The operation of water distribution systems is based on reliable knowledge about the steady state of the system. This involves sensors to measure flow, facilitating a comprehensive overview of the system’s performance. Given the costs associated with sensor installation and operation, it is important to be strategic with sensor allocation. Recently developed Gaussian Processes with topological kernels can efficiently model mass and energy conservative flows and provide uncertainty bounds. Our work proposes a novel method of state estimation and a greedy search algorithm for water flow meter placement based on the uncertainty bounds provided by a Gaussian Process.