Using Physical and Soft Computing Models to Evaluate Discharge Coefficient for Combined Weir–Gate Structures Under Free Flow Conditions

  • Behnam BalouchiEmail author
  • Gholamreza Rakhshandehroo
Research Paper


In this study, a single triangular sharp-crested weir and four combined structures consisting of the weir and rectangular gates with different dimensions were tested to find the effects of water head over the weir (h) and geometric parameters such as gate height (d), gate breadth (b), and the distance between top of the gate and bottom of the weir (y) on discharge coefficient (Cd) under free flow conditions. A new form was proposed for the equation used to compute Cd, which is based on a combination of triangular weir and rectangular gate equations. Experimental results showed that as dimensionless ratios of h/d, h/b, and h/y increased, the discharge coefficient and total discharge increased, too. Additionally, discharge coefficient for the combined weir–gate increased with increasing gate opening at same flow rates. It was concluded that, at low discharges, the gate and its opening are the main water head controllers, while water levels at high discharges are mainly controlled by the weir. The two utilized soft computing models (MLP and SVR) predicted Cd accurately, with R2 values (for total data) of 0.966 and 0.967, respectively. However, MLP was considered superior, due to its better statistical indices of RMSE, MAE, and R2 (0.027, 0.022, and 0.984, respectively) for validation data set compared to those of SVR (0.065, 0.042, and 0.948, respectively). Comparison of results with equations presented in the literature showed that some equations match the observed data much better than others, which are noticeably different. It was concluded that assuming the general form of a gate or a triangular weir equation for a combined weir–gate structure shall be reconsidered before its utilization in particular applications.


Discharge coefficients Free flow Combined structure Triangular weir Rectangular gate MLP SVR 

List of Symbols


Gate area


Gate width


Weir breadth


Channel width


Regularization cost parameter in SVR


Discharge coefficient


Gate height


Froude numbers


Gravity acceleration


Water head over the weir


Upstream water depth


Depth of water just downstream the gate


Kernel function in SVR


Number of data set in RMSE and MAE equation


Total combined structure discharge


Reynolds numbers


Fluid velocity


Weight of the connection between the jth neuron in a layer with the ith neuron in the previous layer of ANN


Weber numbers


Value of the ith neuron in the previous layer of ANN


Distance between top of the gate and bottom of the weir


Prediction parameter in RMSE and MAE equation (Cd in this study)


Output from the jth neuron in a given layer of ANN


Size of error insensitive zone in SVR


Top angle of the triangular weir


Surface tension


Flow density


Fluid dynamic viscosity


Kernel specific parameter in SVR



Authors would like to thank Mr. Mehdi Zinivand, Professor Mahmood Shafai-Bajestan, and Dr. Mohammad-Reza Nikoo for their invaluable help, ideas, and comments.


  1. Alhamid AA, Negm AM, Al-Brahim AM (1997) Discharge equation for proposed self-cleaning device. J King Saud Univ 9(1):13–24CrossRefGoogle Scholar
  2. Altan-Sakaraya A, Kokpinar MA (2013) Computation of discharge for simultaneous flow over weirs and below gates (H-weirs). J Flow Meas Instrum 29:32–38CrossRefGoogle Scholar
  3. Aydin I, Ger AM, Hincal O (2002) Measurement of small discharges in open channels by slit weir. J Hydraul Eng ASCE 128(2):234–237CrossRefGoogle Scholar
  4. Aydin I, Altan-Sakarya AB, Sisman C (2011) Discharge formula for rectangular sharp-crested weirs. J Flow Meas Instrum 22:144–151CrossRefGoogle Scholar
  5. Balouchi B, Nikoo MR, Adamowski J (2015) Development of expert systems for the prediction of scour depth under live-bed conditions at river confluences: application of different types of ANNs and the M5P model tree. J Appl Soft Comput Elsevier 34:51–59CrossRefGoogle Scholar
  6. Bateni SM, Borghei SM, Jeng DS (2007) Neural network and neuro-fuzzy assessments for scour depth around bridge piers. J Artif Intell Elsevier 20:401–414Google Scholar
  7. Bautista-Capetillo C, Robles O, Júnez-Ferreira H, Playán E (2014) Discharge coefficient analysis for triangular sharp-crested weirs using low-speed photographic technique. J Irrig Drain Eng 140(3):06013005CrossRefGoogle Scholar
  8. Baylar A, Hanbay D, Batan M (2009) Application of least square support vector machines in the prediction of aeration performance of plunging overfall jets from weirs. J Expert Syst Appl Elsevier 36:8368–8374CrossRefGoogle Scholar
  9. Belaud G, Cassan L, Baume J (2012) Contraction and correction coefficients for energy-momentum balance under sluice gates. In: World environmental and water resources congress 2012, pp 2116–2127.
  10. Bilhan O, Emiroglu ME, Kisi O (2011) Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels. Adv Eng Softw 42:208–214CrossRefGoogle Scholar
  11. Bos MG (1989) Discharge measurement structures, 3rd edn. International Institute for Land Reclamation and Improvement, WageningenGoogle Scholar
  12. Chanson H, Wang H (2013) Unsteady discharge calibration of a large V-notch weir. J Flow Meas Instrum 29:19–24CrossRefGoogle Scholar
  13. El-Saiad AA, Negm AM, Waheed El-Din U (1995) Simultaneous flow over weirs and below gates. Civ Eng Res Mag 17(7):62–71Google Scholar
  14. Emiroghlu ME, Bilhan O, Kisi O (2011) Neural networks for estimation of discharge capacity of triangular labyrinth side-weir located on a straight channel. Expert Syst Appl 38:867–874CrossRefGoogle Scholar
  15. French RH (1986) Open-channel hydraulics. McGraw Hill Book Company, New YorkGoogle Scholar
  16. Goyal MK, Ojha CSP (2011) Estimation of scour downstream of a ski-jump bucket using support vector and M5 model tree. Water Resour Manag 25:2177–2195CrossRefGoogle Scholar
  17. Habibzadeh A, Vatankhah A, Rajaratnam N (2011) Role of energy loss on discharge characteristics of sluice gates. J Hydraul Eng 137(9):1079–1084CrossRefGoogle Scholar
  18. Haghiabi AH, Azamathulla HM, Parsaie A (2017) Prediction of head loss on cascade weir using ANN and SVM. ISH J Hydraul Eng 23(1):102–110CrossRefGoogle Scholar
  19. Hayawi HAA, Yahia AAA, Hayawi GAA (2008) Free combined flow over a triangular weir and under rectangular gate. Damascus Univ J 24(1):9–22Google Scholar
  20. Homayoon SR, Keshavarzi A, Gazni R (2010) Application of artificial neural network, Kriging, and inverse distance weighting models for estimation of scour depth around bridge pier with bed sill. J Softw Eng Appl 3:944–964CrossRefGoogle Scholar
  21. Hong J, Goyal MK, Chiew Y, Chua LHC (2012) Predicting time-dependent pier scour depth with support vector regression. J Hydrol 468–469:241–248. CrossRefGoogle Scholar
  22. Jahangirzadeh A, Shamshirband S, Aghabozorgi S, Akib S, Basser H, Anuar NB, Kiah MLM (2014) A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier. Neurocomput J 140:172–184CrossRefGoogle Scholar
  23. Johnson MC (2000) Discharge coefficient analysis for flat-topped and sharp-crested weirs. J Irrig Sci 19(3):133–137CrossRefGoogle Scholar
  24. Juma IA, Hussein HH, Al-Sarraj MF (2014) Analysis of hydraulic characteristics for hollow semi-circular weirs using artificial neural networks. Flow Meas Instrum 38:49–53CrossRefGoogle Scholar
  25. Kecman V (2001) Learning and soft computing: support vector machines, neural networks and fuzzy logic models. MIT Press, CambridgezbMATHGoogle Scholar
  26. Keshavarzi A, Gazni R, Homayoon SR (2012) Prediction of scouring around an arch-shaped bed sill using Neuro-Fuzzy model. Appl Soft Comput 12:486–493CrossRefGoogle Scholar
  27. Khalili Shayan H, Farhoudi J (2013) Effective parameters for calculating discharge coefficient of sluice gates. Flow Meas Instrum 33:96–105CrossRefGoogle Scholar
  28. Lee TL, Jeng DS, Zhang GH, Hong JH (2007) Neural network modeling for estimation of scour depth around bridge piers. J of hydrodynamic 19(3):378–386CrossRefGoogle Scholar
  29. Lozano D, Mateos L, Merkley G, Clemmens A (2009) Field calibration of submerged sluice gates in irrigation canals. J Irrig Drain Eng 135(6):763–772CrossRefGoogle Scholar
  30. Malekmohamadi I, Bazargan-Lari MR, Kerachian R, Nikoo MR, Fallahnia M (2011) Evaluating the efficacy of SVMs, BNs, ANNs and ANFIS in wave height prediction. J Ocean Eng 38:487–497CrossRefGoogle Scholar
  31. Martínez J, Reca J, Morillas MT, López JG (2005) Design and calibration of a compound sharp-crested weir. J Hydraul Eng 131(2):112–116CrossRefGoogle Scholar
  32. Mohammadpour R, Shaharuddin S, Chang CK, Zakaria NA, Ab Ghani A, Ngai WC (2015) Prediction of water quality index in constructed wetlands using support vector machine. Environ Sci Pollut Res 22(8):6208–6219CrossRefGoogle Scholar
  33. Munson BR, Young DF, Okiishi TH (1994) Fundamentals of fluid mechanics, 2nd edn. Wiley, New YorkzbMATHGoogle Scholar
  34. Negm AM (1995) Characteristics of combined flow over weirs and under gate with unequal contractions. In: Proceedings of 2nd international conference on hydro-science and engineering, China, vol 2(A), pp 285–292Google Scholar
  35. Negm AM (2000) Characteristics of simultaneous overflow—submerged underflow: (unequal contractions). Eng Bull 35(1):137–154Google Scholar
  36. Negm AM, El-Saiad AA, Saleh OK (1997) Characteristics of combined flow over weirs and below submerged gates. In: Proceedings of Al-Mansoura engineering 2nd international conference on (MEIC’97) Al-Mansoura, Egypt, vol 3(B), pp 259–272Google Scholar
  37. Negm AM, Albarahim AM, Alhamid AA (2002) Combined free flow over weirs and gate. J Hydraul Res 40(3):359–365CrossRefGoogle Scholar
  38. Ozkan F, Kaya T (2010) Using intelligent methods to predict air-demand ratio in venturi weirs. J Adv Eng Softw 41:1073–1079CrossRefGoogle Scholar
  39. Pal M, Singh NK, Tiwari NK (2011) Support vector regression based modeling of pier scour using field data. Eng Appl Artif Intell 24(5):911–916CrossRefGoogle Scholar
  40. Parsaie A, Haghiabi AH, Saneie M, Torabi H (2017) Predication of discharge coefficient of cylindrical weir-gate using adaptive neuro fuzzy inference systems (ANFIS). Front Struct Civ Eng 11(1):111–122CrossRefGoogle Scholar
  41. Qu J, Ramamurthy AS, Tadayon R, Chen Z (2009) Numerical simulation of sharp-crested weir flows. Can J Civ Eng 36(9):1530–1534CrossRefGoogle Scholar
  42. Rajaratnam N (1977) Free flow immediately below sluice gates. Proc J Hydraul Div ASCE 103(HY4):345–351Google Scholar
  43. Swamee PK (1988) Generalized rectangular weirs equations. Proc J Hydraul Eng ASCE 114(8):945–949CrossRefGoogle Scholar
  44. Swamee PK (1992) Sluice gate discharge equations. Proc J Irrig Drain Eng, ASCE 118(1):57–60Google Scholar
  45. Vapnik VN (1995) The nature of statistical learning theory. Springer, New YorkCrossRefGoogle Scholar
  46. Vapnik VN (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringShiraz UniversityShirazIran

Personalised recommendations