普通城门洞断面正常水深的近似计算式

Approximate Method Calculating Normal Depth of Arched-gate Section Tunnel

普通城门洞形过水断面是泄洪隧洞较常采用的断面形式之一,其几何图形由槽形与圆弧曲线构成,过水断面水力要素为分段函数,正常水深的计算无论是查图表法还是迭代试算法都比较繁琐,计算误差较大,且依赖图表,不便于应用。为此,通过城门洞形断面均匀流方程的数学变换,并对引入的无量纲参数与相对临界水深的关系进行分析及计算,应用逐步优化拟合原理进行分段拟和,得到了城门洞形断面均匀流水深的直接计算式。实例计算及误差分析表明:在工程实用范围内(正常水深与拱顶半径之比在1.00到1.80之间),该公式最大相对误差仅为0.40%,且该式物理概念清晰明确、公式形式简捷,能为工程设计及水工设计手册的编制提供有益的参考。

It is difficult to calculate normal water depth of a arched section tunnel for its complex geometrical shape. From using the mathematics transformation method and the theory of optimization and regression to deal with the basis equation of the normal depth in arched section tunnel, a new direct formula is derived in this paper, which overcomes the shortage of other methods, such as chart looking up method, trial and error method and iterative trial method. This method is simpler and more accurate than other approximate methods with a maximum error of less than 0.40% in the utility range （ ratio of critical depth to arch radius of 1.0 - 1.80）. So, it will be useful in engineering practice and in course of compiling handbook of hydraulic structure design.