In this paper, a leak detection, isolation and estimation methodology in pressurized water pipe networks is proposed. The methodology is based on computing residuals which are obtained comparing measured pressures (heads) in selected points of the network with their estimated values by means of a Linear Parameter Varying (LPV) model and zonotopes. The structure of the LPV model is obtained from the non-linear mathematical model of the network. The proposed detection method takes into account modelling uncertainty using zonotopes. The isolation and estimation task employs an algorithm based on the residual fault sensitivity analysis. Finally, a typical water pipe network is employed to validate the proposed methodology. This network is simulated using EPANET software. Parameters of LPV model and their uncertainty bounded by zonotopes are estimated from data coming from this simulator. A leak scenario allows to assess the effectiveness of the proposed approach.