梯形明渠正常水深直接计算公式

A Direct Calculation Formula for Normal Depth in Open Trapezoidal Channel

通过对梯形明渠均匀流基本方程的数学变换，得到计算其无量纲正常水深λ的迭代公式。一方面从数学上证明了迭代函数的收敛性，另一方面，通过对无量纲正常水深λ与已知参数ｍ，α之间关系的分析及数值计算，利用最佳逼近拟合原理得到无量纲正常水深的一次近似计算式。最后以此近似计算式为初值，用迭代方程进行一次迭代得到梯形明渠无量纲正常水深的直接计算公式。计算实例表明此方法简捷、准确且不需依赖图表。

A non-dimensional iterative formula for computing normal depth is derived from transfroming identically the uniform flow equation for open trapezoidal channels. On one hand, according to hydraulic characteristics and iterative theory, the astringency of this iteration formula has been testified, on the other hand, an approximate formula for the same purpose has been obtained by using the principle of best approximation fit. Using the latter formula, an expression for initial value iteration is established. Then, a direct formula was obtained by using the iterative formula. An illustrative calculation indicated that, it is a short cut, correct and effective method not needing any graphic chart or trial computation.