Stochastic Demand Generated Unsteady Flow in Water Distribution Networks

Abstract

This paper presents an attempt to analyze the complex unsteady flow behavior of water distribution networks subject to demand pulses. Relevant elementary concepts from the Poisson Rectangular Pulse model and the elastic water column unsteady flow theory, used later in the analysis, are first presented. Engaging an appliance causes a rapid flow raise and related pressure drop and that propagates with high speed (celerity) along the pipes. Similarly, disengaging an appliance causes a propagating pressure raise. Each of those propagating pressure changes is transformed when a junction node is encountered. Depending on the relation of the areas of the pipes that join at the junction, a portion of the moving pressure change enters into the upstream pipes, and the rest is reflected. On this basis, the unsteady flow behavior following opening or closing of an individual water-using appliance inside a home is discussed, concluding that it may be important in in-home piping and service lines. Arriving at the connection of the service line to the street water main, however, only a small portion of the pressure and flow changes enters the main, since its cross sectional area is normally much larger compared to that of the service line. Because of that, the operation of a single water appliance inside a home is almost imperceptible in water mains and larger distribution network pipes. The subsequent analysis of the unsteady flow in pipe networks shows that the demand pulses deform in their path from the demand point to the pipe supplying the entire network, or the corresponding part of it. This way the commonly used approach to obtain the flow in pipes supplying a group of water users as a simple sum of the downstream demand pulses, is not always justified. The actual effect of the unsteady flow on a particular network depends on the length of the network pipes, the distance from the supplying pipe, the wave celerity and the number of branching points in the path. Since water users are located in different points throughout the network, the travel time and the network topology need to be considered too, as well as the effect of simultaneous demand pulses.