弧底梯形明渠恒定渐变流水面线计算的直接算法  

A New Analytic Method of the Water Surface Curve Computation about the Constant and Gradually Varied Flow in the Open Trapezoidal Dhannel with Spherical Bed

作　　者：黄朝煊 王贺瑶 

机构地区：[1]浙江省水利水电勘测设计院,杭州310002

出　　处：《中国农村水利水电》2015年第3期147-151,共5页China Rural Water and Hydropower

摘　　要：对圆弧底梯形明渠恒定非均匀流沿程水面线进行了深入研究,认为《溢洪道设计规范》推荐的分段求和法在趋近于正常水深附近,水深对流程S影响特别敏感,分段求和法误差较大。基于恒定渐变流基本微分方程,通过无量纲化数值分析,对无量纲流程S取对数函数,并作为新的待求函数得到新的方程,该方程在正常水深、临界水深附近性态相对较好,采用Runge-Kutta法和外推法结合并给出显式解求解式,通过算例分析,该法比规范推荐的分段求和试算法更简单、便捷,特别对水深较敏感段,规范推荐试算法误差较大,而本文方法则能一定程度上降低其敏感性。最后通过工程实例计算比较得出:本文新解析法计算成果与规范推荐法(程序)计算成果基本一致,甚至优于规范推荐的分段试算法,完全满足工程实践要求。Through a thorough research on the water facial suture along the regulation about the constant non-uniform flow under the open Trapezoidal Channel with Spherical Bed.The water depth is particularly sensitive to the process Sby the piecewise summation method Based on the basic differential equation about the constant and gradually varied flow,and through the zero dimension to this differential equation and the numerical analysis theory is used,with the logarithmic function of dimensionless flow S,a new unknown function with good state near the normal depth and critical depth is given.The explicit solution is given by Runge-Kutta method and extrapolation method.The given method is simple and convenient than the method recommended in specifications,this method eliminates the sensitivity of the near normal depth.The computation achievement of the new analytic method of the paper keeps consistent basically with the computation achievement of the method（procedure）which is recommended by＂Design Code for Spillway＂.The request of the project practice is satisfied completely.

关 键 词：恒定渐变流基本微分方程 相对水深 数值拟合 RUNGE-KUTTA法 外推法 

分 类 号：TV651.1[水利工程—水利水电工程]