梯形断面收缩水深计算的迭代法

An Iterative Method Calculating Water Depth at Vena Contracta in Trapezoidal Cross section

通过对梯形渠道收缩断面能量方程的恒等变形，得到计算收缩水深的无量纲迭代计算公式；并根据收缩断面水力特点，证明了该迭代式的收敛性，同时应用马克劳林级数展开迭代式求出了收缩水深的近似计算值。误差分析及实例计算表明，以此为迭代初值进行两次迭代计算，在工程实用范围内最大相对误差小于０．３％，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 water depth at vena contracta is derived from transfroming identically the energy equation at vena contracta in trapezoidal channels. Moreover, according to hydraulic characteristics, for one thing, the astringency of this iteration formula has been testified, for another, an approximate formula for computing water depth at vena contracta has been obtained by using Maclaurin series. Error analysis and a case history computed by using the formula indicate that the absolute value of the maximum relative error of the water depth is not greater than 0.3 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.