Equivalent hydraulic resistance to simulate pipes subject to diffuse outflows

In water distribution network simulation models, pipes subject to diffuse outflow, either due to connections or to distributed demand or to leaks along their length, are generally converted into pipe elements only subject to lumped demand at their ending nodes. This approximation, which disregards the flow variation along the pipes, generates a loss of axial momentum, which is not correctly taken into account in the present generation of water distribution network models. In this paper a correction to the lumped demand approximation is provided and this equivalence is analyzed within the framework of the Global Gradient Algorithm. This is obtained through a correction of the pipe hydraulic resistance; this approach has proven to be more effective than the use of an asymmetrical lumped demand of the total distributed outflow at the pipe ending nodes. In order to assess the effect of the introduced correction, an application to a simple water distribution system is finally provided.