弧底梯形明渠正常水深的直接算法

A Direct Formula Calculating Normal Depth for Open Trapezoidal Channel with Spherical Bed

通过对弧底梯形明渠均匀流基本方程的数学变换，得到其无量纲正常水深的迭代公式，并从数学上证明了该迭代式的收敛性；通过数值计算选取恰当的迭代初值，再经迭代运算，提出了弧底梯形明渠均匀流水深的直接计算公式。实例计算及误差分析表明：在工程实用范围内该法最大相对误差为０．７％，而且克服了以往查图查表法及试算法的缺点，是一种简捷准确的有效方法。

A non dimensional iterative formula for computing normal depth is derived from transfroming identically the uniform flow equation for open trapezoidal channels with spherical bed. Moreover, according to hydraulic characteristics and iterative theory, for one thing, the astringency of this iteration formula has been testified, for another, an approximate formula for the same function has been obtained by using the principle of best approximation fit. Using this formula, an expression for initial value iteration is establisthed. A direct formula calculating normal depth for this type channel has been obtained by using the iterative formula one time. Error analysis and an illustration computed by using the dircet formula indicate that the absolute value of the maximum relative error of the normul depth is not greater than one percent, when we use it as iterative initial value to compute. Indeed, it is a short cut, correct and effective method not needing graphic chart, trial computation.