Leakage represents a large part of the supplied water in Water Distribution Systems (WDS). Consequently, it is important to develop some efficient strategies to manage such a phenomenon. In this paper an improved formulation of the hydraulic network equations that incorporate pressure-dependent leakage, is presented and validated. The formulation is derived from the Navier-Stokes equations and solved using an adequate splitting method. Then, this formulation is used to study a constrained optimization problem with the objective to minimize the distributed water volume reducing the leakage. The problem is described and validated for academic case studies and real networks.