半椭圆断面渠道的水跃方程及其解法
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摘要
半椭圆断面渠道广泛应用于农田灌溉系统,水跃共轭水深作为其重要的水力参数,须寻求其快速有效的解法。首先基于半椭圆断面的断面几何特点推求了其无量纲水跃方程。接着根据半椭圆断面跃前水深与跃后水深均有水深范围限制的特点,分析了无量纲流量及无量纲跃前水深的取值范围。最后在大量计算的基础上绘制了半椭圆断面的无量纲共轭水深关系图,应用该图可快速得到半椭圆断面水跃方程的共轭水深解,该方法是简捷有效,便于工程实际推广应用。
Semielliptical channels are widely used in the farmland irrigation system. The conjugate depth is the essential hydraulic parameter and it is necessary to find its efficient and fast-speed calculation method. Firstly,the dimensionless hydraulic jump equation for semielliptical channels is derived based on its geometric characteristics of cross-section. Both the range of initial depths and the sequent depths are limited for semielliptical channels,so both the dimensionless discharge and dimensionless initial depths are analyzed. In the end,the relationship map of dimensionless conjugate depths is drawn based on a large number of calculations,and the conjugate depth solution of hydraulic jump equation can be obtained rapidly by the map.The method is simple and efficient,and it can be popularized easily in engineering practice.
Semielliptical channels are widely used in the farmland irrigation system. The conjugate depth is the essential hydraulic parameter and it is necessary to find its efficient and fast-speed calculation method. Firstly,the dimensionless hydraulic jump equation for semielliptical channels is derived based on its geometric characteristics of cross-section. Both the range of initial depths and the sequent depths are limited for semielliptical channels,so both the dimensionless discharge and dimensionless initial depths are analyzed. In the end,the relationship map of dimensionless conjugate depths is drawn based on a large number of calculations,and the conjugate depth solution of hydraulic jump equation can be obtained rapidly by the map.The method is simple and efficient,and it can be popularized easily in engineering practice.
引文
[1]Asuquo E Eyo.Model for dredging a horizontal trapezoidal open channel with hydraulic jump[J].Journal of Mathematics Research,2012,4(3):132-141.
[2]JL Liu,ZZ Wang,X Fang.Computing conjugate depths in trapezoidal channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2012,165(9):507-512.
[3]Mitchell SB.Positive surge in trapezoidal and circular channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2010,163(4):199-205.
[4]Mitchell SB.Hydraulic jumps in trapezoidal and circular channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2008,161(3):161-167.
[5]Mohd Jamil,Suhail A Khan.Theoretical study of hydraulic jump in circular channel section[J].ISH Journal of Hydraulic Engineering,2010,16(1):1-10.
[6]I M H Rashwan.Analytical solution to problems of hydraulic jump in horizontal triangular channels[J].Ain Shams Engineering Journal,2013,(4)3:365-368.
[7]Vatankhah,Ali R,Omid,M H.Direct solution to problems of hydraulic jump in horizontal triangular channels[J].Applied Mathematics Letters,2010,23(9):1 104-1 108.
[8]Mahmoud Debabeche,Sonia Cherhabil,Amin Hafnaoui,et al.Hydraulic jump in a sloped triangular channel[J].Canadian Journal of Civil Engineering,2009,36(4):655-658.
[9]AE Eyo.Flow in a triangular open channel with hydraulic jump[J].Journal of the Nigerian Association of Mathematical Physics,2009,15(1):123-132.
[10]代述兵,刘韩生,杨吉健.三种抛物线形渠道共轭水深的显式计算公式[J].长江科学院院报,2015,32(8):51-56.
[11]Ma ZP,Zhang GG,Zhao CL,et al.Iterative algorithm of conjugate depth for parabolic channels[J].Flow Measurement and Instrumentation,2013,32(1):1-4.
[12]马吉明,谢省宗,梁元博.城门洞形及马蹄形输入隧洞内的水跃[J].水利学报,2000,(7):20-24.
[13]李若冰,张志昌.标准Ⅰ型马蹄形断面水跃共轭水深的计算[J].西北农林科技大学学报(自然科学版),2012,40(8):230-234.
[14]张志昌,贾斌,李若冰.六圆弧蛋形断面共轭水深计算方法的研究[J].西北农林科技大学学报(自然科学版),2015,43(1):220-228.
[15]张志昌,李若冰.U形渠道临界水深、弗劳德数和水跃的研究[J].西安理工大学学报,2012,28(2):198-203.
[16]Vatankhah,Ali R.Critical and normal depths in semielliptical channels[J].ASCE Journal of Irrigation and Drainage Engineering,2015,141(10):06015002.
[2]JL Liu,ZZ Wang,X Fang.Computing conjugate depths in trapezoidal channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2012,165(9):507-512.
[3]Mitchell SB.Positive surge in trapezoidal and circular channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2010,163(4):199-205.
[4]Mitchell SB.Hydraulic jumps in trapezoidal and circular channels[J].Proceeding of the Institution of Civil Engineers-Water Management,2008,161(3):161-167.
[5]Mohd Jamil,Suhail A Khan.Theoretical study of hydraulic jump in circular channel section[J].ISH Journal of Hydraulic Engineering,2010,16(1):1-10.
[6]I M H Rashwan.Analytical solution to problems of hydraulic jump in horizontal triangular channels[J].Ain Shams Engineering Journal,2013,(4)3:365-368.
[7]Vatankhah,Ali R,Omid,M H.Direct solution to problems of hydraulic jump in horizontal triangular channels[J].Applied Mathematics Letters,2010,23(9):1 104-1 108.
[8]Mahmoud Debabeche,Sonia Cherhabil,Amin Hafnaoui,et al.Hydraulic jump in a sloped triangular channel[J].Canadian Journal of Civil Engineering,2009,36(4):655-658.
[9]AE Eyo.Flow in a triangular open channel with hydraulic jump[J].Journal of the Nigerian Association of Mathematical Physics,2009,15(1):123-132.
[10]代述兵,刘韩生,杨吉健.三种抛物线形渠道共轭水深的显式计算公式[J].长江科学院院报,2015,32(8):51-56.
[11]Ma ZP,Zhang GG,Zhao CL,et al.Iterative algorithm of conjugate depth for parabolic channels[J].Flow Measurement and Instrumentation,2013,32(1):1-4.
[12]马吉明,谢省宗,梁元博.城门洞形及马蹄形输入隧洞内的水跃[J].水利学报,2000,(7):20-24.
[13]李若冰,张志昌.标准Ⅰ型马蹄形断面水跃共轭水深的计算[J].西北农林科技大学学报(自然科学版),2012,40(8):230-234.
[14]张志昌,贾斌,李若冰.六圆弧蛋形断面共轭水深计算方法的研究[J].西北农林科技大学学报(自然科学版),2015,43(1):220-228.
[15]张志昌,李若冰.U形渠道临界水深、弗劳德数和水跃的研究[J].西安理工大学学报,2012,28(2):198-203.
[16]Vatankhah,Ali R.Critical and normal depths in semielliptical channels[J].ASCE Journal of Irrigation and Drainage Engineering,2015,141(10):06015002.