Pressure-Discharge Law of Local Tanks Connected to a Water Distribution Network: Experimental and Mathematical Results

In many Mediterranean countries, users store water resources in private tanks, which are typically located on rooftops. These local reservoirs are generally connected directly to the water distribution network (WDN). This installation scheme causes a disconnection of the WDN from the users, and thus, the users’ water supply is no longer linked to their consumption, which changes the network operating conditions from the designed conditions. For WDNs characterized by the presence of several private tanks, specific models have to be developed to correctly simulate the operation of the WDN while accounting for reservoirs located between the hydraulic network and users. Some mathematical models that are able to reproduce the tank emptying/filling cycles have already been developed, which combine a tank continuity equation with a float valve emitter law. In the present work, a new emitter law is proposed that improves the predictability of actual models. The new formulation takes into account the variation of the emitter coefficient and of the discharge area during the phases of the filling process of private tanks. Specifically, hyperbolic tangent laws were adopted. A comparison between the proposed mathematical model and the experimental data demonstrated the ability of the new law to estimate the flow discharging into private tanks independently of the float valve branch and of the pressure in the network. The developed model can easily be implemented in hydrodynamic models to take private tanks into account.