Optimal Control Strategy to Distribute Water Through Loop-Like Planar Networks

Abstract

In this article, loop like planar networks formed by circular cross sectioned conduits with possibly different geometric measurements are studied to supply the required amount of isothermal water within the optimal time and through the shortest path. The flow optimization procedure is controlled by time varying pressures at nodes throughout the network for given specifications about pressure value at multiple demanding and single supply nodes. The flow governing equation is solved analytically to correlate transient flow rate and pressure and then studied using analogous electrical circuit. For each possible path between source and demand node, minimum equivalent flow impedance criterion is considered to pick the optimum path. This sets a multi-objective dynamic flow optimization algorithm and the same is executed under the assumption of fully developed and laminar flow. The optimum flow impedance can further be used to measure the pumping power as the cost of flow of a particular path. The algorithm can be extended to reduce the water wastages by controlling pressures efficiently.