Extended-period modeling of water pipe networks-a new approach

Abstract

The extended-period (time-varying or dynamic) equations describing incompressible flow in pipe networks can be classified mathematically as a set of first-order, non-homogenous, non-linear differential equations. Since this set of equations cannot normally be solved analytically, numerical integration or regression methods are typically used. In this paper, a new method for extended-period simulation, called the explicit integration method, is proposed for water pipe networks without demands. The method is based on the premise that a complex water pipe network can be represented by a number of simple base networks. The simple base networks are selected in such a way that their dynamic equations can be solved through explicit integration. In this paper a simple base network consisting of a fixed-head reservoir feeding a tank through a single pipeline is analyzed. It is then illustrated how a complex water pipe network can be decoupled into its constituent simple base networks and its dynamic behavior simulated using a step-wise procedure. The explicit integration method is then compared to the commonly used Euler numerical integration method. It is shown that the accuracy of the explicit integration method is considerably better than that of the Euler method for the same computational effort.