圆形无压隧洞恒定渐变流水面线计算的近似法

The New Analysis Method of the Water Surface Curve Computation about the Constant and Gradually Varied Flow in the Circular Section Tunnel under Free Flow

基于恒定渐变流基本微分方程,采用数值分析理论,得到流程与始、末段水深的解析函数,通过该函数可直接计算沿程水面线。该方法比《水工隧洞设计规范》中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,并且逐段试算推求水深,将导致末端断面水深误差逐步累积,误差大,精度下降。通过工程实例计算比较得出:新解析法计算结果与规范推荐法(程序)计算结果基本一致,甚至优于规范推荐的分段试算法,完全满足工程实践要求。

Based on the basic differential equation about the constant and gradually varied flow,through the zero dimension to this differential equation and using the numerical analysis theory,new equivalent basic differential equation about the constant and gradually varied flow was obtained,which was composed by the simple hyperbolic function;Through the variable separation and the direct integral,the analytic function between the flow and the beginning and final part water depth was obtained,through which the water facial suture along the regulation was obtained.This method was simpler and more convenient than the trial and error procedure about the partition and summation which was recommended by Specification for design of hydraulic tunnel,Specially to the more sensitive section of the water depth,and the error of the trial and error procedure was bigger which was recommended by Standard,Inquiring water depth by making a trial balance section by section would cause the error of the terminal cross section to accumulate gradually,and cause the error to increase and the precision drop.Finally,through the computation and comparison to the project example,the computation achievement of the new analysis method of the article maintained consistent basically with the computation achievement of the method recommended by Standard which satisfied the request of the project practice completely.