Much of the world's rapidly growing urban population relies upon water distribution systems to provide treated water through networks of pipes. Rather than continuously supplying water to users, many of these distribution systems operate intermittently, with parts of the network frequently losing pressure or emptying altogether. Such intermittent water supply deleteriously impacts water availability, infrastructure, and water quality for hundreds of millions of people around the world. In this work I introduce the problem of intermittent water supply through the lens of applied mathematics. I first introduce a simple descriptive mathematical model that captures some hydraulic features of intermittency not accounted for by existing water distribution system software packages. I then consider the potential uses of such a model in a variety of optimization examples motivated by real-world applications. In simple test networks, I show how to reduce pressure gradients while the network fills by changing either the inflow patterns or the elevation profile. I also show test examples of using measured data to potentially recover unknown information such as initial conditions or boundary outflows. I then use sensitivity analysis to better understand how various parameters control model output, with an eye to figuring out which parameters are worth measuring most carefully in field applications, and also which parameters may be useful in an optimization setting. I lastly demonstrate some progress in descriptively modeling a real network, both through the introduced mathematical model and through a fluid-mechanics-based method for identifying data where the model is most useful.
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