Abstract The existing methods for calculating critical depths of open channels were summarized and their characters have been clarified. In order to identify simple, universal, accurate explicit equations for calculating the critical depth in open channels with typical crosssections, two dimensionless variables related to channel crosssection geometry and discharge were defined. Then, those explicit equations available for five sorts of open channels with typical crosssections in literature were expressed by the dimensionless variables, thus the most appropriate ones could be selected by comparing their complexity, accuracy and application range. Also, by applying the best approximations algorithm, a new explicit equation expressed as a series of piecewise power functions was developed for the openchannel with standard citygate crosssection. For the new equations, the results of error analyses indicate that all the maximum relative errors in critical depth are less than 1% in the channel normal application range. The results of the study may provide a reference for the design and hydraulic calculations of typical open channels applied in drainage and irrigation.
Zhao Yanfeng, Wang Zhengzhong, Fang Xing, et al. Calculation method for normal depth of semicubic parabolic channels[J]. Journal of Drainage and Irrigation Machinery Engineering, 2011, 29(3): 241-245.(in Chinese)
Patil R G, Murthy J S R, Ghosh L K. Uniform and critical flow computations[J]. Journal of Irrigation and Drainage Engineering, 2005, 131(4):375-378.
Kanani A, Bakhtiari M, Borghei S M, et al. Evolutionary algorithms for the determination of critical depths in conduits[J]. Journal of Irrigation and Drainage Engineering, 2008, 134(6):847-852.
Zhang Kuandi, Wang Guangqian, Lü Hongxing, et al. Applying particle swam optimization algorithm on normal depth calculation of horseshoe section tunnel[J]. Journal of Drainage and Irrigation Machinery Engineering, 2011, 29(1): 54-60.(in Chinese)
Wang Zhengzhong, Yuan Si, Wu Chenglie. A final inquiry on a formula for calculating critical depth of open channel with trapezoidal cross section[J].Journal of Hydraulic Engineering, 1999(4):14-17.(in Chinese)
Zhao Yanfeng, Song Songbai, Li Yu. Approximate formula for calculating the critical water depth at circular cross section[J]. Advances in Science and Technology of Water Resources, 2008,28(2):62-64.(in Chinese)
Vatankhah A R, Bijankhan M. Chokefree flow in circular and ovoidal channels[J]. Water Management, 2010, 163(4): 207-215.
Wang Zhengzhong, Shen Yongkang, Peng Yuanping, et al. Direct formula calculating critical depth for open trapezoidal channel with spherical bed[J]. Journal of Yangtze River Scientific Research Institute, 2005,22(3):6-8.(in Chinese)
Zhao Yanfeng, Song Songbai, Meng Qinqian. Approximate method calculating critical water depth in common cityopening shaped crosssection[J]. Journal of Yangtze River Scientific Research Institute, 2008,25(4):14-15.(in Chinese)
Zhang Kuaidi, Wang Guangqian, Lü Hongxing, et al. A direct method for calculating the critical depth of an arched section tunnel[J]. Journal of Sichuan University: Engineering Science Edition, 2010,42(3):101-106.(in Chinese)