摘要
德式蛋形断面明渠均匀流正常水深和临界水深的基本方程均为隐式三角函数方程，无法直接求解。在充满度α=0.0667~0.85区间选取一系列数值，通过计算相应的圆心角θ，再计算与α对应的一系列正常水深模数η0和临界水深模数浊k 的精确值并点绘成曲线，在分段曲线拟合和优化分析的基础上，分别给出了以正常水深模数η0为自变量的充满度α0直接计算公式和以临界水深模数ηk为自变量的充满度αk直接计算公式。算例表明，该简化算法具有简单快捷、方便实用和结果精度高等特点，可极大方便工程设计人员在德式蛋形断面排水涵管设计中的使用。
The basic equation of normal depth and critical depth of uniform flow in open channel with German egg-shape cross-section is implicit trigonometricfunction equation, which can not be solved directly. In this study, the exact values of the modulus of normal depth η0 and critical depth ηk are obtained by calculating the central angle θ corresponding to a set of fullnessαchosen from 0. 066 7~0. 85 and the relation curves are plotted. On the basis of the segmented curve fitting and optimi-zation analysis, the direct calculation formulas of normal depthη0 （α0 ） and critical depth ηk （αk ） are obtained. The application example shows that the simplified algorithm is characterized as form simple, calculation fast, convenient and practical with high precision, which can be used in the design of the German egg-shape cross section drainage culvert.
出处
《人民长江》
北大核心
2014年第4期73-76,共4页
Yangtze River
基金
国家自然科学基金资助项目(51379097)
关键词
德式蛋形断面
明渠
正常水深
临界水深
隐式三角函数方程
简化算法
German egg-shape cross section
open channel
normal depth
critical depth
implicit trigonometric equation
simplified algorithm
