摘要:针对目前圆形断面临界水深普遍采用的试算法、图表法存在计算误差大、适用范围小的缺点，提出一种新的近似计算公式。通过对圆形断面临界流公式的数学变换，得到其临界水深的数学模型，并采用最小二乘法进行编程计算，得到了一种求解圆形断面临界水深的新近似直接计算公式。实例计算及误差分析表明，在工程实用范围内该公式最大相对误差小于1%。与现有圆形断面临界水深的计算公式比较，该计算公式计算便捷且适用范围广，可供工程实际参考应用。

关键词:数学建模  水力计算  临界水深

AbstractAimed at the problems of large error and narrow applicable scope exiting in the trial and diagram methods generally used, a new approximate formula of critical water depth in circular cross-section was proposed. The mathematical model of critical water depth was set up through the mathematical transformation of critical flow formula in circular cross-section, and the new approximate formula of critical water depth in circular cross-section was obtained by using least squares for programming computation. The example computation and error analysis indicated that the largest relative error of this formula was smaller than 1% in the practical scope of project. Compared with the existing formula of critical water depth in circular cross-section, the new formula is more convenient in computation and broader in applicable scope, and it can be applied for reference in engineering practices.

Key wordsmathematics model  hydraulic computation  critical water

文章编号： 0258_7106 (2016) 01_0018_15 中图分类号： P618.41 文献标志码：A

投稿时间：2012-09-03修订日期：2012-10-30 改回日期：2015_07_11

基金项目

**通讯作者耿新霞， 女， 1979年生， 助理研究员， 成矿规律研究方向。 Email： gen gxinxia@cags.ac.cn