44 HYDRAULIC JUMP IN NON-RECTANGULAR CHANNELS 



of solutions is required, another diagram may be plotted in which the 

 P -\- M function has been eliminated in the same way that the total 

 head was eliminated in preparing Fig. 402 from the data of Fig. 401. 

 Several other methods are discussed by P. S. Hsing, who came to the 

 conclusion that unless a very great number of solutions is to be made for 

 the same channel, the amount of work involved in the preparation of 

 charts or nomographs is not justified, and the problem should be solved 

 by simple cut-and-try solution of equation (402).^ Table 402 provides 

 a solution for trapezoidal channels which is sufficiently accurate for most 

 purposes. 



In determining the location of a jump in a non-rectangular channel, 

 the procedure described in Chapter III may be followed, but a slightly 

 different method will usually be more convenient. Curves represent- 

 ing values oi P -\- M are plotted above the bottom of the channel, cor- 

 responding to the depths of flow of the upstream and downstream water 

 surface profiles. The jump will form where the upstream and down- 

 stream values oi P -\- M are equal at a distance apart equal to the 

 estimated length of the jump. This method differs from that of Chapter 

 III in that two P -\- M curves are plotted instead of one curve of sequent 

 depths. Unless values of sequent depths are readily available it is more 

 convenient. 



Experimental work on the hydraulic jump in non-rectangular chan- 

 nels has been reported by Lane and Kindsvater, for circular channels, 

 and by Posey and Hsing, for trapezoidal channels.^ In both investi- 

 gations, the observed relation of the sequent depths verified the con- 

 clusions of the momentum theory. The length of the jump increases 

 rapidly as the deviation from the rectangular shape becomes marked. 

 If the width after the jump is appreciably greater than the width before 

 the jump, eddies will be formed at each side, modifying the character 

 of the jump and reducing its capacity to dissipate most of the energy 

 within a short space. 



The depth after the jump in a circular conduit may be below the top 

 of the section, or the conduit may flow full, under pressure if necessary, 

 for the balance of pressure and momentum required by the theory. If 

 the pipe does flow full, the air drawn into the jump is carried away down- 

 stream. As with the jump in a rectangular channel, the impact is 

 violent. The velocity distribution becomes nearly uniform only a 



^ " The Hydraulic Jump in Trapezoidal Channels," by Pei-su Hsing, thesis, 

 State University of Iowa, 1937. 



^ " Hydraulic Jump in Enclosed Conduits," by E. W. Lane and C. E. Kinds- 

 vater, Engineering News-Record, Dec. 29, 1938; " Hydraulic Jump in Trapezoidal 

 Channels," by C. J. Posey and P. S, Hsing, Engineering News-Record, Dec. 22, 1938. 



