标准U形断面渠槽正常水深的简化计算法

A Brief Calculation Method of the Normal Depth of a Standard U-shaped Section of Canal

标准U形断面渠槽正常水深计算涉及超越方程求解,无法直接通过解析法获解。由于常规的试算法及图表法不但计算繁琐且精度不高,利用计算机求解又涉及编程,不便实际应用,而现有的近似算法均属分段函数形式给出,也不便实际应用。采用优化拟合的方法,以标准剩余差最小为目标函数,在工程适用参数范围内,经逐次逼近拟合计算获得了表达形式简单、求解精度较高、且由一个表达式给出的近似计算公式,具有一定的实用意义。

The normal depth of a standard U - shaped section of canal involves the solution of transcendental equations; it can not be calculated directly by analytical method. It is redundant and inaccurate to calculate through conventional test algorithm and chart method. Computer programming for the solution is inconvenient; meanwhile, it is also impractical by the existing approximate algorithms for their multi- partition functional form. In this paper, the optimization of the fitting method was used by the way of taking the minimum residual standard deviation as the objective function, giving an approximate equation by successive approximation fitting calculation in the range of parameters applicable to engineering. This approximate equation has some practical significance for its simple expression form and high solution precision.