CHAPTER VII 

 BACKWATER CURVES IN UNIFORM CHANNELS 



Backwater curves in uniform channels of standard rectangular or 

 trapezoidal cross section may be computed by means of Bresse's function 

 if the cross section is comparatively shallow and wide and the curve 

 does not cover too great a range of depths. Otherwise, profiles com- 

 puted with the aid of Bresse's function may differ appreciably from 

 profiles determined by field measurements. The experiments reported 

 by Nagaho Mononobe show that for close agreement between the com- 

 puted and the observed curves in channels of narrow deep cross section, 

 a better friction formula than Chezy's must be used, and the actual 

 shape of the channel must be considered.^ 



The method to be used, if Bresse's is judged to be unsatisfactory, 

 will depend upon the type of problem to be solved. When only a few 

 curves have to be computed and elevations are needed all along the 

 length of each curve, the step method for uniform channels described 

 in Chapter IX is most convenient. For another type of problem, 

 such as the determination of the flow in a channel connecting two res- 

 ervoirs, a large number of curves may be needed, and the labor of 

 computation, if the step method is used, may become excessive. The 

 elevations determined for the intermediate steps are not necessary 

 except in that they must be computed to obtain the desired elevation 

 at the far end of the channel. The graphical method for uniform 

 channels avoids this difficulty, and is most convenient for the solution 

 of problems of this type. 



Graphical method for computing backwater curves in miiform chan- 

 nels. In the derivation of Bresse's function, it was assumed that the 

 rate of loss of energy through friction, in non-uniform flow, is the same 

 as in uniform flow at the same velocity and depth. This assumption is 

 again necessary, but the friction loss will be evaluated by a modern 

 type of formula. The actual shape of the channel cross section will be 

 taken into account, in its effect on both friction loss and velocity head 

 changes. The friction slope, or rate of loss of head through friction, 



^ " Backwater and Drop-down Curves for Uniform Channels," by Nagaho 

 Mononobe, Trans. Am. Soc. Civil Eng., v. 103 (1938), p. 950. 



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