马蹄形断面隧洞临界水深的直接计算

The direct solution on critical depth of horseshoe section tunnel

马蹄形过水断面因其几何图形复杂,水力计算无论是采用查图查表还是迭代试算或是编程计算都是比较繁琐,计算误差较大,且易出错,为此本文通过对马蹄形断面临界流方程的数学变换,应用最优逼近拟合原理,提出了两种典型断面临界水深的直接计算公式,该公式物理概念清晰明确,直观简捷。综合评价表明:该公式简单、准确、适用范围广,最大误差不超过1.6%,对生产实践及水工设计手册编制均有参考价值。

The hydraulic calculation of horse-shoe section tunnel is trouble because of its complex shape. Using the mathematics transformation method and the theory of optimization and regression to deal with the basis equation of the critical depth in horse-shoe section tunnel, a new brief and exact direct formula is presented in the paper,which overcomes the shortage of other methods, such as chart look-up method, trial-and-error method and iterative trial method. The new method has clear physical concept, makes the course straight and short and the max. error is less than 1.6 %, so it will be useful in engineering practice and in course of compiling handbook of hydraulic structure design.