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《Journal of Hydroelectric Engineering》 2013-01
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General explicit equations for calculation of contracted flow depths in channels of parabolic cross-sections

ZHAO Yanfeng1,2,WANG Zhengzhong1,2,LIU Jiliang1,2(1.College of Water Resources and Architectural Engineering,Northwest A.& F.University, Yangling,Shanxi 712100;2.Institute of Water Resources and Hydropower Engineering, Northwest A.& F.University,Yangling,Shanxi 712100)  
To obtain general explicit equations for contracted flow depth in the channel of parabolic cross-section,this paper puts forward for the first time a concept of incremental method of baseline function that can be used to obtain the equation parameters.By identical transformation of the governing equations for contracted depth,we developed iterative formulae of simple form and fast convergence.Then,explicit equations of n-th-order were derived for direct calculation of contracted depths for parabolic cross sections,through numerical calculation for establishing a relationship of dimensionless contracted depth versus a comprehensive parameter that represents the given quantities.The initial value of iterative solution to the equations can be obtained by using the incremental method and the iteration theory.Calculation of a practical case and error analysis of the depth calculations show that in the common range of α∈(0,0.5],the relative error is less than 0.52% for n∈ and less than 0.85% for n∈.The proposed simple equations are very accurate and general for practical design of channel.
【Fund】: 陕西省农业科技创新项目(2011NXC01-20)
【CateGory Index】: TV133
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