悬链线形渠道临界水深的计算方法

Computation of critical depth for catenary-shaped channel

根据悬链线形渠道断面几何条件及临界水深基本方程,导出了关于悬链线形渠道临界水深的隐性关系式。通过引入恰当的无量纲量,对悬链线形渠道收缩水深的隐函数方程作数学变换,推导出适用于悬链线形渠道临界水深的迭代公式。利用最优一致逼近原理得到了无量纲公式中两参数的近似计算式,用于迭代公式初值的求解。工程实例表明,该方法不仅具有精度高、适用范围广等特点,且物理概念清晰明确,公式形式简捷、直观,便于应用。

The implicit formula of the critical depth for catenary - shaped channel is derived from fundamental equation of criti- cal depth and the geometric condition of the catenary - shaped cross - section channel. Moreover, the appropriate dimensionless parameters are introduced to the mathematical transformation of implicit equation of contraction depth, and the interactive formula of critical depth is obtained. An approximate formula for calculating the initial iteration value is obtained according to optimal uni- form approximation principle. The results show that the computation is high precision with wide scope of application and explicit physical conception.