排灌机械工程学报
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Journal of Drainage and Irrigation Machinery Engin  2012, Vol. 30 Issue (2): 181-187    DOI: 10.3969/j.issn.1674-8530.2012.02.012
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Calculation of water critical depth in channels with common shapes
Liu Jiliang1, Wang Zhengzhong1, Su Dehui2, Yang Xiaosong1, Liu Quanhong1
(1.Institute of Water Resources and Hydropower Engineering, Northwest A & F University, Yangling, Shaanxi 712100, China; 2.Montgomery & Barnes, Inc., Houston, Texas 77067, USA)
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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 crosssections, two dimensionless variables related to channel crosssection geometry and discharge were defined. Then, those explicit equations available for five sorts of open channels with typical crosssections 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 openchannel with standard citygate crosssection. 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 typical open channels applied in drainage and irrigation.
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Articles by authors
LIU Ji-Liang
WANG Zheng-Zhong
SU De-Hui
YANG Xiao-Song
LIU Quan-Hong
Key wordschannels for drainage and irrigation   channel shapes   characteristic depths;critical depth   relative error   explicit equations     
Received: 2011-10-31; Published: 2012-03-30
Cite this article:   
LIU Ji-Liang,WANG Zheng-Zhong,SU De-Hui et al. Calculation of water critical depth in channels with common shapes[J]. Journal of Drainage and Irrigation Machinery Engin, 2012, 30(2): 181-187.
 
[1] 参考文献(References)
[2] Wang Zhengzhong. Formula for calculating critical depth of trapezoidal open channel[J]. Journal of Hydraulic Engineering, 1998, 124(1):90-91.
[3] 赵延风,王正中,方兴,等. 半立方抛物线形渠道正常水深算法[J]. 排灌机械工程学报, 2011, 29(3): 241-245.
Zhao Yanfeng, Wang Zhengzhong, Fang Xing, et al. Calculation method for normal depth of semicubic parabolic channels[J]. Journal of Drainage and Irrigation Machinery Engineering, 2011, 29(3): 241-245.(in Chinese)
[4] 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.
[5] Kanani A, Bakhtiari M, Borghei S M, et al. Evolutionary algorithms for the determination of critical depths in conduits[J]. Journal of Irrigation and Drainage Engineering, 2008, 134(6):847-852.
[6] 吕宏兴.马蹄形过水断面临界水深的迭代计算[J]. 长江科学院院报, 2002, 19(3): 10-12.
Lü Hongxing. Calculation on critical depth of horseshoe cross section by iterative method[J]. Journal of Yangtze River Scientific Research Institute, 2002, 19(3): 10-12.(in Chinese)
[7] 张宽地,王光谦,吕宏兴,等. 基于改进粒子群算法求解马蹄形断面正常水深[J]. 排灌机械工程学报, 2011,29(1): 54-60.
Zhang Kuandi, Wang Guangqian, Lü Hongxing, et al. Applying particle swam optimization algorithm on normal depth calculation of horseshoe section tunnel[J]. Journal of Drainage and Irrigation Machinery Engineering, 2011, 29(1): 54-60.(in Chinese)
[8] 王正中,陈涛,芦琴,等.马蹄形断面隧洞临界水深的直接计算[J]. 水力发电学报, 2005, 24(5): 95-98.
Wang Zhengzhong, Chen Tao, Lu Qin, et al. The direct solution on critical depth of horseshoe section tunnel[J]. Journal of Hydroelectric Engineering, 2005, 24(5):95-98. (in Chinese)
[9] Merkley G P. Standard horseshoe cross section geometry[J]. Agricultural Water Management, 2005, 71(1): 61-70.
[10] Liu Jiliang, Wang Zhengzhong, Fang Xing. Formulas for computing geometry and critical depth of general horseshoe tunnel[J]. Transactions of the ASABE, 2010, 53(4):1159-1164.
[11] Swamee P K. Critical depth equations for irrigation canals[J]. Journal of Irrigation and Drainage Engineering, 1993, 119(2):400-409.
[12] 王正中,袁驷,武成烈. 再论梯形明渠临界水深计算法[J]. 水利学报,1999(4): 14-17.
[13] 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)
[14] 廖云凤. 梯形断面渠道临界水深显式计算[J]. 陕西水力发电, 2001,17(4): 22-23.
Liao Yunfeng. Direct calculation formula of critical depth for trapezoidal canal[J]. Journal of Shaanxi Water Power, 2001,17(4):22-23.(in Chinese)
[15] Vantankhah A R, Kouchakzadeh S. Discussion of “Exact equations for critical depth in a trapezoidal canal”[J]. Journal of Irrigation and Drainage Engineering, 2007, 133(5): 508.
[16] Vatankhah A R, Easa S M. Explicit solutions for critical and normal depths in channels with different shapes[J]. Flow Measurement and Instrumentation, 2011, 22(1): 43-49.
[17] 苏鲁平. 梯形明渠临界水深解法综述[J]. 人民长江, 1995, 26(5):39-41.
Su Luping. Commentary on solutions for critical depth in a trapezoidal channel[J]. Yangtze River, 1995, 26(5):39-41.(in Chinese)
[18] Swamee P K, Rathie P N. Exact equations for critical depth in a trapezoidal canal[J]. Journal of Irrigation and Drainage Engineering, 2005, 131(5): 474-476.
[19] 王正中,陈涛,万斌,等. 圆形断面临界水深的新近似计算公式[J]. 长江科学院院报, 2004,21(2):1-2.
Wang Zhengzhong, Chen Tao, Wan Bin, et al. A new approximate formula to critical depth of round section canal[J]. Journal of Yangtze River Scientific Research Institute, 2004,21(2):1-2.(in Chinese)
[20] 赵延风,宋松柏,李宇. 圆形断面临界水深的近似计算公式[J]. 水利水电科技进展, 2008,28(2):62-64.
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)
[21] Vatankhah A R, Bijankhan M. Chokefree flow in circular and ovoidal channels[J]. Water Management, 2010, 163(4): 207-215.
[22] 王正中,申永康,彭元平,等. 弧底梯形明渠临界水深的直接算法[J]. 长江科学院院报, 2005,22(3):6-8.
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)
[23] 王正中,陈涛,张新民,等. 城门洞形断面隧洞临界水深度的近似算法[J]. 清华大学学报:自然科学版, 2004,44(6):812-814.
Wang Zhengzhong, Chen Tao, Zhang Xinmin, et al. Approximate solution for the critical depth of an arched tunnel[J]. Journal of Tsinghua University: Sci & Tech, 2004,44(6):812-814.(in Chinese)
[24] 赵延风,宋松柏,孟秦倩. 普通城门洞形断面临界水深的近似计算方法[J]. 长江科学院院报, 2008,25(4):14-15.
Zhao Yanfeng, Song Songbai, Meng Qinqian. Approximate method calculating critical water depth in common cityopening shaped crosssection[J]. Journal of Yangtze River Scientific Research Institute, 2008,25(4):14-15.(in Chinese)
[25] 张宽地,王光谦,吕宏兴,等. 明流条件下城门洞形隧洞临界水深的直接计算法[J]. 四川大学学报:工程科学版, 2010,42(3):101-106.
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)
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