| 摘要: |
| [目的]寻求梯形明渠正常水深的直接计算方法.[方法]针对梯形明渠正常水深计算时需求解高次隐函数方程,以及传统的查图表法或试算法计算复杂、误差大、适用范围小的缺点,通过引入无量纲水面宽度,根据数值计算方法,对梯形明渠均匀流的基本方程进行了恒等变形,得到了快速收敛的迭代公式,并与合理的迭代初值进行配合使用.[结果]提出了梯形明渠正常水深的直接计算公式.误差分析及实例计算表明,在工程最常用范围内,即无量纲水深x∈[0.1,2.0],梯形断面边坡系数m∈[0.5,4.0]时,正常水深的最大相对误差仅为0.78%.[结论]与现有公式相比,该直接计算公式物理概念明确、计算简捷、精度高、适用范围广. |
| 关键词: 梯形明渠 正常水深 直接计算方法 无量纲水深 无量纲水面宽度 |
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| 基金项目:国家高技术研究发展计划(863计划)，陕西省水利科技专项计划项目 |
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| A direct formula for normal depth in trapezoidal open channel |
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| Abstract: |
| 【Objective】 The aim was to find the direct calculating formula for trapezoidal open channel of normal depth.【Method】 The calculation of trapezoidal open channel of normal depth needs solving latent function formula with high exponent,which is hard to obtain;the traditional methods,trial computation or needing graphic chart method with complex calculating course,have high errors and small using area.So this study obtains iterative formula for quick calculation by introducing non dimensional surface’s width and doing identical transfiguration to basic equation of normal depth for open trapezoidal channel based on calculating method,then it was used with rational quantity for the first iteration.【Result】 This paper gets direct calculating formula,in the commonest fields of engineering,namely non dimensional water depth x∈［0.1,2.0］,slope coefficient of cross section m∈［0.5,4.0］,error analysis.The application shows that the maximum error of normal depth is less than 0.78%.【Conclusion】 This formula has definite physics concept,easy calculation,high precision and wide range compared with the existing formulas. |
| Key words: trapezoidal open channel normal depth direct calculating method non dimensional depth non dimensional surface width |
