Water Resources Management

, Volume 22, Issue 12, pp 1881–1898 | Cite as

Transfer Function Formulation of Saint-Venant’s Equations for Modeling Drainage Channel Flow: An Experimental Evaluation

  • P. SreejaEmail author
  • Kapil Gupta


Space constraints in developed urban cities necessitate utilizing existing capacity of the drainage system for actively controlling and optimizing the flow during a flood event. This is mainly achieved by the use of non-structural control measures (in the form of suitable controllers and control strategies) for controlling existing structures such as gates in the drainage system. However, the timely opening and closing of gates is fully governed by the rapid feedback and real time control of these structures. Hence, for an extreme rainfall event and flooding, it is necessary to rapidly model the peak flow and time to peak in the drainage system, the results of which can be used for the timely operation of the control structures. Owing to the fact that the conventional modeling methods are quite time consuming and cumbersome, a simplified approach based on transfer function formulation of Saint-Venant’s equations have been proposed in this study. The simplified approach has been validated with the help of carefully planned laboratory experiments in which a test setup consisting of a model drainage channel with upstream and downstream gates have been developed. This laboratory model was used to simulate different flow conditions by the appropriate opening and closing of upstream and downstream gates. It was noted that the results obtained using the simplified approach matches well with the experimentally observed trends. This demonstrates the robustness of the new simplified approach for modeling flow conditions in drainage system.


Drainage Gate Laboratory experiment Transfer function 


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  1. Adams BJ, Papa F (2000) Urban stormwater management planning with analytical probabilistic models. Wiley, New YorkGoogle Scholar
  2. Arnold V (1978) Ordinary differential equations. MIT Press, Cambridge, MAGoogle Scholar
  3. Cembrano G, Quevedo J, Salamero M, Puig V, Figueras J, Marti J (2004) Optimal control of urban drainage systems—a case study. Control Eng Pract 12:1–9CrossRefGoogle Scholar
  4. Chaudhry MH (1993) Open channel flow. Prentice Hall, Eaglewood Cliffs, NJGoogle Scholar
  5. Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw Hill International Edition, New YorkGoogle Scholar
  6. Clemmens AJ, Wahlin BT (2004) Simple optimal downstream feedback controllers: ASCE test case results. J Irrig Drain Eng ASCE 130(1):35–46CrossRefGoogle Scholar
  7. Cluckie ID, Lane A, Yuan J (1999) Modelling large urban drainage systems in real time. Water Sci Technol 39(4):21–28CrossRefGoogle Scholar
  8. Corriga G, Fanni A, Sanna S, Usai G (1982) A constant–volume control method for open channel networks. Int J Model Simul 2:108–112Google Scholar
  9. Corriga G, Sanna S, Usai G (1983) Sub-optimal constant–volume control for open channel networks. Appl Math Model 7:262–267CrossRefGoogle Scholar
  10. Corriga G, Salembeni D, Sanna S, Usai G (1988) A control method for speeding up response of hydroelectric stations power canals. Appl Math Model 12:627–633CrossRefGoogle Scholar
  11. Delis AI, Skeels CP, Ryrie SC (2000) Implicit high resolution methods for modelling dimensional open channel flow. J Hydraul Res 36(5):301–308Google Scholar
  12. Ermolin YA (1992) Study of open channel dynamics as controlled process. J Hydraul Eng ASCE 118(1):59–71CrossRefGoogle Scholar
  13. Garcia-Navarro P, Alcrudo F, Priestley A (1994) An implicit method for water flow modeling in channels and pipes. J Hydraul Res 32(5):721–742CrossRefGoogle Scholar
  14. Gupta K, Sreeja P (2004) Urban flood management by non-structural measures. Workshop on Flood and Drought Management, CBIP, New Delhi, 16–17 September, FM 160-FM170Google Scholar
  15. Henderson FM (1966) Open channel flow. Macmillan, New YorkGoogle Scholar
  16. Joshi MC (2005) Ordinary differential equations: modern perspective. Narosa Publishing House, New DelhiGoogle Scholar
  17. Katopodes ND (1984) A dissipative galerkin scheme for open channel flow. J Hydraul Eng ASCE, 36(3):450–466CrossRefGoogle Scholar
  18. Levin O (1969) Optimal control of a storage reservoir during a flood season. Automatica 5:27–34CrossRefGoogle Scholar
  19. Litrico X, Fromion V (2004) Frequency modeling of open channel flow. J Hydraul Eng ASCE 130(8):806–815CrossRefGoogle Scholar
  20. Litrico X, Fromion V, Baume JP, Arranja C, Rijo M (2005) Experimental validation of a methodology to control irrigation canals based on Saint-Venant equations. Control Eng Pract 13(11):1425–1437CrossRefGoogle Scholar
  21. Liu F, Feyen J, Berlamont J (1995) Downstream control of multi reach canal systems. J Irrig Drain ASCE 121(2):179–190CrossRefGoogle Scholar
  22. Manual-P-ems (1998) Programmable electromagnetic liquid velocity meter. Delft Hydraulics, NetherlandsGoogle Scholar
  23. Norreys R, Cluckie I (1997) A novel approach to real time modeling of large urban drainage systems. Water Sci Technol 36(8–9):19–24CrossRefGoogle Scholar
  24. Noto L, Tucciarelli T (2001) DORA algorithm for network flow models with improved stability and convergence properties. J Hydraul Eng ASCE 127(5):380–391CrossRefGoogle Scholar
  25. Salas JD (1993) Analysis and modeling of hydrologic time series. Mcgraw-Hill Book Company, New YorkGoogle Scholar
  26. Schuurmans J, Bosgra O, Brouwer R (1995) Open channel flow model approximation for controller design. Appl Math Model 19:525–530CrossRefGoogle Scholar
  27. Schuurmans J, Clemmens AJ, Dijkstra S, Hof A, Brouwer R (1999) Modeling of irrigation drainage canals for controller design. J Irrig Drain Eng ASCE 125(6):338–344CrossRefGoogle Scholar
  28. Sreeja P, Gupta K (2002) Real time control strategy for urban drainage management in India. Proceedings of International Conference on Water and Wastewater: Perspectives of Developing Countries, WAPDEC, New Delhi, India, 11–13 December, pp 351–358Google Scholar
  29. Sreeja P, Gupta K (2005) Dynamic modeling of urban drainage systems for controller design. Proceedings of 5th International R&D Conference on Developments and Management of Water and Energy Resources, CBIP, February 15–18, Bangalore, India, I 87–I 96Google Scholar
  30. Sreeja P, Gupta K (2006) Modeling of detention tank-gate system using frequency and time domain approach. Journal of Indian Society for Hydraulics 12(1):110–120Google Scholar
  31. Sreeja P, Gupta K (2007) An alternate approach for transient flow modeling in urban drainage systems. Water Resour Manag 21:1225–1244CrossRefGoogle Scholar
  32. Sreeja P, Gupta K, Mark O (2005) Dynamic modeling of detention tanks for flood control in urban drainage systems in developing countries. Proceedings of 10th International Conference on Urban Drainage, Copenhagen/Denmark, August, 21–26Google Scholar
  33. UFM-Manual (2004) Ultrasonic Flow Meter, KROHNE -ALTOSONIC UFM 610P Portable systemGoogle Scholar
  34. WM-Manual (1998) Wave monitor manual. Churchill Control, UKGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology BombayMumbaiIndia

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