Losses from water distribution systems are reaching alarming levels in many towns and cities throughout the world. Leakage represents a large part, frequently more than 30 %, of the water supplied. One of the major factors affecting leakage is pressure in distribution systems. Consequently, it is important to model the hydraulics of water distribution systems with pressure-dependent leakage included. The objective of this paper is to present and validate an improved formulation of the hydraulic network equations that incorporates pressure-dependent leakage. Particular effort has been made to assess the magnitude of the different terms in the equations, including leakage, inertia and head loss. Moreover, a comparison with an extended period simulation model is performed to determine the impact of pressure-dependent demands. The formulation was derived from the Navier-Stokes equations. A system of partial differential equations is solved using a finite-difference method. The feasibility of this method and efficiency of the proposed algorithms are illustrated using a number of case studies.