标准Ⅱ型马蹄形断面水面线的积分算法

Integral Algorithm for Water Surface Profile of Horseshoe Cross Section of Standard TypeⅡ

标准Ⅱ型马蹄形断面由于几何形状复杂,水面线的计算较为困难,研究其工程设计中的简化计算方法是完全必要的。根据标准Ⅱ型马蹄形断面的几何关系分析了标准Ⅱ型马蹄形断面不同区域内相对断面面积、相对湿周、相对水力半径、相对水深和相对水面宽度的计算方法。根据明渠恒定非均匀流水面线的微分方程,给出了标准Ⅱ型马蹄形断面水面线的分段试算法公式。根据最小二乘法拟合原理,给出了j',Fr'2与相对水深h/r1的近似关系,并以此关系给出了标准Ⅱ型马蹄形断面水面线的积分公式,积分公式为显函数关系式,计算方便。通过3个算例比较了试算法和积分法的结果,其中试算法的步高取为1 mm,积分法与试算法相比,最大误差为0.965%,计算精度满足工程设计要求。

The complex geometrical shape of standard type-II horseshoe cross section makes it difficult to calculate the water surface profile in it.It is necessary to work out a simplified calculation method for engineering design. According to the geometrical shape,the calculation methods of relative cross section area,relative wetted perime-ter,relative hydraulic radius,relative water depth and relative width of water surface in different areas of standard type-II horseshoe cross section are given.Furthermore,according to differential equation of water surface profile in open-channel with constant non-uniform flow,the trial-and-error method of flow profile is given.On the basis of least square method,the approximation relationship between j′,Fr′2 and relative depth h /r1 are given,and accord-ing to the relationship,the integral formula of water surface profile which is an explicit function with convenient cal-culation and high accuracy is obtained.The trial-and-error method and the integral method are applied to three ex-amples and comparison between the results shows that the calculation accuracy of integral method meets the require-ment of engineering design.The maximum error of integral method is 0.965% compared with the trial-and-error method with 1 mm step high.