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## The explicit calculation formula of normal and critical water depth for egg-shaped section

BIAN Xiao-wei;ZHENG Xin-qiao;DAI Shu-bing;JIAN Yue;MA Yu-lei;Power China Guiyang Engineering Corporation Limited;Sinohydro Corporation Engineering Bureau 15 Co.,Ltd.;Faculty of Infrastructure Engineering,Dalian University of Techlonogy;Yunnan Jiangong Water Resource and Hydroelectric Construction Co.,Ltd.;
The calculating formulas of normal and critical water depth for egg-shaped section are sectional transcendental equations,which can't be solved directly. In this article,the normal and critical depth formula is simplified by mathematical deformation,and then the relation of filling degree x with nondimensional normal water depth H and nondimensional critical depth P is gotten. The 1stopt software is adopted to optimize and fit the established nonlinear model parameters based on genetic algorithm and set up the explicit calculation formula of normal and critical water depth for egg-shaped section. The error analysis and example calculation show that,within the large range of common project application,the largest relative errors of normal and critical water depth for egg-shaped section are just 0. 3691% and-0. 0726%,relatively. Compared with the existing formulas,the explicit formula is characterized by a larger application range,a higher precision and a more convenient calculation. The proposed formula will provide a theoretical basis and useful reference for project design,operation and management.
【CateGory Index】： TV133
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 【Citations】
 Chinese Journal Full-text Database 7 Hits
 1 WU Zhouhu;School of Environmental and Municipal Engineering,Qingdao Technological University;;Simplified algorithm of normal depth and critical depth of egg-shape cross-section open channel[J];人民长江;2014-04 2 TENG Kai;Qiqihar Municipal Water Affairs Bureau;;Analytical algorithm for water surface profile of free-flow tunnel with egg-shaped cross-section[J];水利水电科技进展;2014-02 3 ZHANG Xinyan;LU Hongxing;College of Water Resources and Architectural Engineering, Northwest Agriculture and Forestry University;;Direct calculation method for normal depth in non-pressure circular tunnel[J];水力发电学报;2014-01 4 TENG Kai;Qiqihar Municipal Water Affairs Bureau;;A Simple Calculation Method for the Normal Water Depth of Tunnel with Egg-shaped Section[J];长江科学院院报;2013-12 5 TENG Kai;Qiqihar Municipal Water Affairs Bureau;;Simple algorithm for the critical depth of an egg-shaped section water tunnel[J];水利水电科技进展;2013-06 6 Zhang Xinyan,Lü Hongxing ※,Zhu Delan(College of Water Resources and Architectural Engineering,Northwest Agriculture and Forestry University,Yangling 712100,China);Direct calculation formula for normal depth of U-shaped channel[J];农业工程学报;2013-14 7 LI Ruobing,ZHANG Zhichang(Xi'an University of Technology,Xi'an 710048,China);Calculation of critical water depth and contraction section water depth in egg-shaped cross-section with six arcs of open channel[J];武汉大学学报(工学版);2012-04
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 CHEN Cheng;GONG Yi;SHEN Gang;ZHU Weibin;NIU Jiamin;CAO Mengye;School of Hydraulic Energy and Power Engineering,Yangzhou University;Liyang Water Conservancy Bureau;Administrative Office of Yanyun Irrigated Area in Jiangdu District;Suzhou Water Conservancy Bureau;;Study on application of iterative approximation—progressive optimization fitting approach to hydraulic calculation[J];水利水电技术;2017-06 2 BIAN Xiao-wei;ZHENG Xin-qiao;DAI Shu-bing;JIAN Yue;MA Yu-lei;Power China Guiyang Engineering Corporation Limited;Sinohydro Corporation Engineering Bureau 15 Co.,Ltd.;Faculty of Infrastructure Engineering,Dalian University of Techlonogy;Yunnan Jiangong Water Resource and Hydroelectric Construction Co.,Ltd.;;The explicit calculation formula of normal and critical water depth for egg-shaped section[J];干旱地区农业研究;2017-02 3 Han Yancheng;Xu Zhenghe;Gao Xueping;Said M.Easa;College of Resources and Environment, University of Jinan;State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University;Dept.of Civil Engineering, Ryerson Univ.;;Design of two and a half parabola-shaped canal and its effect in improving hydraulic property[J];农业工程学报;2017-04 4 CHEN Cheng;GONG Yi;WANG Jie;YAN Yue-tong;HU Jing;College of Hydraulic,Energy and Power Engineering,Yangzhou University;Suqian Water Control Project Administration Bureau;Hongze Lake Water Conservancy Project Management Office in Jiangsu Province;;Research on Direct Calculation of Contracted Water Depth in Cubic Parabolic Cross-sections[J];中国农村水利水电;2017-02 5 LEI Jiaxin;TENG Kai;Heilongjiang Provincial Construction Quality and Safety Supervision Center of Water Conservancy;Qiqihar Municipal Bureau of Water Affairs;;Simplified Calculation of Conjugate Water Depth for the Six-arc Egg-shaped Cross Section[J];水利与建筑工程学报;2015-04 6 ZHANG Zhi-chang;JIA Bin;LI Ruo-bing;Institute of Water Resources and Hydro-electric Engineering,Xi'an University of Technology;;Direction calculation of normal water depth of egg-shaped cross section with six arcs in open channel[J];西北农林科技大学学报(自然科学版);2015-08 7 Zhang Zhichang;Jia Bin;Xi'an University of Technology;;Hydraulic calculation of standard type-I four arcs egg-shaped cross section[J];应用力学学报;2015-03 8 Wen Hui;Li Fengling;Department of Architecture and Civil Engineering, Huizhou University;;Numerical integration method for calculating water surface profile of gradually varied steady flow in parabola shaped channel[J];农业工程学报;2014-24 9 Zhang Zhichang;Jia Bin;Xi'an University of Technology;;Approximate calculation method of water surface profile in egg-shaped cross section with six arcs in open channel[J];应用力学学报;2014-06 10 ZHANG Zhi-chang;JIA Bin;LI Ruo-bing;Institute of Water Resources and Hydro-electric Engineering,Xi'an University of Technology;;Calculation method of conjugate water depth of egg-shaped cross section with six arcs in open channel[J];西北农林科技大学学报(自然科学版);2015-01
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 Chinese Journal Full-text Database 10 Hits
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