再论圆管明渠均匀流正常水深的直接计算公式

Further study on explicit formula for normal water depth of uniform flows in circular pipes

在总结前人圆管明渠均匀流正常水深计算公式的基础上,引入无量纲参数α和无量纲正常水深β,对圆管明渠均匀流基本方程进行数学变换,应用曲线拟合和优化原理,提出新的圆管明渠均匀流正常水深的直接计算公式;根据给水排水工程和水利工程设计规范的要求,并考虑工程实际情况,确定计算公式的工程适用范围。误差分析和计算实例表明:该公式形式简捷,精度较高,在工程适用范围内最大相对误差小于0.72%,可以方便工程设计人员在设计中直接使用。

Based on the summarization of the existing formulae for normal depth of uniform flows in circular tube open channels, the dimensionless parameter α and the dimensionless normal depth β are introduced to perform mathematical transformation of the basic equation for uniform flows in circular tube open channels. A new explicit formula for the normal water depth of the uniform flows in circular tube open channels is proposed by means of the curve fitting and optimization principles. According to the requirements of Structural design code for special structures of water supply and waste water engineering and Design specification for hydraulic engineering, the scope of project application for the proposed formula is determined considering the specific situations of projects. The error analysis and case studies indicate that the proposed explicit formula has advantages of concise form and high precision. The maximum relative error is less than 0.72%, and it is convenient for designers to directly use it.