牛顿法在汊道水力计算中的应用

The Application of Newton's Method to Hydraulic Calculation about Branches of a Channel

本文首先将能量方程归纳为简单的形式，再根据汊道水力计算的基本方法和牛顿法求解方程根的基本原理，导出了求解汊道（双方程）分流量的迭代初值和迭代增值的计算公式，并用实例计算证明了该方法大大加快了计算速度、提高了成果精度。同时，分析了双方程牛顿法与一般牛顿法的区别，讨论了双方程牛顿法的几何意义。并对分、汇流断面位置的确定方法作了较为详细的说明。

First, in this paper, the energy equation is described in a simple form. Then, according to basic method of hydrauliccalculation about branches of a channel and basic principle of extraction the root with Newton'smethod, the formulas ofinitial value and increment of Newton's sucessive approximation(double equations)to calculate the folw dividing of branches of channel is established.It is clear that this method can speed up computation rate and improve accuracy of theresults by example. In addition, the difference between Newton's method for double equations and usual Newton's methodis analysed,and the geometric implication of Newton's method for double equations is discussed,and the method of deter-mining section of flow dividing and flow together is also explained.