Back-Water and Drop-Down Curves for Uniform Channels

Most of the existing formulas for determining back-water and drop-down curves in open channels, are applicable only to channels of simple geometric cross-section. Moreover, these formulas usually yield inaccurate results because in their derivation the effects of variation of velocity head are neglected, or the coefficient, C, in Chezy's mean-velocity formula is considered constant. In the present study, rational back-water and drop-down formulas are derived in such a manner that they are applicable to a wide variety of commonly used cross-sections. These formulas are based on accurate mean-velocity expressions of the exponential type, and make full allowance for velocity-head effects. The results of numerous tests in experimental channels are presented, and these results the compared with values computed by existing formulas and by the new formulas derived by the writer. In a thorough treatise entitled "Hydraulics of Open Channels", B. A. Bakhmeteff, M. Am. Soc. C. E., has also introduced the hydraulic exponent to express the characteristics of a channel cross-section. The writer's manuscript was prepared independently and has the merit of simplifying the computation in its application to various cases. This statement does not imply a criticism of Professor Bakhmeteff's treatment, but is intended merely to establish a line of demarcation, in the hope that discussers will avoid confusing the two treatments.