梯形明渠临界水深的迭代解法

An iteration method calculating critical water depth in an open trapezoidal channel

迭代法作为一种基本算法，适用于求解梯形明渠的临界水深。本文化迭代函数为无因次形式，并给出良好的初始近似值及适当的加权系数，证明了对于任一梯形明渠，迭代过程都是收敛的，而且计算效率甚高：使用函数计算器作一次或两次“迭代修正”，临界水深的相对误差绝对值即小于６．６‰或２．２‰。

The iteration method, as a basic calculation tool, is suitable for calculating the critical water depth in an open trapezoidal channel. This paper presents a nondimensional iteration function, an approximate initial value and a proper weight allocation. With these, for various trapezoidal channels, the convergence of iteration process is proved and the calculation speed is fast. When the iterations are carried out once or twic,the relative errors of calculated results are less than 6.6‰, and 2. 2‰ respectively