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| DOI：10.13522/j.cnki.ggps.2017.11.010 |
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| Calculating Optimal Channel Cross Section with Parabolic Slope and Flat Bed Using the Lagrangian Method |
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LI Gang, HE Wuquan, ZHAI Donghan
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College of Water Resources and Architectural Engineering , Northwest A &F University, Yangling 712100, China: The Ministry of Education Key Laboratory of Agricultural Water and Soil Engineering, Yangling 712100, China
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| Abstract: |
| Channels with parabolic cross section are deep and widely open, not suitable for use in medium-large canals. In this paper, we present a channel with parabolic slopes and flat bed and then calculated its hydraulic parameters. Taking water depth and widths of water surface and channel bed as variables, we calculated the relationship between flow rate and water depth after optimizing the channel cross section using the Lagrangianiterative method and the Mathcad software. The dependence of wetting perimeter of the channel on water depth and widths of water surface and channel bed was also analyzed. Numerical calculations showed that when the optimal flow rate was 12 m3/s, the associated water depth was 2.263 m, the width of water surface was 4.538 m, and the cross-section area for water flow was 7.463 m2. This means a reduction in water-flow cross section by 1.67% compared to trapezoidal cross section, 0.84% compared to cross section with trapezoidal slopes and parabolic bed, and 1.05% compared toparabolic cross section. |
| Key words: channel; optimal hydraulic section; Lagrange multiplier method; hydraulic calculation |
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