弧底梯形明渠临界水深的直接计算公式  

Direct calculation formula for critical depth of rounded-bottom trapezoidal open channels

作　　者：赵延风[1] 王正中[1] 刘计良[1] 

机构地区：[1]西北农林科技大学水利水电工程研究所,陕西杨凌712100

出　　处：《水力发电学报》2012年第3期114-118,共5页Journal of Hydroelectric Engineering

基　　金：国家"863"高技术研究与发展计划项目(2002AA62Z3191);陕西省农业科技创新项目(2011NXC01-20)

摘　　要：弧底梯形渠道是由底部圆弧段与上部梯形段边坡相切组成的几何断面,其临界水深方程为超越方程及高次方程不容易直接求解。该文首先引入判定水深位置的分界流量,并对其临界水深方程进行数学变换,根据迭代理论提出了无量纲水深及无量纲水面宽度的快速迭代公式,进而得到弧底梯形明渠临界水深的直接计算公式。误差分析及实例计算表明:在全部水深范围内,临界水深的最大相对误差小于0.122%,公式形式简单,计算精度高,便于工程应用。If the bottom of a trapezoidal cross section is rounded tangent to each of its two sloping edges,then analytical solution of critical depth is impossible to be derived from the governing equation of transcendental high degree.To overcome this difficulty in the present work,a demarcating flow discharge is introduced first to determine the location of water surface and an iterative formula for dimensionless water depth,and water surface width is derived through mathematical transformation of the governing equation for critical depth and by iteration theory.Then,a formula for direct calculation of critical depth is developed for the rounded-bottom channels.It is simple for engineers to use and of high accuracy.Error analysis in case studies indicates that in the full range of water depth,its maximum relative error is less than 0.12%.

关 键 词：水力学 直接计算公式 迭代理论 临界水深 弧底梯形 分界流量 

分 类 号：TV131.4[水利工程—水力学及河流动力学]