抛物线类渠道断面收缩水深的计算通式  

General explicit equations for calculation of contracted flow depths in channels of parabolic cross-sections

作　　者：赵延风[1,2] 王正中[1,2] 刘计良[1,2] 

机构地区：[1]西北农林科技大学水利与建筑工程学院,陕西杨凌712100 [2]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》2013年第1期126-131,共6页Journal of Hydroelectric Engineering

基　　金：陕西省农业科技创新项目(2011NXC01-20)

摘　　要：为了得到抛物线类渠道收缩水深的显函数计算通式,该文首次提出基线函数增量法的概念并采用该方法确定函数的参数。通过对抛物线型渠道断面收缩水深的基本方程进行恒等变换,取得简单快速收敛的迭代公式;根据无量纲收缩水深与已知量综合参数之间的数值分析,采用基线函数增量法确定迭代初值函数中的参数并应用迭代理论,得到了n次抛物线型渠道收缩水深的直接计算通式。误差分析及实例计算表明,在工程常用范围即无量纲收缩水深α∈(0,0.5]范围内,在工程常用抛物线指数n∈[1,5]范围,收缩水深最大相对误差小于0.52%,在抛物线指数n∈[1,100]范围内,收缩水深的最大相对误差小于0.85%,计算公式形式简单、精度高、通用性强。To obtain general explicit equations for contracted flow depth in the channel of parabolic cross- section, this paper puts forward for the first time a concept of incremental method of baseline function that can be used to obtain the equation parameters. By identical transformation of the governing equations for contracted depth, we developed iterative formulae of simple form and fast convergence. Then, explicit equations of n-th- order were derived for direct calculation of contracted depths for parabolic cross sections, through numerical calculation for establishing a relationship of dimensionless contracted depth versus a comprehensive parameter that represents the given quantities. The initial value of iterative solution to the equations can be obtained by using the incremental method and the iteration theory. Calculation of a practical case and error analysis of the depth calculations show that in the common range of α ∈ （0,0.5 ] , the relative error is less than 0.52% for n ∈ [ 1,5] and less than 0.85% for n ∈ [ 1,00]. The proposed simple equations are very accurate and general for practical design of channel.

关 键 词：水力学 收缩水深 基线函数增量法 抛物线型断面 

分 类 号：TV131.4[水利工程—水力学及河流动力学]