| 李蕊，王正中，王志刚.圆形断面临界水深新近似计算式[J].干旱地区农业研究,2013,31(4):54~56 |
| 圆形断面临界水深新近似计算式 |
| A new approximate formula of critical water depth in circular cross-section |
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| DOI：10.7606/j.issn.1000-7601.2013.04.010 |
| 中文关键词: 数学建模 水力计算 临界水深 |
| 英文关键词:mathematics model hydraulic computation critical water |
| 基金项目:国家863计划项目(2002AA62Z3191)；国家自然科学基金项目(51279168) ；陕西省农业科技创新项目(2011NXC01-20) |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| Aimed 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. |
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