Proposing a Discharge Coefficient Equation for Triangular Labyrinth Spillways Based on Laboratory Studies

Document Type: Research Paper


Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, Hamadan, Iran.


Labyrinth spillways are considered as suitable and economic structures because, firstly, their discharge flow rate, under low hydraulic heads, is high, and secondly, they occupy less space. The flow over these spillways is three-dimensional and is influenced by several parameters. This study endeavors to offer a new equation for the calculation of the discharge flow of triangular labyrinth spillways by using the Buckingham Theory, Genetic Algorithm, the equations offered by other researchers and non-dimensional laboratory parameters. To do so, several experiments were carried out in the hydraulic laboratory of the Department of water science at BuAli Sina University in Hamedan. These experiments were done on triangular labyrinth spillways in a straight condition in certain flumes which were 10 meters long, 0.83 meters wide, and 0.5 meters height. To verify the recommended equation, the authors used the information related to the labyrinth spillway design of Bartletts Ferry dam in the US and the equation for triangular spillways suggested by previous researcher. The results indicated that the equation recommended in this study is far more accurate than the previous one.


  1. Bilhan, O., Emiroglu, M. and Miller, C. (2016). ”Experimental Investigation of Discharge Capacity of Labyrinth Weirs with and without Nappe Breakers.” World Journal of Mechanics 6(6):207-221.
  2. Carollo F., Ferro V., and Pampalone V. (2012). ”Experimental Investigation of the Outflow Process over a Triangular Labyrinth-Weir.” J. Irrig. Drain Eng., 138(1), 73–79.
  3. Coley D. A., (1999)."An Introduction to Genetic Algorithms for Scientists and Engineers". World Scientific Publishing, Singapore.
  4. Crookston B. M. (2010). “Labyrinth weirs.” Ph.D. dissertation, Utah State Univ., Logan, UT.
  5. Copeland R. And Fletcher B. (2000). “Model study of Prado Spillway, California, hydraulic model investigation.” Report ERDC/CHL TR-00-17, U.S. Army Corps of Engineers, Research and Development Center.
  6. Erpicum S., Laugier F., Boillat J. L., Pirotton M., Reverchon B., Schleiss A. (2012)." Labyrinth and Piano Key Weirs – PKW 2011 , Proceedings of the International Conference on Labyrinth and Piano Key Weirs (PKW 2011), Liège, Belgium, 9-11 February 2011", Taylor & Francis Group, London, ISBN 978-0-415-68282-4
  7. Falvey H. T. (2003)." Hydraulic Design of Labyrinth Weirs". American Society of Civil Engineers, Reston, Virginia.
  8. Fox D. G. (1981)." Judging air quality model performance", Bull. Am. Meteorol. Soc., 62, 599-609.
  9. Ghare A.D., Mhaisalkar V.A., Porey, P.D. (2008). “An Approach to Optimal Design of Trapezoidal Labyrinth Weirs", World Applied Sciences Journal 3 (6): 934-938.
  10. Ghodsian M. (2009). “Stage-discharge relationship for a triangular labyrinth spillway.” Proc. Inst. Civ. Eng.Water Manage, 162(3), 173–178.
  11. Gupta S. and Singh V. (2013). ”"Discussion of “Experimental Studies on Flow over Labyrinth Weir” by B. V. Khode, A. R. Tembhurkar, P. D. Porey, and R. N. Ingle.",” J. Irrig. Drain Eng., 139(12), 1048–1051.
  12. Houston K. (1982). “Hydraulic model study of Ute Dam labyrinth spillway.” Report No. GR-82-7, U.S. Bureau of Reclamation, Denver, Colo.
  13. Houston, K.L., (1983). "Hydraulic model study of Hyrum Dam auxiliary labyrinth spillway." Report No. GR 82-13, U.S. Bureau of Reclamations, Denver, Colo.
  14. Khode B., Tembhurkar A., Porey P., and Ingle R. (2012). ”Experimental Studies on Flow over Labyrinth Weir.” J. Irrig. Drain Eng., 138(6), 548–552.
  15. Mayer, Paul G., (1980). "Bartletts Ferry Project Labyrinth Weir Model Studies." Project No. E-20-610, Georgia Institute of Technology, Atlanta, Georgia.
  16. Mehboudi A., Attari J., Hosseini, S.A. (2015). ” Experimental study of discharge coefficient for trapezoidal piano key weirs.” Flow Measurement and Instrumentation.,Vol. 50 , 65-72.
  17. Novak P., Guinot V., Jeffrey A., Reeve D.E. (2010). "Hydraulic Modelling - An Introduction: Principles, Methods and Applications", Spon Press, London and New York.
  18. Ramakrishnan K., Banupriya R., Rajashree R. (2014). "Determination of Coefficient of Discharge for Piano Key Weirs of Varying Geometry.", Asian Journal of Applied Sciences, 7: 499-509.
  19. Savage B. M., Crookston B. M, and Paxson G.S. (2016). "Physical and Numerical Modeling of Large Headwater Ratios for a 15° Labyrinth Spillway." ASCE Journal of Hydraulic Engineering, Vol. 142, Issue 11, 04016046.
  20. Tacail F. G., Evans B., Babb A. (1990)."Case Study of a Labyrinth Weir Spillway", Canadian Journal of Civil Engineering, 1990, 17(1): 1-7.
  21. Taylor G. (1968)." The Performance of Labyrinth Weir". PhD thesis, University of Nottingham, Nottingham, England.
  22. Tullis J. P., Amanian N. and Waldron D. (1995). “Design of labyrinth spillway". ASCE Journal of Hydraulic Engineering, 121, No. 3, 247–255.
  23. U. S. Department of the Interior. (1980). "Hydraulic Laboratory Techniques: A Guide for Applying Engineering Knowledge to Hydraulic Studies Based on 50 Years of Research and Testing Experience", Bureau of Reclamation, U. S. Government Printing Office, Denver, Colorado.