明槽中二维恒定渐变流水面曲线的流场分析法

Water surface profiles of the gradually varied steady flow in open channals by the method of flow field analysis

本文用流场分析法研究明槽中二维恒定渐变流的水面曲线,从不计惯性平方项到计入主流方向的惯性平方项,到计入全部惯性平方项,建立了相应的水面曲线微分方程,或给出了解析解,或给出了近似解,可求数值解。得到断面上流速分布的计算式,主流速U_x和法向流速U_y的关系,法向惯性力对动水压强分布和流速分布的影响,指出缓流时会出现波状曲线,这些都是总流分析法未能提供的。本文还探讨了棱柱形明槽中恒定渐变流水面曲线的求解问题。

In this paper, the water surface profiles of two-dimensional gradually varied steady flow in open channels are analysed by the method of flow field. The author at first neglects all the inertia terms, and then takes account the inertia terms in the direction of main flow only, and then the inertia terms both in the directions along and normal to the main flow. The corresponding differential equation of the water surface profiles, and their analytical or appoximative solution are given in the paper. These equation can also be solved by numerical analysis. The formula of main velocity distribution on the cross section as well as the relationship between main velocity and normal velocity are presented. It is indicated that the effect of normal inertia terms on the distribution of dynamic pressure and velocity on the cross section may be considerable and is pointed out that when the flow is subcritical, the water surface profile will be wavy. None of these results can be obtained by the method of total flow analysis.