Continuous and discrete operation of water distribution networks with demand nodes at dissimilar heads

Nodal demand satisfaction in potential flow networks, including water distribution networks, often requires a scheduled manipulation of edge resistances. The actuators (valves) used to implement the resistance variations can broadly be classified into (i) discrete (edge fully OPEN or fully CLOSED) and (ii) continuous (continuously vary edge resistance). Previously, we presented theoretical bounds on the ratio of time required to transport a given quantum of water with either type of actuators, assuming all demand nodes were at the same hydraulic head. Here, through numerical optimization, we extended the results to a basic class of networks with demand nodes located at different heads. Based on our results, we conjecture that the bounds on the ratio of operational times remain the same regardless of whether the demand nodes are at the same head or not.