Nowadays, the operation of drinking water supply networks are generally assessed using hydraulic computer models. However, for such a model consumption is an input and has to be estimated without considering the available pressure. Thus, demand is often overestimated at the times of network failure, such as pipe breaks, pump failures and failing water resources. For the last ten years, authors have proposed numerous demand models that take an assumed pressure-leakage relationship into account. Such models are known as a "Pressure Driven Models" (PDM). In PDM, consumption at network nodes are typically calculated using an orifice formulation such as the emitter function in Epanet. However, theoretical problems occur when several subscribers are aggregated in a single node or simply because the leak area is itself pressure-dependent. In addition, some numerical problems and inadequate results have recently been reported. In a previous paper (Piller and Van Zyl 2007) the authors have introduced a unified optimization framework that considers implicitly integrity non-negative constraints for pressure. In particular, mass equality constraints are released to non-negative mass inequality constraints and it has been shown than consumption at nodes is automatically reduced if the pressure becomes zero. As a result there is no need to introduce a PDM relationship between pressure and consumption. Nevertheless, the author's contribution was only theoretical. In this paper, it is proposed to analyse the applicability of the above method. Two novel solution methods are tested. The first one is a projection method on the non-negative mass inequality constraints. The global convergence is assured but can be low because of the nature of the method. The second method overcomes this point and come down to regularize the Heaviside step function and solve the co-content model by a primal-dual method. Numerical results on three previously published pipe networks are discussed and the efficiency of this method is illustrated by solving former problematic cases.