复式河槽水位流量计算误差分析及方法对比

水位流量关系是推算水面线的重要依据。复式河槽的水流漫滩时，直接运用曼宁公式计算水位流量关系会产生很大的误差，并会出现流量随水深增加而减小的不合理现象，为此分析了复式河槽垂线平均流速的横向分布及曼宁公式中流量-水深函数的单调性，探讨了这种误差及现象出现的原因；然后以实测资料为依据，对比分析了以曼宁公式为基础的水平分割法、垂直分割法、对角线分割法、湿周修正法及权重分割法与传统理论方法(谢汉祥法、河槽协同度法)计算复式河槽水位流量关系的精度，进而讨论了改进后的曼宁公式在复式河槽中的适用性。结果表明，主槽与滩地的流速差使漫滩水流发生横向运动，并在滩槽交界处形成大量的动量交换，其作用机理完全不同于单一河槽，故曼宁公式不能直接应用于复式河槽；复式断面的水力半径增长率与湿周增长率满足一定的条件时，曼宁公式中流量-水深函数单调递减，漫滩初期流量随水深增加而减小；对比不同计算方法的结果发现，湿周修正法精度最低而不推荐使用；水平分割法、垂线分割法、对角线分割法及权重分割法的精度与传统理论方法接近甚至更高，因此这些改进后的曼宁公式能够较好地适用于复式河槽。由于对角线分割法在所有方法中精度最高且计算简便，故计算复式河槽水位流量关系时推荐采用对角线分割法。

Error analysis and method comparison for calculating stage-discharge relation in compound channel

The stage-discharge relationship is an important basis for estimating water surface line. Using the Manning formula directly to calculate the relationship of water level and flow will produce great errors, and the unreasonable phenomenon is that the decrease of flow with the increase of water depth will occur when flood is out of bank. In this paper, the transverse distribution of the average vertical velocity and the monotonicity of the flow- depth function of the Manning formula are first analyzed, and then the reasons for such errors and unreasonable phenomena are discussed. In addition, the calculation accuracy of different methods such as horizontal segmentation, vertical segmentation, diagonal segmentation, wetted perimeter correction, weight segmentation, Xie Hanxiang method and synergism method is compared to demonstrate the applicability of the improved Manning formula in the compound channel. The results show that the velocity difference between the main channel and the floodplain makes the flow move laterally, which will lead to produce a large amount of momentum exchange at the junction, and its mechanism of action is completely different from the single channel, so the Manning formula cannot be applied directly to the compound channel. When the growth rate of hydraulic radius and the wetted perimeter satisfy a certain condition, the flow-depth function is monotonically decreasing, and the flow decreases with the increase of water depth. Compared with the results of different calculation methods, it is found that the precision of wetted perimeter correction is the lowest and not recommended. The precision of horizontal segmentation, vertical segmentation, diagonal segmentation and weight segmentation is close to the traditional theoretical method, so the improved Manning formula can be better applied to the compound channel. Diagonal segmentation is recommended in this paper because the diagonal segmentation method has the highest accuracy and the most simple calculation in all the methods.