梯形渠道水跃共轭水深理论计算方法初探

Preliminary study on the theoretical method for calculating conjugate depth of trapezoidal channel

梯形渠道水跃方程为一含多个未知参数的一元5次方程,形式复杂,理论上无法求解;现行所有求解方法适用范围小且计算过程非常烦琐。为此根据梯形渠道水跃共轭水深、临界水深的物理意义,通过对水跃函数曲线的性质的分析,并结合临界水深的解析计算方法,得出共轭水深与临界水深之间的函数关系形式,从而提出了梯形明渠共轭水深的理论计算公式;通过大量的数值算例得出反映断面形状尺寸与流量及动量的无量纲参数β的计算公式。该套公式形式简捷,物理概念明确,适用范围广,精度分析表明除了个别点处最大相对误差为5%外,其他区域的相对误差均小于1%,满足工程要求。为梯形明渠水跃共轭水深的计算提供一种简捷准确的计算方法。

The equation of hydraulic jump in trapezoidal channel is a quintic equation with one unknown and several undetermined parameters and it is can not be solved analytically.Calculation processes with all the existing solution methods are cumbersome and all the solutions are in a narrow application range.To establish a theoretical formula,this paper starts at an analysis on the physical meanings of conjugate depth and critical depth of trapezoidal channel and an analysis on the property of hydraulic jump function curve,then establishes a theoretical relationship between conjugate depth and critical depth in combination with the critical depth formula,and finally derives the formulas for theoretically computing the conjugate depth.The dimensionless parameter β of the derived formula reflects the effects of the shape and size of channel cross section,the discharge and the momentum,and its values are determined through a large number of calculations of study cases.The formulas are simple and accurate and have a clear physical concept with wide application.Accuracy analysis indicates that the relative error is less than 1% in most of the calculation range,except for some points where the relative error is about 5%.The formulas are easy to use and they provide a new method for computing conjugate depth of trapezoidal open channel.