马蹄形断面正常水深的直接计算公式  

Direct calculation formulae for normal depth of horseshoe section

作　　者：赵延风[1] 王正中[1] 芦琴[2] 

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 [2]杨凌职业技术学院水利系,陕西杨凌712100

出　　处：《水力发电学报》2012年第1期173-177,188,共6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：马蹄形断面是由两个不同半径的4段圆弧组成,几何断面形式复杂,其正常水深的计算需求解超越方程,不易求解。该文通过对马蹄形断面正常水深方程进行变换,引入准一次函数、准二次函数的概念,并将准一次函数及准二次函数作为逼近函数的标准模板,对马蹄形两种标准断面正常水深的原函数方程在无量纲正常水深(0.01,1.8)范围内进行函数逼近。得到了马蹄形标准Ⅰ、Ⅱ型断面正常水深用准一次函数和准二次函数表达的计算公式,并进行误差分析及评价。结果表明,准一次函数和准二次函数表达的计算公式在工程常用范围内均可适用,正常水深的最大相对误差小于0.31%。计算公式具有形式简单、精度高、适用范围广泛的特点。Horseshoe section has complex geometry of four arcs with two different radii,and its calculation formula must be derived from a transcendental equation that is in general difficult to solve.To overcome this problem,this paper starts with transformation of the normal depth equation,introduces concepts of quasi-linear function and quasi-quadratic function,and treats these two functions as the standard form of approximating functions.Then the formulas for the two reference horseshoe shapes of standards I and II are approximated under the conditions of engineering application,or in the range（0.01,1.80） of a dimensionless normal depth.Formulae expressed in the two functions for the two reference shapes were obtained,and their errors were analyzed and evaluated.The results show that either the expression in quasi-linear function or quasi-quadratic function is applicable to the commonly-used depth range,and that the maximum error of calculated normal depth is less than 0.31%.Thus the expression of quasi-linear function that is simpler and of better accuracy and wider application is recommended.

关 键 词：水力学 正常水深 准一次函数 准二次函数 马蹄形断面 直接计算 

分 类 号：TV131.4[水利工程—水力学及河流动力学]