无压圆形隧洞正常水深直接算法

Direct calculation method for normal depth in non-pressure circular tunnel

明渠均匀流正常水深是渠道设计、运行管理的重要水力要素。圆形断面是水力最佳断面,正常水深计算需求解超越方程,计算复杂。针对目前现有计算公式存在误差大且适用范围小的问题,根据明渠均匀流基本原理,采用SAS软件的NLIN过程,给定非线性函数模型,利用Marquardt法建立圆形隧洞无压流正常水深直接水力计算公式。通过误差分析和实例计算,表明:该公式在较大工程适用范围内最大计算相对误差小于0.093%。与现有公式相比,不仅工程适用范围扩大,具有较强的通用性,且计算精度高。另外计算公式为二次多项式形式,物理概念清晰,计算便捷。研究成果可为渠道工程设计和运行管理提供可靠的理论依据和有益参考。

Normal depth is an important parameterfor design and operation of open channel, but its direct calculation for circular tunnel needs to solve a transcendental equation. And the accuracy of the existing formulas for calculation of normal depth in circular tunnel is very low and their application ranges are not wide enough. This paper presents a new and explicit formula for normal depth in circle tunnel by applying the theory of uniform flow in open channel. This formula was derived by optimizing the model parameters with the Marquardt method and the NLIN process in SAS software. Error analysis and calculations in demonstration exampleshave showedthat themaximum relative error of the formula is below 0.093 percent in a wide range of engineering design. Compared with the existing ones, the new formula is more general and more accurate with a wider application range, and based on physical conception it is quadratic and easy to use. Thus, the proposed formula would provide a theoretical basis and practical tool for design and operation management of circular tunnels.