城门洞形断面隧洞正常水深的近似算法

Approximate solution of the normal depth inside tunnel with arch cross-section

城门洞形断面隧洞是输水工程中较常采用的一种形式,但其正常水深方程是超越方程,数学上无解析解。目前采用的图解、试算等方法存在着计算过程繁琐且计算精度差的缺陷。应用拟合法提出了近似计算公式,其形式简捷、结论准确。在工程常用范围内(0<h/r≤1.8)最大误差<0.2%。

The normal depth equation for arch cross-section tunnel is a transcendental equation and no analytical solution. Chart look-up methods and trial-and-error methods are currently used to compute the normal depth, but these methods are slow and complex. This paper presents an approximate formula by using fitting methods. This method is simpler and accurate. It ＇s maximum relative error are less than 0. 2 % in the utility range O〈h/r≤1. 8.