基于牛顿法的梯形明渠临界水深直接算法

A direct formula based on Newton algorithm for calculating critical depths of trapezoidal open channels

依据牛顿算法及渐近解分析 ,本文提出了一种梯形明渠临界流方程的直接算法。由该方法所构造的临界水深近似公式结构简明 ,精度较高 ,计算经济 ,便于工程实际应用 ,在区间 ( 0 ,∞ )上的最大相对误差绝对值达 10 -10 。

By Newton algorithm and the analysis for asymptotic solution, this paper presents a direct formula for calculating critical depths of trapezoidal open channels. The approximate formula has many advantages, such as concise formation, high precision, less computation and easy use in engineering. Its maximal absolute value of relative error is 10 -10 in the interval (0,∞).