蛋形断面的正常水深和临界水深的直接计算公式

The explicit calculation formula of normal and critical water depth for egg-shaped section

蛋形断面的正常水深和临界水深的计算公式为分段超越方程,无法直接求解。通过数学变换对正常水深和临界水深公式化简,最终得到充满度x和无量纲正常水深参数H、无量纲临界水深参数P之间的关系,利用1stopt软件基于遗传算法编程对给定非线性函数模型进行参数优化拟合建立蛋形断面正常水深和临界水深的显示计算公式。经过误差分析及实例计算,表明在较大工程常用范围内,蛋形断面正常水深、临界水深的最大相对误差分别仅为0.3691%、-0.0726%。与现有公式比较直接计算公式适用范围扩大,精度更高,形式较为简捷。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。

The calculating fomiulas of nomial and critical water depth for egg-shaped section are sectional transcen-dental equations,which can ＇t be solved directly. In this article, the nomal and critical depth fomiula is simplified bymathematical deformation,and then the relation of filling degree x with nondimensional noirnal water depth H and nondi-mensional critical depth P is gotten. Te lstopt software is adopted to optimize a d fit the established nonlinear model parameters based on genetic algorithm and set up the explicit calculation formula of normal and critical water depth for egg -shape setion. The error analysis and example calculation show that, within the large range of common project appli-cation ,the largest relative error of nomial and critical water depth for egg-shaped section are just 0. 3691 % and -0.0726%,relatively. Compared with the existing fonnulas,the explicit fonnula is characterized by a larger applica-tion range,a higher precision and a more convenient calculation. Te proposed formula will provide a theoretical basisand useful reference for project design,operation and management.