摘要
梯形明渠临界水深的求解过程是求解一个单变量超越方程的过程,理论上无解析解。通过引入无量纲参数——单位水面宽度,对梯形明渠临界水深的基本公式进行恒等变形,得到计算梯形明渠临界水深的迭代公式,再与合理的迭代初值配合使用。推导出4套梯形断面临界水深的直接计算公式,其中2套计算公式印证了前人的成果,并为前人的公式推导提供了简捷、充分的理论依据。通过对多家公式形式的表述和比较,并根据精度1%和1‰的不同要求进行误差分析,结果表明:4套直接计算公式理论性强,形式简单,适用范围广,计算精度高,值得推广。
The solution process of critical depth on trapezoidal channel is to solute a single variable. There is no analytic solution in theory. With a reasonable initial interaction, by introducing a dimensionless parameter unit surface width and doing on identical deformation of a critical depth formula on trapezoidal channel, the critical depth formula on the trapezoidal channel can be obtained. There are four sets of direct critical depth formulas on trapezoidal cross-section, in which two sets of formulas confirmed previous results and provide a simple, full theory basis for the previous formula derived. The calculated results show that the four sets of direct formulas possess stronger theoretic and simple forms, may be applied to a wide range with high accuracy, and in accordance with the accuracy of 1% and 1‰ to the different requirements, errors of every formula are analyzed.
出处
《长江科学院院报》
CSCD
北大核心
2009年第4期18-21,47,共5页
Journal of Changjiang River Scientific Research Institute
基金
国家自然科学基金资助项目(50579065)
西北农林科技大学优秀科技人才基金(04ZR014)
关键词
梯形明渠
临界水深
精确计算
单位水面宽度
trapezoidal channel
critical depth
accurate calculation
unit surface width
