Hydraulics of free overfall in smooth triangular channels

Ain Shams Engineering Journal - Tập 12 - Trang 2471 - 2021
Bahzad Mohammad Ali Noori, Karzan Abdullah Muhsin

Tóm tắt

The present study deals with the hydraulic behavior of smooth triangular channels with free overfall in order to obtain useful relationships for the estimation of end depth discharge (EDD) in terms of brink depth (yb), channel side slopes (m) and channel bed slope (So). For this purpose, twelve triangular channel models have been built and tested having 3.6 m length and 19 cm drop at brink with different values of side slopes (m = 0.75, 1.0 and 1.25) and different channel bed slopes (So = 0.0, 0.0033, 0.0067 and 0.02). Experimental results of all models showed straight line relationships for the end depth ratio (EDR) for different values of (So) and (m) with high determination coefficients and low values of root mean square error. A quadratic equation is obtained for the variation of EDR with (So). An empirical expression is obtained for a dimensionless discharge in terms of (So) for all channel models tested for both subcritical and supercritical flow conditions with the range of Froude number in the approach channel between 0.64 and 4.15. Two methods (direct and indirect) are proposed for the estimation of EDD in which the outcome results compared quite well with the available data of previous studies.

Từ khóa

#Triangular channels #Free overfall #Hydraulics #End depth ratio #End depth discharge

Tài liệu tham khảo

[1] B.M.A. Noori S.S. Ibrahim Effect of bed and side slopes on flow measurements in trapezoidal free overfall channels Arabian J Sci Eng 41 2016 4187 4194 Noori, BMA, Ibrahim SS, Effect of bed and side slopes on flow measurements in trapezoidal free overfall channels, Arabian Journal for Science and Engineering, April 2016; 41;4187-4194. [2] J.S. Maatooq End discharge relationship for free overfall affected by upstream bed roughness and slope Am J Eng Appl Sci 10 2 2017 603 610 Maatooq JS, End discharge relationship for free overfall affected by upstream bed roughness and slope, American Journal of Engineering and Applied Sciences, 2017; 10(2); 603-610. [3] S.V. Nabavi Flow measurement in rectangular channels Bull Environ, Pharmacol Life Sci 4 1 2015 457 467 Nabavi SV, Flow measurement in rectangular channels, Bulletin of Environment, Pharmacology and Life Sciences, 2015; 4(1); 457-467. [4] S. Swetapadma S.K. Mittal M.K. Choudhary Experimental analysis of brink depth in smooth rectangular channel Int J Innov Sci Eng Technol 2 10 2015 639 646 Swetapadma S, Mittal SK, Choudhary MK, Experimental analysis of brink depth in smooth rectangular channel, International Journal of Innovative Science, Engineering & Technology, April 2015; 2 (10); 639-646. [5] H. Rouse Engineering hydraulics 1949 Wiley New York Rouse H, Engineering hydraulics, Wiley, New York, 1949. [6] L. Anastasiadou-Partheniou E. Hatzigiannakis General end-depth discharge relationship at free overfall in trapezoidal channel J Irrigat Drainage Eng, ASCE 121 2 1995 143 151 Anastasiadou-Partheniou L, Hatzigiannakis E, General end-depth discharge relationship at free overfall in trapezoidal channel, Journal of Irrigation and Drainage Engineering, ASCE, 1995; 121 (2); 143-151. [7] V. Ferro Theoretical end-depth discharge relationship for free overfal J Irrigat Drainage Eng, ASCE 125 1 1999 40 44 Ferro V, Theoretical end-depth discharge relationship for free overfal, Journal of Irrigation and Drainage Engineering, ASCE, 1999; 125 (1); 40-44. [8] J.W. Delleur J.C. Dooge K.W. Gent Influence of slope and roughness on the overfall J Hydraulic Eng, ASCE 82 4 1956 1038-30 1038-35 Delleur JW, Dooge JC, Gent KW, Influence of slope and roughness on the overfall, Journal of Hydraulic Engineering, ASCE, 1956; 82(4); 1038-30-1038-35. [9] M.V. Anderson Non-uniform flow in front of a free overfall Acta Polytech Scand 42 1967 1 24 Anderson MV, Non-uniform flow in front of a free overfall, Acta Polytech. Scand., 1967; 42; 1-24. [10] N. Rajaratnam D. Muralidhar S. Beltaos Roughness effects on rectangular free overfall J Hydraulic Eng, ASCE 102 1976 599 614 Rajaratnam N, Muralidhar D, Beltaos S, Roughness effects on rectangular free overfall, Journal of Hydraulic Engineering, ASCE,1976; 102;599-614. [11] W.H. Hager Hydraulics of plane free overfall J Hydraulic Eng, ASCE 109 12 1983 1683 1697 Hager WH, Hydraulics of plane free overfall, Journal of Hydraulic Engineering, ASCE, 1983; 109(12); 1683-1697. [12] V. Ferro Flow measurement with rectangular free overfall J Irrigat Drainage Eng, ASCE 118 6 1992 956 964 Ferro V, Flow measurement with rectangular free overfall, Journal of Irrigation and Drainage Engineering, ASCE, 1992; 118(6); 956-964. [13] A.C. Davis B.G.S. Ellett R.P. Jacob Flow measurement in sloping channels with rectangular free overfall J Hydraulic Eng, ASCE 124 7 1998 760 764 Davis AC, Ellett BGS, Jacob RP, Flow measurement in sloping channels with rectangular free overfal, Journal of Hydraulic Engineering, ASCE,1998; 124(7);760-764. [14] Z. Ahmad Quasi-theoretical end-depth-discharge relationship for rectangular channels J Irrigat Drainage Eng, ASCE 129 2 2013 138 141 Ahmad Z, Quasi-theoretical end-depth-discharge relationship for rectangular channels, Journal of Irrigation and Drainage Engineering, ASCE, 2013; 129(2); 138-141. null [16] M.K. Beirami S.V. Nabavi M.R. Chamani Free overfall in channels with different cross sections and sub-critical flow Iran J Sci Technol Trans B Eng 30 B1 2006 97 105 Beirami MK, Nabavis SV, Chamani MR, Free overfall in channels with different cross sections and sub-critical flow, Iranian Journal of Science & Technology, Transaction B, Engineering, 2006; 30(B1); 97-105. [17] Y. Guo L. Zhang Y. Shen J. Zhang Modeling study of free overfall in a rectangular channel with strip roughness J Hydraulic Eng, ASCE 134 5 2008 664 667 Guo Y, Zhang L, Shen Y, Zhang J, modeling study of free overfall in a rectangular channel with strip roughness, Journal of Hydraulic Engineering, ASCE, 2008; 134(5); 664-667. [18] S. Tigrek C.E. Firat A.M. Ger Use of brink depth in discharge measurement J Irrigat Drainage Eng, ASCE 134 1 2008 89 95 Tigrek S, Firat CE, Ger AM, Use of brink depth in discharge measurement, Journal of Irrigation and Drainage Engineering ASCE, 2008; 134(1); 89-95. [19] A.R. Vatankhah Power-law free overfall in subcritical flow regime Ain Shams Eng J Elsevier 6 2 2015 399 402 Vatankhah AR, Power-law free overfall in subcritical flow regime, Ain Shams Engineering Journal, Elsevier, 2015; 6 (2); 399–402. [20] E. Abrari M. Ergil M.K. Beirami Flow measurement using free overfall in generalized trapezoidal channels based on one velocity point Flow Measur Instrum, Elsevier 69 2019 101615 [[20]] Abrari E, Ergil M, Beirami MK, Flow measurement using free overfall in generalized trapezoidal channels based on one velocity point, Flow Measurement and Instrumentation, Elsevier,2019; 69;101615. [21] R.J. Keller S.S. Fong Flow measurement with trapezoidal free overfall J Irrigat Drainage Eng, ASCE 115 1 1989 125 136 [[21]] Keller RJ, Fong SS, Flow measurement with trapezoidal free overfall, Journal of Irrigation and Drainage Engineering, ASCE, 1989; 115(1);125-136. [22] M Diskin The end depth at a drop in trapezoidal channel J Hydraulic Eng, ASCE 87 4 1961 11 32 Diskin M The end depth at a drop in trapezoidal channel . J Hydraulic Eng, ASCE 1961 ; 87 ( 4 ): 11 – 32. [23] R.D. Gupta M. Jamil M. Mohsin Discharge prediction in smooth trapezoidal free overfall (positive, zero and negative slopes J Irrigat Drainage Eng, ASCE 119 2 1993 215 224 [[23]] Gupta RD, Jamil M, Mohsin M, Discharge prediction in smooth trapezoidal free overfall (positive, zero and negative slopes, Journal of Irrigation and Drainage Engineering, ASCE, 1993; 119(2);215-224. [24] R.H. Irzooki S. Hassan Characteristics of flow over the free overfall of triangular channel MATEC Web Conf 162 2018 03006 [[24]] Irzooki RH, Hassan S, Characteristics of flow over the free overfall of triangular channel, MATEC Web of Conferences, 2017; 162; 03006. [25] V.T. Chow Open channel hydraulics 1959 McGraw Hill Publishing Company, Inc. New York [[25]] Chow VT, Open channel hydraulics. McGraw Hill Publishing Company, Inc. New York, 1959. null [27] N. Rajaratnam D. Muralidhar End depth for exponential channels J Irrigat Drainage Eng, ASCE 90 1964 17 36 [[27]] Rajaratnam N, Muralidhar D, End depth for exponential channels, Journal of Irrigation and Drainage Engineering, ASCE, 1964; 90; 17-36. [28] K.H.M. Ali A. Sykes Free-vortex theory applied to free overfall J Hydraulic Div, ASCE 98 5 1972 973 979 [[28]] Ali KHM, Sykes A, Free-vortex theory applied to free overfall, Journal of Hydraulic Division, ASCE, 1972; 98(5); 973–979. [29] S. Murty Bhallamudi End depth in trapezoidal and exponential channels J Hydraul Res 32 2 1994 219 232 [[29]] Murty Bhallamudi S, End depth in trapezoidal and exponential channels, Journal of Hydraulic Research, 1994; 32 (2); 219–232. [30] Z. Ahmad Free overfall as measuring device in triangular channels, conference of Hydraulics Water Resour Ocean Eng 2002 115 119 [[30]] Ahmed Z, Free overfall as measuring device in triangular channels, conference of Hydraulics, Water Resources and Ocean Engineering, 2002;115-119.