| The explicit calculation formula of normal and critical water depth for egg-shaped section |
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| DOI：10.7606/j.issn.1000-7601.2017.02.31 |
| Key Words: egg-shaped section normal water depth critical water depth 1stopt software explicit calculation formula |
| Author Name | Affiliation | | BIAN Xiao-wei | Power China Guiyang Engineering Corporation Limited， Guiyang, Guizhou 550811， China | | ZHENG Xin-qiao | Sinohydro Corporation Engineering Bureau 15 Co., Ltd., Xi'an, Shaanxi 710068, China | | DAI Shu-bing | Faculty of Infrastructure Engineering, Dalian University of Techlonogy, Dalian, Liaoning 116024, China | | JIAN Yue | Yunnan Jiangong Water Resource and Hydroelectric Construction Co., Ltd., Kunming, Yunnan 650000, China | | MA Yu-lei | Faculty of Infrastructure Engineering, Dalian University of Techlonogy, Dalian, Liaoning 116024, China |
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| Abstract: |
| The calculating formulas of normal and critical water depth for egg-shaped section are sectional transcendental equations, which can't be solved directly. In this article, the normal and critical depth formula is simplified by mathematical deformation, and then the relation of filling degree x with nondimensional normal water depth H and nondimensional critical depth P is gotten. The 1stopt software is adopted to optimize and fit the established nonlinear model parameters based on genetic algorithm and set up the explicit calculation formula of normal and critical water depth for egg-shaped section. The error analysis and example calculation show that, within the large range of common project application, the largest relative errors of normal and critical water depth for egg-shaped section are just 0.3691% and -0.0726%, relatively. Compared with the existing formulas, the explicit formula is characterized by a larger application range, a higher precision and a more convenient calculation. The proposed formula will provide a theoretical basis and useful reference for project design, operation and management. |
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