|
|
|
| Simple calculation method for normal depth of a kind of water supply tunnel for irrigation and drainage |
| Zhao Yanfeng1, Wang Zhengzhong1, Fang Xing2, Liu Jiliang1, Hong Anyu1 |
| (1.Institute of Water Resources and Hydropower Engineering, Northwest A & F University, Yangling, Shaanxi 712100, China; 2.Department of Civil Engineering, Auburn University, Auburn, Alabama 36849, U.S.A.) |
|
|
|
|
Abstract In order to obtain an explicit formula for normal depth of standard citygate section,first,the identical transformation of the governing equation for normal depth of standard citygate section was made,including the transcendental equation for normal depth in the bottom corner arc and the top arc,and the higher degree equation for normal depth in the lateral side.The single variable equation was obtained for dimensionless normal depth and the comprehensive parameter of the known quantities.Second,the concept of quasilinear function was introduced and treated as the standard template.The standard template for quasilinear function was applied to the single variable equation for normal depth.Using optimization and approximation to quasilinear function,the estimation substitution formula for the transcendental equation and higherdegree equation was developed in the practical range of y∈［0.05,1.80］,and the substitution formula has the same form as the linear function,i.e.,the quasilinear explicit expression for normal depth.Finally,error analysis of the formula was made.The result indicates that the maximum relative errors of the formula for normal depth are less than 0.36%,0.31%,and 0.39% in the bottom arc,the lateral side,and the top arc,respectively.The relative errors indicate that the quasilinear equation has high accuracy in the practical range,which can provide simple method for computing the normal depth of the uniform flow in the design of water supply tunnel for drainage and irrigation and controlling the water level.
|
|
Received: 08 March 2011
Published: 30 November 2011
|
|
|
|
| ［1］Swamee P K.Normaldepth equations for irrigation canals［J］.Journal of Irrigation and Drainage Engineering,1994,120(5):942-948.［2］Babaeyan-Koopaei K.Dimensionless curves for normal depth calculations in canal sections［J］.Journal of Irrigation and Drainage Engineering, 001,127(6):386-389.［3］吕宏兴,辛全才,花立峰.马蹄形过水断面正常水深的迭代计算［J］.长江科学院院报,2001,18(3):7-10.Lü Hongxing,Xin Quancai,Hua Lifeng.Calculation on normal depth of horseshoe cross section by iterative method［J］.Journal of Yangtze River Scientific Research Institute,2001,18(3):7-10.(in Chinese)［4］吕宏兴,把多铎,宋松柏.无压流圆形断面水力计算的迭代法［J］.长江科学院院报,2003,20(5):15-17.Lü Hongxing,Ba Duoduo,Song Songbai.Hydraulic calculation for free flow in circular section by iterative method［J］.Journal of Yangtze River Scientific Research Institute,2003,20(5):15-17.(in Chinese)［5］王顺久,侯 玉,张欣莉,等.马蹄形过水断面正常水深计算的遗传算法［J］.灌溉排水,2002,21(3):43-45.Wang Shunjiu,Hou Yu,Zhang Xinli,et al.Genetic algorithm for calculating normal water depth of horseshoe cross section［J］.Irrigation and Drainage,2002,21(3):43-45.(in Chinese)［6］Swamee P K,Rathie P N.Exact solutions for normal depth problem［J］.Journal of Hydraulic Research,2004,42(5):541-547.［7］Srivastava R.Exact solutions for normal depth problem［J］.Journal of Hydraulic Research,2006,44(3):427-428.［8］Wong T S W.Exact solutions for normal depth problem［J］.Journal of Hydraulic Research,2007,45(4):567-571.［9］Shrestha R C,Barkdoll B.A direct solution to normal depth in open channels［C］∥Proceedings of the 2005 World Water and Environmental Resources Congress.Reston,US:American Society of Civil Engineers,2005:405.［10］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 Swarm Optimization algorithmon normal depth calculation of horse shoe section tunnel［J］.Journal of Drainage and Irrigation Machinery Engineering,2011,29(1):54-60.(in Chinese)［11］赵延风,芦 琴,张宽地.圆形断面均匀流水深的近似计算公式［J］.西北农林科技大学学报:自然科学版,2008,36(5):225-228.Zhao Yanfeng,Lu Qin,Zhang Kuandi.An approximate formula for calculating water depth of uniform flow in circular cross section［J］.Journal of Northwest A ＆ F University:Natural Science Edition,2008,36(5):225-228.(in Chinese)［12］张宽地,吕宏兴,赵延风.明流条件下圆形隧洞正常水深与临界水深的直接计算［J］.农业工程学报,2009,25(3):1-5.Zhang Kuandi,Lü Hongxing,Zhao Yanfeng.Direct calculation for normal depth and critical depth of circular section tunnel under free flow［J］.Transactions of the CSAE ,2009,25(3):1-5.(in Chinese)［13］张宽地,吕宏兴,王光谦,等.普通城门洞形隧洞正常水深的直接计算方法［J］.农业工程学报,2009,25(11):8-12.Zhang Kuandi,Lü Hongxing,Wang Guangqian,et al.Direct calculation method for normal depth of arched section tunnel［J］.Transactions of the CSAE,2009,25(11):8-12.(in Chinese)［14］赵延风,刘 军,梅淑霞,等.普通城门洞形断面正常水深的近似计算方法［J］.武汉大学学报:工学版,2009,42(6):773-775.Zhao Yanfeng,Liu Jun,Mei Shuxia,et al.Approximate method for calculating normal water depth in common cityopening shaped crosssection［J］.Engineering Journal of Wuhan University,2009,42(6):773-775.(in Chinese)［15］吴持恭.水力学［M］.北京:高等教育出版社,1979. |
|
|
|
