U形断面渠道收缩水深迭代计算初值的研究

Research on Initial Iterative Value for Calculating Water Depthin U-Shaped Channel with Contracted Section

对U形断面收缩水深的基本方程进行恒等变形,通过优化拟合分析得到了收缩水深的迭代公式,再与合理的迭代初值配合使用,迭代结果快速收敛。在工程常用范围内,只需一次迭代即可使最大相对误差小于0.50%。误差分析及实例计算表明,收缩水深的迭代计算公式形式简捷、精度高、适用范围广。

An iteratlve formula calculating water depth in U-shaped channel with contracted section was obtained through an identical deformation of the basic equation. The iterative formula displayed fast convergence by choosing reasonable initial iterative value and fitting analysis. Its maximum relative error can be reduced to less than 0.5% with its first iteration in the utility range. Error analysis and numerical example by using the formula indicate that it is a short cut, correct and effective method.