抛物线形断面正常水深简化解析式

Simplified Analytical Formula of Cubic Parabola-shaped Cross Section Normal Depth

由于三次抛物线形断面正常水深求解涉及不可积分函数和超越方程计算问题,无法采用解析法完成。但通过引入二次抛物线近似积分法及优化拟合法,经逐次逼近拟合,获得了表达形式简单、计算过程简捷,实用范围广、便于工程设计人员实际应用的近似计算通式。误差分析及算例计算表明,在工程实用范围内,该算式的最大计算相对误差为0.941%,完全满足工程的设计精度要求,具有推广应用价值。

As the cubic parabola-shaped cross section normal depth integral function and can not be involved in solving the transcendental equation calculation, using the analytical method can not be completed. By introducing the quadratic parabola approximation integration and optimization of fitting by successive approximation fitting, expressing simple form, the calculation process is simple, practical wide range of engineering staff to facilitate the practical application of the ap- proximate calculation formula, error analysis and numerical examples calculations show that in practical engineering range, the formula for calculating the maximum relative error is only 0.941%, fully meet the accuracy requirements of the design, with application value.