Explicit solution for normal depth of parabolic section of open channels |
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| Affiliation: | 1. College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, PR China;2. Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling 712100, PR China;1. State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, PR China;2. Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, PR China;1. Key Laboratory of Optoelectronic Materials Chemistry and Physics of CAS, Fujian Institute of Research on the Structure of Matter, CAS, Fuzhou, Fujian 350002, PR China;2. University of Chinese Academy of Sciences, Beijing 100039, PR China;3. School of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243002, PR China;4. Crystech Inc., Qingdao 266107, PR China;1. Beijing Key Laboratory of Polymorphic Drugs, Institute of Materia Medica, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100050, China;2. Beijing City Key Laboratory of Drug Target Identification and Drug Screening, Institute of Materia Medica, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100050, China;3. Key laboratory of Polymorph Pharmaceutical of Shandong Province, Tengzhou 277500, China;1. State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China;2. School of Chemistry and Engineering, Shandong University, Jinan 250100, China |
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| Abstract: | To obtain the normal depth of parabolic section of open channels, multiple known parameters were incorporated into a comprehensive one by transforming basic equations, and a concept of the non-dimensional normal depth was introduced. The normal depth equations were simplified into a non-dimensional iterative formula that was proved to have a high velocity of convergence. By analyzing the comprehensive parameter and dimensionless normal depth under condition of usually adopted sizes of parabolic channels and through establishing their relationship, the iterative initial value of normal depth was obtained. The normal depth of parabolic channels was acquired by substituting the initial value into the iteration formula. The error analysis was made and a case study was provided as an application example. The case study showed that the iteration formula was very simple, convenient and precise for determining the normal depth of parabolic channels with the maximum relative error of normal depth being less than 0.34% when the ratio of width to depth was between 0.2 and 20. |
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| Keywords: | Irrigation channel Normal depth Parabolic section Explicit solution |
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