排灌机械工程学报
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排灌机械工程学报  2011, Vol. 29 Issue (6): 523-528    DOI: 10.3969/j.issn.1674—8530.2011.06.013
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排灌输水隧洞正常水深的简捷算法
赵延风1, 王正中1, 方   兴2, 刘计良1, 洪安宇1
(1.西北农林科技大学水利水电工程研究所, 陕西 杨凌 712100; 2.奥本大学土木工程系, 美国 阿拉巴马州 奥本 36849)
Simple calculation method for normal depth of a kind of water supply tunnel for irrigation and drainage
Zhao Yanfeng1, Wang Zhengzhong1, Fang Xing2, Liu Jiliang1, Hong Anyu1
(1.Institute of Water Resources and Hydropower Engineering, Northwest A & F University, Yangling, Shaanxi 712100, China; 2.Department of Civil Engineering, Auburn University, Auburn, Alabama 36849, U.S.A.)
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摘要 为了使标准城门洞形断面正常水深的求解具有简单的显函数计算公式,对标准城门洞形断面正常水深的基本方程进行恒等变形,将水面位于底角圆弧段和顶弧段正常水深的超越方程以及水面位于侧边直线段正常水深的高次方程,变成无量纲化正常水深与已知量综合参数的单变量函数方程.引入准线性函数的概念并将准线性函数作为标准模板,再对正常水深的单变量函数方程应用准线性函数标准模板,在工程常用范围即无量纲化正常水深y∈[0.05,1.80]范围内进行优化计算及准线性函数逼近,得到了超越方程和高次方程的替代函数方程,替代函数具有类似于线性函数形式,即正常水深的准线性显函数表达式,并进行误差分析.结果表明,在隧洞底部圆弧段正常水深的最大相对误差小于0.36%,侧边直线段正常水深的最大相对误差小于0.31%,顶弧段正常水深的最大相对误差小于0.39%,说明准线性公式在隧洞有效水深范围内计算的水深准确度较高,可为排灌输水隧洞的断面设计及实现渠道水位控制时确定均匀流水深提供参考.
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赵延风
王正中
方兴
刘计良
洪安宇
关键词排灌输水隧洞   标准城门洞   正常水深   准线性函数   函数逼近     
Abstract: In order to obtain an explicit formula for normal depth of standard citygate section,first,the identical transformation of the governing equation for normal depth of standard citygate section was made,including the transcendental equation for normal depth in the bottom corner arc and the top arc,and the higher degree equation for normal depth in the lateral side.The single variable equation was obtained for dimensionless normal depth and the comprehensive parameter of the known quantities.Second,the concept of quasilinear function was introduced and treated as the standard template.The standard template for quasilinear function was applied to the single variable equation for normal depth.Using optimization and approximation to quasilinear function,the estimation substitution formula for the transcendental equation and higherdegree equation was developed in the practical range of y∈[0.05,1.80],and the substitution formula has the same form as the linear function,i.e.,the quasilinear explicit expression for normal depth.Finally,error analysis of the formula was made.The result indicates that the maximum relative errors of the formula for normal depth are less than 0.36%,0.31%,and 0.39% in the bottom arc,the lateral side,and the top arc,respectively.The relative errors indicate that the quasilinear equation has high accuracy in the practical range,which can provide simple method for computing the normal depth of the uniform flow in the design of water supply tunnel for drainage and irrigation and controlling the water level.
Key wordswater supply tunnel for irrigation and drainage   standard citygate cross section   normal depth   quasilinear function   function approximation   
收稿日期: 2011-03-08; 出版日期: 2011-11-30
基金资助:

国家863 计划项目( 2002AA62Z3191) ; 陕西省农业科技创新项目( 2011NXC01-20)

通讯作者: 赵延风( 1963-),男,陕西西安人,副研究员( zhyf2009@yahoo.cn) ,主要从事工程水力学研究.   
作者简介: 王正中( 1963-) ,男,陕西彬县人,教授,博士生导师( wangzz0910@ yahoo.com.cn) ,主要从事水工结构工程及工程水力学研究.
引用本文:   
赵延风,王正中,方兴等. 排灌输水隧洞正常水深的简捷算法[J]. 排灌机械工程学报, 2011, 29(6): 523-528.
ZHAO Yan-Feng,WANG Zheng-Zhong,FANG Xing et al. Simple calculation method for normal depth of a kind of water supply tunnel for irrigation and drainage[J]. Journal of Drainage and Irrigation Machinery Engin, 2011, 29(6): 523-528.
 
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