六圆弧蛋形断面共轭水深计算方法的研究
Calculation method of conjugate water depth of egg-shaped cross section with six arcs in open channel

【目的】建立明渠六圆弧蛋形断面水跃共轭水深的计算方法，为该断面的设计提供支持。【方法】通过分块计算六圆弧蛋形断面不同水深时的面积、分块形心位置和总形心位置，并以此为依据分析相对面积、相对形心位置与相对水深的关系，根据动量方程研究并建立水跃共轭水深的计算方法。【结果】给出了不同水深时六圆弧蛋形断面形心和面积的计算公式以及水跃共轭水深的试算方法；拟合了相对断面形心和相对面积与相对水深的关系，给出了水跃共轭水深的简化迭代计算公式，并验证了公式的收敛性。与采用理论公式的试算法相比，简化计算方法对同一算例的跃前、跃后水深计算误差分别为0.04%和0.16%。【结论】推导的水跃共轭水深的试算法和简化计算方法，其计算精度完全可以满足工程实际要求，可为工程设计提供参考。
【Objective】The calculation method of conjugate water depth of egg-shaped cross section with six arcs in open channel was established to support the design of this kind of section.【Method】Blocking method was used to calculate areas and centroids under different water depths,and the relationships between relative area,relative centroid position and relative depth were analyzed.Then the calculation method of conjugate water depth of egg-shaped cross section with six arcs was established according to momentum equation.【Result】The computational formulas of centroids and areas of egg-shaped cross section with six arcs under different water depths and trial method of conjugate water depth were established.The relationships between the relative area,relative centroid position and relative depth were fitted,the simplified calculation method and processes of conjugate water depth were supplied and the convergence was verified.Compared with the theoretical formula of trial method,the errors of depths before and after water jump by simplified calculation method were 0.04% and 0.16%,respectively.【Conclusion】The accuracy of simplified calculation method for conjugate water depth met the requirement of actual projects