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| Calculation method for normal depth of semi- cubic parabolic channels |
| Zhao Yanfeng1,Wang Zhengzhong1,Fang Xing2,Liu Jiliang1,Hong Anyu1 |
| (1.Research Center of Water Engineering Safety and Disaster Prevention,Northwest A & F University,Yangling,Shaanxi 712100,China;2.Department of Civil Engineering,Auburn University,Auburn,Alabama 36849,U.S.A.) |
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Abstract In order to obtain the simple and general explicit formula with high accuracy for computing the normal depth of semi-cubic parabolic channels,formula for direct computation of the normal depth was developed by obtaining initial function using iteration theory and optimization.Mathematical transformation on the basic equation for determining the normal depth of semi-cubic parabolic channel was made by introducing the concept of characteristic depth of cross-section,and the iterative formula with high convergence rate was derived.According to the optimization of the iterative formula in the range of 0.025 to 40 for dimensionless normal depth H,the reasonable initial function was developed.Direct calculation formula for computing the normal depth of semi-cubic parabolic channels was obtained by using the reasonable initial value and iterative formula.Error analysis of the formula was also carried out.The result indicates that the maximum relative error of the formula is less than 0.3% for the most frequently used range of characteristic depth of cross-section.The formula developed in this paper is simple and has high accuracy with wide range of applications,and it can provide simple method for computing the normal depth when the channel section is designed for irrigation and drainage and controlling the water level
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Received: 21 October 2010
Published: 30 May 2011
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