SELECTION OF CHEZY'S C 71 



In general, if the flow follows any of the backwater curves, it must be 

 because of some departure from the conditions that sustain uniform 

 flow at the normal depth. There must be some change, such as a dam, 

 a constriction, or a change of grade, to cause the flow to follow one of 

 the curves rather than to continue parallel to the bottom of the channel. 

 Imagine the change to be suddenly introduced into the uniform channel. 

 A disturbance of the water surface will result, starting waves. If the 

 velocity of the uniform flow is higher than the critical, any small waves 

 that form will be swept downstream by the current. Large waves will 

 cause a hydraulic jump, which may travel upstream for a short distance, 

 but which must become stationary as soon as the point is reached where 

 the downstream depth is sequent to the depth of the uniform flow. 



If the velocity is less than critical, however, the waves will progress 

 upstream without causing a jump, and the effect of the dam or con- 

 striction will extend upstream a considerable distance. 



Thus it is seen that the control is downstream when the depth is 

 greater than critical, and upstream when the depth is less than the 

 critical. Experiments indicate that this criterion holds even when the 

 depth is very near the critical. For example, submergence has no 

 effect on the discharge of a broad-crested weir until the tailwater has 

 reached the level of the critical depth over the crest. 



Selection of Chezy's C. In using equations (608) or (609), the 

 variation of the friction loss throughout the length of the backwater 

 curve is evaluated by means of Chezy's formula. The error from this 

 source can be minimized by using a more accurate friction formula to 

 evaluate the average rate of loss. This is accomplished by choosing a 

 value of C that will make Chezy's formula agree with Manning's (or 

 Kutter's) at an intermediate depth. This value of C is then used 

 throughout the range of the backwater curve. The intermediate depth 

 used for determining C can be the arithmetical average of the depths at 

 each end of the range, or it can be selected on the side of the mean in 

 which the greater portion of the backwater curve will lie. The effect 

 of convergence or divergence of the flow upon the friction loss can also 

 be allowed for in this manner. 



By Kutter's formula, C is a function of the slope. Care must be 

 taken not to use the bottom slope, but rather the slope that would 

 sustain uniform flow at the selected depth in the given channel. 



The value of C determined upon should be used throughout the entire 

 length of the curve. To break the curve into short lengths and use a 

 different value of C in each may seem to offer an improvement in accu- 

 racy. This procedure is not justified, however, for the convenience of 

 Bresse's method is lost, and the errors resulting from the assumption of 



