Guan'gai paishui xuebao (Dec 2021)

Formulae for Calculating the Critical Water Depth in Standard I and II Horseshoe-shaped Open Channels

  • LIU Xile,
  • ZHAO Mingyan,
  • LI Ruyi,
  • LIU Zihui,
  • ZHAO Yafeng,
  • SUN Jie

DOI
https://doi.org/10.13522/j.cnki.ggps.2021005
Journal volume & issue
Vol. 40, no. 12
pp. 142 – 148

Abstract

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【Background and objective】 Critical water depth is an important design parameter of open channels. Since standard horseshoe-shaped open channel does not have strict requirements on geological environment and is convenient to construct, it has been widely used in water conveyance projects in both irrigation and other areas. However, the horseshoe-shape is geometrically complex and the calculation of its critical water depth is more difficult than other types of channels. The objective of this paper is to propose an alternative method to overcome this shortcoming. 【Method】 We first transformed the critical water depth problem to a nonlinear constrained optimization problem via the identity- transformation of the open channel critical flow equation. We then constructed an inverse function model with the optimization solved by the PSO algorithm with particle release. The results calculated in the practical range was approximated by a pre-set function, from which we derive a formula to calculate the critical water depth for standard I and II horseshoe-shaped channels. 【Result】 ①Comparison with existing formulas showed that the proposed formula is simple and does not need segmentation; it is thus more efficient and physically sound as it comprises compounded power functions only. The formula can be used to design the bottom arch section, side arch section and top arch section of the open channels, it is thus practically useful for practitioners because its ease for use. ②Comparison with experimental data showed the maximum relative error of the proposed formula for standard I and II channel was 0.37% and 0.40%, respectively, which is comparable to, if not lower than, the existing formulae. 【Conclusion】 The formula we proposed for calculating the critical water depth in horseshoe-shaped open channels is accurate and efficient. It can be used by researchers and practitioners to design water-conveyance channels in irrigation projects and other areas.

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