关键词：
水力学模型;坝;灌渠;直接计算;梯形断面;收缩水深;无量纲水面宽度
摘 要：
梯形断面渠道是比较常用的断面形式之一,其收缩水深的计算需求解高次隐函数方程,传统的图解法或者试算法计算过程复杂,费时费力且误差较大,针对此种状况欲提出一种直接计算公式。通过引入无量纲水面宽度,对梯形断面收缩水深的基本方程进行恒等变形,得到了快速收敛的迭代公式,在工程常用范围即无量纲收缩水深在[0.01,0.5]范围内,对公式进行了优化计算,取得了合理的迭代初值。从而得到梯形断面收缩水深的直接计算公式。误差分析及实例计算表明,在工程常用范围内,收缩水深的最大相对误差仅为0.26%,直接计算公式形式简捷、精度高、适用范围广。
译 名：
Formula for direct calculation of contracted depth of channel with trapezoidal section
作 者：
Zhao Yanfeng1,2,Wang Zhengzhong1,2,Lu Qin1 (1.College of Water Resources and Architectural Engineering,Northwest Agriculture and Forestry University,Yangling 712100,China;2.Reseach Center of Water Engineering Safety and Disaster Prevention,Northwest Agriculture and Forestry University,Yangling 712100,China)
关键词：
hydraulic models,dams,irrigation canals,direct calculations,trapezoidal section,contracted depth,non-dimensional surface width
摘 要：
The channel with trapezoidal section is used commonly in practical engineering.To get the contracted depth in the section,high order implicit equation need to be solved.Conventional methods,such as graphic approach and trial calculation method,are complex,inefficient and with large error.So a direct calculation formula with simple form,high efficiency and high precision,is presented in the current work.By introducing a non-dimensional width of water surface,an iterative formula with high efficiency for calculating contracted depth is obtained by identical transformation of the fundamental equation of contracted depth.The reasonable iterative initial value is also given by optimizing the formula form.The non-dimensional contracted depth ranges from 0.01 to 0.5,which satisfies the requirement of practical engineering.Finally,the direct formula for calculating the contracted depth is obtained.Error analysis and a practical engineering example are given to show the advantages of the current direct calculation formula.
