悬链线形断面渠道临界水深的直接计算方法

Direct Computation Method for Computing Critical Depth in Channels of Catenary Sections

针对悬链线形断面临界水深的计算问题,引入无量纲临界水深,对各计算参数的取值范围进行了讨论,确定了适用于工程实际的无量纲临界水深的取值区间,并运用逐次优化拟合方法建立了新的临界水深计算公式。结果表明,工程适用范围内的最大相对误差绝对值小于0.072%,以0.001为步长的平均相对误差绝对值小于0.026%。相比于现有的计算公式,新建立的公式精度高,形式较为简捷,且适用范围完全能够满足工程应用的需要。

Dimensionless critical depth was introduced for the problem of critical depth calculation in catenary cross-sections. The interval of its values suitable for practical engineering was determined after the discussion of the ranges of each parameter. A new formula was established for computing critical depth based on the method of optimal fitting. The results indicated that within the scope of practical engineering, maximum relative error was less than 0.072% and average relative error with steps of 0.001 was less than 0.026%. Compared with the present- ly available formulae, the newly proposed formula had high accuracy, brief form and could completely meet the requirements of applicable range for engineering application.