A Pressure Driven Model is presented for inclusion within a slow transient model (rigid water column) in water distribution networks. Special emphasis is made to consider the available pressure in calculating the resulting consumption. Nevertheless, integrity pressure constraints are also discussed and solved. Differently from conventional approaches, a formulation involving not only inertia terms for head at free level tank nodes and flow rates at links but also for head at fixed demand nodes, is proposed. With this extension, it is not possible anymore, as in a conventional demand driven analysis, to reduce the system so that it is loop-based nor even node-based. Nevertheless, the approach can be related to hybrid methods for steady states and extended period simulations. It is well known that numerical instability can appear due to initial conditions far from working mode, small diameter pipes, valve closures, pumping turn off/on, deficient water resources. This paper presents an efficient method for numerically integrating this stiff ordinary differential equation. A convenient Lyapunov function allows the reduction of time stepsize when possible.