数值积分法计算抛物线形渠道恒定渐变流水面线  

Numerical integration method for calculating water surface profile of gradually varied steady flow in parabola shaped channel

作　　者：文辉[1] 李风玲 

机构地区：[1]惠州学院建筑与土木工程系,惠州516007

出　　处：《农业工程学报》2014年第24期82-86,共5页Transactions of the Chinese Society of Agricultural Engineering

基　　金：惠州学院引进教授;博士科研启动基金项目(C510.0211);惠州学院重点培育学科项目(ZDPYXK1404)

摘　　要：针对目前差分试算法、迭代法及图解法求解水面线存在着计算过程繁复、误差较大的问题,该文通过对抛物线断面渠道恒定渐变流水面线微分方程进行恒等变形,并对引入的特征水深与特征湿周的关系进行分析及计算,重点考察工程实际中常用的特征水深范围为0.6-1.5 m的抛物线形断面渠道,依据最小二乘法进行回归分析将方程中的特征湿周由不可积函数替代为可积分的幂函数,实现了由有限差分逐一断面推算到数值积分法的直接求解。与现有方法相比,该抛物线形断面渠道恒定渐变流水面线简化计算公式具有工作效率明显提高、精度好的特点。实例计算及误差分析表明：在工程实用范围内（特征水深范围0.6-1.5 m）该公式最大相对误差仅为0.17%,对生产实践具有实用推广意义。The parabola shaped channel has an excellent hydraulic performance and strong ability of anti-frost heave, and is used widely in the field of spillway and irrigation channels. The water surface profile of gradually varied steady flow is an important hydraulic element for the channel design and the operational management, but the differential equation of water surface profile is the transcendental equation with no analytic solution. The current differential test algorithm, iterative method and graphical method for solving the water surface profile has complex calculation process, large errors and low efficiency, so on. To obtain the simplified calculation formula of water surface profile of parabolic cross-section, we introduced the concepts of the parabolic cross-sectional characteristic water depth（that is the product of the water depth and the parabolic shaped perimeter） and characteristic wetted perimeter（2 times of the product of parabolic shaped perimeter and wetted perimeter）, and did the identical deformation for the basic differential equations of the gradually varied steady water surface profile of the parabolic cross-sectional channel. The optimal hydraulic cross-sectional parabolic cross-sectional characteristic water depth is 0.947 m. In practical engineering, the design of the parabolic cross-sectional channel is required to be close to the optimal hydraulic cross-section as far as possible under permissive conditions so that it would obtain good hydraulic conditions, save the substantial cultivated land, reduce project expense and achieve better economic benefits. The study here focused on the common parabolic cross-sectional channel in the engineering practice with the range of characteristics water depth of 0.6-1.5 m. Since the characteristic wetted perimeter of the original differential equations is a complex non-integrable function within the most commonly used scope in practical engineering, we analyzed the interrelation between characteristic water depth and characteristic wetted perim

关 键 词：水力学 计算 设计 抛物线形渠道 数值积分法 恒定渐变流 水面线 

分 类 号：TV131.4[水利工程—水力学及河流动力学]