立方抛物线形渠道正常水深的显式计算  

Explicit Solution to Normal Depth in Cubic Parabola-shaped Channel

作　　者：黄腾 许晓阳 李可利 HUANG Teng;XU Xiao-yang;LI Ke-li(Hebei Second Survey and Design Institute of Water Conservancy and Hydropower,Shijiazhuang 050021, China;College of Water Resources and Architectural Engineering, Northwest Agricultural and Forestry University, Yangling 712100, Shaanxi Province, China)

机构地区：[1]河北省水利水电第二勘测设计研究院,石家庄050021 [2]西北农林科技大学水利与建筑工程学院,陕西杨凌712100

出　　处：《中国农村水利水电》2020年第6期116-119,124,共5页China Rural Water and Hydropower

摘　　要：鉴于立方抛物线形断面正常水深的计算表达式一般均为超越方程,且含有不可积分函数,不能直接求解。本文借助高斯-勒让德求积公式,建立了计算湿周的三点格式和四点格式表达式;通过引入特征水深概念,对立方抛物线形断面正常水深基本方程进行数学变换,得到特征水深的隐函数方程。基于准二次函数概念和对数形式下的回归分析,提出了正常水深两套显式计算公式;通过与其他计算公式比较及误差分析发现,两套显式公式最大相对误差的绝对值分别为0.41%和0.36%,高于现有计算公式精度,且公式结构简捷、物理概念清晰、适用范围广。在计算精度要求较高时,建议采用显式公式一计算;在简捷程度要求较高时,建议采用显式公式二计算。The calculation expression of the normal depth of the cubic parabola-shaped channel is a transcendental equation and contains an integrable function,which cannot be directly solved.The Gauss-Legendre qua-drature is used to establish the three-point format and four-point format expression for calculating the wet period.By introducing the concept of characteristic water depth,the basic equation of the normal depth of the cubic parabola-shaped channel is mathematically transformed to obtain the implicit function equation of the characteristic water depth.Based on the concept of quasi-quadratic function and regression analysis under logarithmic form,two sets of explicit calculation formulas for normal depth are proposed.Compared with other calculation formulas and error analysis,the absolute relative errors of the two explicit formulas are 0.41%and 0.36%,respectively,which is higher than the accuracy of the existing calculation formula,and the formula is simple in structure,clear in physical concept and wide in scope of application.When the calculation accuracy requirement is high,it is recommended to use the explicit formula 1 calculation;when simplicity is high,this paper suggests using the explicit formula 2 calculation.

关 键 词：立方抛物线形渠道 正常水深 优化计算 湿周 高斯-勒让德求积公式 显式计算 

分 类 号：TV131.4[水利工程—水力学及河流动力学]