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| DOI：10.13522/j.cnki.ggps.20180188 |
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| Optimal Design of Hydraulic and Practical Cross-section of Parabolic Canals |
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CHEN Bairu , WANG Yi, ZHAO Yanfeng, WANG Zhengzhong
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1. College of Water Resources and Architectural Engineering, Northwest A & F University, Yangling 712100, China；2. Cold and Arid Regions Water Engineering Safety Research Center, Northwest A & F University, Yangling 712100, China；3. State Key Laboratory of Frozen Soils Engineering, Cold and Arid Region Environmental and Engineering Research Institute, CAS, Lanzhou 730000, China
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| Abstract: |
| 【Objective】 There are no analytical solutions to calculate the wetted perimeter in parabolic canals and this paper is to present an alternative method to calculate the hydraulic and practical cross section of the parabolic canals. 【Method】 The proposed method was based on the Gauss-hypergeometric function, from which the exact solutions for the wetted-perimeter of the canals with parabolic cross section was obtained. Taking water depth and width of the water surface as variables, the optimal hydraulic cross-section can be obtained by using the Lagrange multiplier method. 【Result】 Based on the relationship between the practically economic cross section and the optimal hydraulic cross-section, the practically economic cross-section parametric equation for the parabolic canal was obtained. The datum table of the ratio between the water width and the water depth of the practically economic cross-section of parabolic canals was provided. 【Conclusion】 The proposed method is easy to be used to design the optimal hydraulic cross-section and practically economic cross-section of any parabolic canals. It can also be used as a tool in channel planning and design, and provided a theoretical basis for revising standards. |
| Key words: parabola-shaped canal; Gaussian hypergeometric function; optimal hydraulic cross-section; practically economic cross-section; open channel hydraulics; uniform design method |
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