The observability problem in water systems consists in determining whether the available set of measurements provides sufficient information for the computation of the full system state (this latter operation is called state estimation): given a set of network measurements including some flow, head, consumption and/or resistance values, is it possible to derive all the other hydraulic unknowns of the network? This question is crucial especially for water systems, where the pipe resistances and the consumptions at the nodes are often roughly estimated. One may thus want to use all available measurements for calibrating or estimating these parameters. The aim of this contribution is to determine which variables are structurally observable from the available measurements in a systematic way. This is achieved using a graph-theoretic approach. We split the variables into three classes: the redundant variables, the variables which can be estimated without redundancy (they will be called calculable) and finally the unobservable variables. This provides some insight in where to add new measurements for improving the observability of the system. This classification is also used to formulate a well conditioned least square problem and to compute the values of redundant and calculable variables. We then show how to use optimization techniques for solving this least square problem, with a special emphasis put on the choice of the weighting coefficients, depending on what kind of result is expected (calibration, leak detection, …). Finally, we present results obtained for calibration and leak detection on a real life network, and we give an idea of how to extend these results obtained in the static case to the case when the dynamical behaviour of the system is taken into account (measurements being available at every time).