首页 | 简介 | 作者 | 编者 | 读者 | Ei(光盘版)收录本刊数据 | 网络预印版 | 点击排行前100篇 | English

 作者 单位 张宽地 西北农林科技大学水利与建筑工程学院，杨凌 712100 吕宏兴 西北农林科技大学水利与建筑工程学院，杨凌 712100 赵延风 西北农林科技大学水利与建筑工程学院，杨凌 712100

Zhang Kuandi,Lü Hongxing,Zhao Yanfeng.Direct calculation for normal depth and critical depth of circular section tunnel under free flow[J].Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE),2009,25(3):1-5.DOI:
Direct calculation for normal depth and critical depth of circular section tunnel under free flow
 Author Name Affiliation Zhang Kuandi College of Water Conservancy and Architectural Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China Lü Hongxing College of Water Conservancy and Architectural Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China Zhao Yanfeng College of Water Conservancy and Architectural Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China
Key words:tunneling, hydraulic models, circular wetted cross section, hydraulic calculation, Newton iteration method
Abstract:There is no analytical expression to solve the normal depth and critical depth of circular section tunnel under free flow. The traditional solving methods, such as trial method and chart method, are very complicated and low precision. In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative. Results of the example calculation and error analysis showed that the maximum relative error of normal depth and critical depth was 0.32% and 0.0049%, respectively with the application scope of engineering. The precision will be 103 and 105 times higher than the original one after using the iterative formula once again.