| 引用本文: | 刘西乐,赵名彦,李如意, 等.标准I、II型马蹄形断面临界水深直接计算式[J].灌溉排水学报,2021,(12):142-148. |
| LIU Xile,ZHAO Mingyan,LI Ruyi, et al.标准I、II型马蹄形断面临界水深直接计算式[J].灌溉排水学报,2021,(12):142-148. |
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| 摘要: |
| 【目的】针对马蹄形断面几何形式复杂，其临界水深为高次超越方程，难以直接求解，现有公式多为分段函数且存在误差大、适用范围小等问题，提出一种方便实用且具有较高精度的临界水深直接算法。【方法】通过对明渠临界流方程进行恒等变换，统一标准I、II型马蹄形断面临界水深计算方程，基于数学理论构造替代函数模型，并通过带粒子释放的优化PSO算法对研究范围内的真值按照预设函数模型进行逼近。【结果】建立了标准I、II型马蹄形断面临界水深直接计算式。通过对现有公式的归纳比选、误差分析及实例计算表明，该式形式简单不分段、计算方便快捷且物理概念明确，在工程实用范围内计算相对误差绝对值最大分别为0.37%和0.40%，具有较高的计算精度。【结论】建立的马蹄形断面临界水深直接计算式在简捷性、适用范围、精度等方面综合评价较好，实用推广性强。 |
| 关键词: 水力学；临界水深；马蹄形断面；PSO算法 |
| DOI：10.13522/j.cnki.ggps.2021005 |
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| Formulae for Calculating the Critical Water Depth in Standard I and II Horseshoe-shaped Open Channels |
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LIU Xile, ZHAO Mingyan, LI Ruyi, et al
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| Abstract: |
| 【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. |
| Key words: Hydraulics; critical water depth; horseshoe-shaped open channel; PSO algorithm |
