Piped networks are extensively used for transporting and distributing water. As the equilibrium flow rates in these systems may not be proportional to the consumer demands, we require appropriate control systems to ensure that consumer demands are met. In water networks, the final control elements are the valves and pumps in the network. The valves may broadly be classified into two types - discrete and continuous. Discrete valves can have only two operational states, viz., fully open or fully closed. On the other hand, continuous control valves may be operated in any intermediate positions, in addition to the fully open and fully closed states. This increased flexibility of continuous control valves comes with a higher cost and operational complexity. The present work (i) quantifies the performance of networks based on the time required to transport a given quantum of water and (ii) presents analytical results for the variation in performance of a general class of networks with either type of valve.
We begin the analysis using a three-pipe network, making the problem easy to define and, at the same time, capturing certain critical elements from the behavior of a general network. Analytical results are derived for the unconstrained network optimization problem, and numerical solutions are presented for constrained (more realistic) scenarios. This is followed by the analysis of the performance of a real-world network with either type of valve. Finally, we present the analytical results for a larger class of networks that is a generalization of the results identified for the three-pipe network.
The results highlight the role of network topology in the variations in time required for transporting water. An extension of the results also throws light on the optimal and selfish operation of a network with continuous control valves.
