A hydraulic model for water distribution systems incorporating both inertia and leakage

Fresh water is considered to be one of the most critical strategic and economic resources in coming decades. However, leakage often makes up a substantial fraction, frequently more than 30 %, of the water supplied. The objective of this paper is to present an improved formulation of the hydraulic network equations that incorporates both fixed and pressure dependent leakage. Particular effort has been made to assess the magnitude of the different terms in the equations, including leakage inertia and head loss. A sensitivity analysis was also conducted as part of this study. Two formulations were derived from the Navier-Stokes equations and subsequently solved: the first considers constant leakage in the water distribution network and leads to an ordinary differential equation. This equation is solved using a generalised Runge-Kutta method. In the second formulation, pressure dependant leakage is taken into account. A partial differential equation is then solved using the finite difference method.