马蹄形无压隧洞恒定渐变流水面线计算的新解析法

A New Analytic Method of Water Surface Curve Computation about Constant and Gradually Varied Flows in the Horseshoe Section Tunnels under Free Flows

对马蹄形无压隧洞的恒定非均匀流沿程水面线进行了深入研究,基于恒定渐变流基本微分方程,通过采用数值分析理论,得到流程S与始、末段水深h1、h2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,导致误差大,精度下降。最后通过工程实例计算比较得出: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 study of water facial suture along regulation about the constant nonuniform flow under the horseshoe section tunnels under free flows.Based on the basic differential equation concerning the constant and gradually varied flow,through the zero dimension to this differential equation and by using the numerical analysis theory,new equivalent basic differential equation about the constant and gradually varied flow are obtained by the simple hyperbolic function.Through the variable separation and the direct integral,the analytic function between the flow S and the beginning final part water depth h1 h2 are obtained.This method is simpler and more convenient than the trial and error procedure about the partition and summation,which is recommended by Specifications for Design of Hydraulic Tunnels.The error of the trial and error procedure is bigger.Inquiring water depth by making a trial balance section by section will cause the error of the terminal cross section to accumulate gradually.The errors caused to increase and precision drop.Finally through computation and comparison,the project example is obtained.The computation achievement of the new analytic method of this paper is basically in agreement with the computation results of the method They satisfy the requirements of project practice completely.