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通过对梯形明渠均匀流基本方程的数学变换,得到计算其无量纲正常水深λ的迭代公式。一方面从数学上证明了迭代函数的收敛性,另一方面,通过对无量纲正常水深λ与已知参数m,α之间关系的分析及数值计算,利用最佳逼近拟合原理得到无量纲正常水深的一次近似计算式。最后以此近似计算式为初值,用迭代方程进行一次迭代得到梯形明渠无量纲正常水深的直接计算公式。计算实例表明此方法简捷、准确且不需依赖图表。
Through the mathematical transformation of the basic equation of uniform flow in a trapezoidal open channel, an iterative formula for calculating the dimensionless normal depth of water λ is obtained. On the one hand, the convergence of iterative function is proved mathematically. On the other hand, by the analysis and numerical calculation of the relationship between the dimensionless normal depth λ and the known parameter m, α and using the best approximation fitting principle, An approximate calculation of normal depth. Finally, using the approximate calculation formula as the initial value, a direct calculation formula of the dimensionless normal depth of the trapezoidal channel with an iterative equation is obtained. The calculation example shows that this method is simple, accurate and does not need to rely on charts.