Water Resources Management

, Volume 32, Issue 2, pp 641–657 | Cite as

Automated Framework for Water Looped Network Equilibrium

  • Zahreddine Hafsi
  • Sami Elaoud
  • Manoranjan Mishra
  • Mohsen Akrout


In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.


Water looped network Minimum spanning tree Kirchhoff’s laws Independent loops Hardy cross Newton Raphson 



The financial support from the Centre for Science and Technology of the Non-aligned and Other Developing Countries (NAM S&T Centre) is gratefully acknowledged. Also, the authors extend their thanks to Professor E. Creaco for his valuable suggestions.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Laboratory of Applied Fluids Mechanics, Process and Environment EngineeringNational Engineering School of SfaxSfaxTunisia
  2. 2.Department of MathematicsIndian Institute of Technology RoparRupnagarIndia
  3. 3.Department of Chemical EngineeringIndian Institute of Technology RoparRupnagarIndia

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