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张宽地,吕宏兴,赵延风.明流条件下圆形隧洞正常水深与临界水深的直接计算[J].农业工程学报,2009,25(3):1-5.DOI:
明流条件下圆形隧洞正常水深与临界水深的直接计算
投稿时间:2008-04-25  修订日期:2009-01-18
中文关键词:  渠道,水力模型,圆形过水断面,水力计算,牛顿迭代法
基金项目:国家973计划课题(2007CB407201);国家自然科学基金重点项 目(40335050);西北农林科技大学创新团队建设计划(01140202);黄土高 原土壤侵蚀与旱地农业国家重点实验室基金项目(10501-182)
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 
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中文摘要:无压流圆形断面水力计算中的正常水深、临界水深求解无解析表达式,传统的试算法或查图法不仅计算过程繁琐复杂,而且计算精度不高。该文通过对圆形断面均匀流方程与临界流方程的数学变换,分别得到其正常水深与临界水深的牛顿迭代公式,同时,通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算,利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式,并以此近似计算式为初值,用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。实例计算及误差分析表明:在工程实用范围内该法正常水深与临界水深最大相对误差分别为0.32%和0.0049%,如用该近似结果再迭代一次,精度高出103倍和105倍。
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 NameAffiliation
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.
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