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| DOI：10.13522/j.cnki.ggps.20180379 |
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| Analytical Method for Calculating Water Depth at Contracted Section in Catenary Channel |
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XU Xiaoyang, ZHANG Genguang*, WANG Yule, LI Qing, CHEN Xuebiao
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College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China
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| Abstract: |
| 【Objective】The purpose of this paper to present a method to calculate water depth at contracted section in catenary channel. 【Method】 Using dimensionless parameters, the equation for water depth at contracted section in catenary channel was mathematically transformed to derive an implicit function for the dimensionless water depth. Based on the definition of a special equation with one unknown variable, a regression model with α and x in the range of α∈[0.01,0.5] and x∈[0.5,7] was established to obtain a alternative to the special quadratic equation for the dimensionless contracted water depth. Solving this special equation using the root-finding formula can obtain the contracted water depth. We also analyzed the errors of this method.【Result】For engineering application, the absolute value of the maximum relative error of the formula was less than 0.94%, more accurate than the existing formulae.【Conclusion】The calculation formula for the contracted water depth in catenary channel is applicable to a wide range of problems. It is simple and accurate, meeting the requirement of most projects. |
| Key words: catenary channel; contracted water depth; quadratic equation with one unknown variable; special quadratic equation with one unknown variable; regression analysis; direct computation formula |
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