Experimental analysis of pressure-discharge relationship in a private water supply tank

In Mediterranean countries, users are often equipped with private tanks, which provide a temporary water storage capacity, able to compensate service interruptions due to either scarcity or irregularity of water supply. In the presence of private water storages, water supply is no longer linked to users’ consumption and network-operating conditions can be off-design, therefore specific models have to be introduced in simulation models of water distribution networks. Here, a new mathematical model is proposed that is able to reproduce tank’s emptying/filling cycles. Specifically, by means of experimental analysis, a hyperbolic tangent law was tested to reproduce the filling process of private tanks. The flow rate is calculated by means of the classical Torricelli law, where the float valve emitter coefficient and the valve area are calculated using a function that take into account for the water level within the private tank. The comparison obtained through the mathematical model and those observed with experiments confirmed the ability of the model to predict the flow rate balance within private tanks. The results show that the model is suitable for any length of float valve branch. The mathematic system can be easily used in a transient model to correctly estimate the supplied demand.