A linear programming technique is proposed to balance the flows in a network, matching flow measurements where available. Where necessary, a "leak-out" flow is invoked on a pipe section in order to achieve the balance. Usually, multiple solutions are possible, and these are sounded out by progressively increasing an integrity weight for each pipe section. A feature of the method is that it overlays "snapshots" of the network at a series of points in time, in order to progressively narrow down the part of the network which can commonly account for all observations. (c) 2013 Elsevier Ltd. All rights reserved.