible, order of sequence. 



Near the critical depth there is very little loss of energy in the jump, 

 compared with its height. The standing waves which occur easily, when 

 the flow is critical, might be considered to be small jumps. This is an- 

 other way of explaining the instability of the water surface for depths 

 of flow near the critical depth. 



Experimental verification of the jump theory. The first measure- 

 ments of the hydraulic jump phenomenon apparently preceded the 

 development of the correct theory. It should be remembered, in com- 

 paring the results of experiments with the theory, that many of the 

 experiments were made in small channels, or in channels with artificially 

 roughened bottoms, in which case the effect of friction prevents exact 

 agreement. Figure 303, adapted from Riegel and Beebe, shows a dimen- 

 sionless plot of observed data, the momentum formula, and the formula 

 which would be correct if Bernoulli's theorem applied to the hydraulic 

 jump; that is, if there were no loss of energy through the jump. It is 

 seen that Gibson's experiments verify the law most closely. This is to 

 be expected, for his channel was wide, and most nearly approached the 

 ideal rectangular frictionless channel. For very low jumps, the points 

 scatter, some even showing an apparent gain of energy. This illustrates 

 the difficulty of making precise measurements in the immediate neigh- 

 borhood of the critical depth. 



Length of the hydraulic jimip. It has been shown that if water is 

 flowing in a smooth, uniform, rectangular open channel with level 

 bottom, it is impossible for the flow to change to a different depth in 

 accordance with Bernoulli's theorem, unless the flow is at critical stage, 

 when small fluctuations only may occur. It has been shown subse- 



