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The aim of this paper is to present how data collected from a water distribution network (WDN) can be used to reconstruct flow rate and flow direction all over the network to enhance knowledge and detection of unforeseen events. The methodological approach consists in modeling the WDN and all available sensor data related to the management of such a network in the form of a flow network graph G = (V, E, s, t, c), with V a set of nodes, E a set of edges whose elements are ordered pairs of distinct nodes, s a source node, t a sink node and c a capacity function on edges. Our objective is to reconstruct a real-valued function f(u,v): VxV => R on all the edges E in VxV from partial observations on a small number of nodes V = {1, ..., n}. This reconstruction method consists in a data-driven Ford-Fulkerson maximum-flow problem in a multi-source, multi-sink context using a constrained bidirectional breadth-first search based on Edmonds-Karp method. The innovative approach is its application in the context of smart cities to operate from sensor data, structural data from a geographical information system (GIS) and consumption estimates.