Abstract:
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.
