【摘要】 无压流圆形断面的临界水深目前没有解析解,传统的图表法精度不够,迭代法计算过程繁琐,而现有的近似公式又普遍存在精度不高或公式复杂的问题。针对圆形断面临界水深近似公式所存在的问题,通过对圆形断面临界水深基本方程进行数学变换,再借助Matlab的Cftool工具对1000余组数据进行不同形式函数的拟合,在拟合过程中选用正弦函数和幂函数,最终得到了圆形断面临界水深的直接计算公式。通过与各家公式进行误差分析及比较,结果表明,在工程实用范围内,计算公式最大相对误差为0.016%,明显高于现有近似公式的精度,且计算公式更加简捷。更多还原

【Abstract】 At present, there is no analytical solution for the critical water depth of the circular section without pressure flow. The traditional chart method is not accurate enough, and the iterative method has a cumbersome calculation process. However, the existing approximate formula is generally not accurate or the formula is complex. Aiming at the problems of the approximate formula of critical water depth for circular section, the basic equation of circular section critical depth is transformed mathematically, and then more than 1000 sets of data are fitted with different forms of functions by means of the Cftool of MATLAB. In the process of fitting choose sine function and power function, it finally obtained the formula of critical water depth of circular section directly. Through error analysis and comparison with other formulas, the results show that within the scope of engineering practice, the maximum relative error of the calculation formula in this paper is 0.016%, which is obviously higher than the accuracy of the existing approximate formula, and the calculation formula is simple and convenient.更多还原