In cities throughout the developing world, piped water is supplied only intermittently, as valves are used to direct water to different parts of a water distribution system at different times. The causes of intermittency are complex, but several consequences are clear: degradation of water quality and of distribution system components. The goal of this work is to model transient dynamics and use BFGS optimization to identify operating conditions that might mitigate certain negative effects of intermittent water supply. Specifically, we will look at valve parameters which occur as boundary conditions in a network model of transition flow through pipes. Variation of these parameters will be used to minimize the average pressure gradient in the system over the duration of a water supply cycle. Practical considerations such as delivering a specific volume of water will also be addressed.