圆形断面临界水深的直接计算公式

详细信息    查看全文 | 推荐本文 |

英文篇名：Direct Formula for Calculating Critical Water Depth of Circular Section 作者：何育聪 英文作者：HE Yu-cong;College of Water Resources and Architectural Engineering,Northwest A&F University; 关键词：水力学 ; 圆形断面 ; 临界水深 ; 直接计算 ; MATLAB 英文关键词：hydraulics;;circular section;;critical water depth;;direct calculation;;MATLAB 中文刊名：云南水力发电 英文刊名：Yunnan Water Power 机构：西北农林科技大学水利与建筑工程学院; 出版日期：2019-06-15 出版单位：云南水力发电 年：2019 期：03 语种：中文; 页：84-86 页数：3 CN：53-1112/TK ISSN：1006-3951 分类号：TV135

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。
        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.

引文

[1]张文倬,圆形断面临界水深计算[J].四川水力发电,2002,21(1):15-17.
    [2]张宽地,吕宏兴,赵延风.明流条件下圆形隧洞正常水深与临界水深的直接计算[J].农业工程学报,2009,25(3):1-5.
    [3]刘刚,滕凯.圆形断面临界水深简化近似计算方法[J].水利与建筑工程学报,2011,9(6):81-83a.
    [4]王正中,陈涛,万斌,等.圆形断面临界水深的新近似计算公式[J].长江科学院院报,2004,21(2):15-17.
    [5]文辉,李风铃,彭波,等.圆管明渠临界水深的直接近似计算公式[J].人民黄河,2007,29(4):67-68.
    [6]孙建,李宇.圆形和U形断面明渠临界水深的直接计算公式[J].陕西水力发电,1996,12(3):39-42.
    [7]赵延风,何晓军,祝晗英,等.无压流圆形断面临界水深的新近似计算公式[J],人民长江,2009,40(11):76-79.
    [8]韩会铃,孟庆芝.非满流圆管均匀流水力计算的近似数值解法[J].给水排水,1994(10):25-26.
    [9]李蕊,王正中,王志刚.圆形断面临界水深新近似计算式[J].干旱地区农业研究,2013,31(04):54-56+103.
    [10]马子普,张根广.一种新型图解法在无压流圆形断面水力计算中的应用[J].中国农村水利水电,2011(11):95-98.
    [11]吕宏兴,把多铎,宋松柏.无压流圆形断面水力计算的迭代法[J].长江科学院院报,2003,20(5):15-17.
    [12]吴持恭.水力学[M].北京:高等教育出版社,1979.
    [13]赵延风,宋松柏,李宇.圆形断面明渠临界水深的近似计算公式[J].水利水电科技进展,2008,28(2):62-64.