  Addressing challenges in urban water infrastructure systems including aging
infrastructure, supply uncertainty, extreme events, and security threats,
depend highly on water distribution networks modeling emphasizing the
importance of realistic assumptions, modeling complexities, and scalable
solutions. In this study, we propose a derivative-free, linear approximation
for solving the network water flow problem (WFP). The proposed approach takes
advantage of the special form of the nonlinear head loss equations and, after
the transformation of variables and constraints, the WFP reduces to a linear
optimization problem that can be efficiently solved by modern linear solvers.
Ultimately, the proposed approach amounts to solving a series of linear
optimization problems. We demonstrate the proposed approach through several
case studies and show that the approach can model arbitrary network topologies
and various types of valves and pumps, thus providing modeling flexibility.
Under mild conditions, we show that the proposed linear approximation
converges. We provide sensitivity analysis and discuss in detail the current
limitations of our approach and suggest solutions to overcome these. All the
codes, tested networks, and results are freely available on Github for research
reproducibility.
