Utilization of Smoothing Formulae for Describing Hydraulic Relationships in Water Networks

1. Introduction Operational control of any water distribution network requires that a reliable picture of the present operating state of the system is available. This state is uniquely determined by nodal pressures which, in turn, determine flows through network elements and indicate the amount of water in storage reservoirs. The state vector of pressures needs, however, to be interpreted in the context of the static information about hydraulic elements comprising the network, such as pipes, valves, pumps etc.. For some elements, such as pipes, calculation of flows from the information on pressure drop and static parameters is simple, but for some others, like pressure reducing valves, which exhibit strongly nonlinear and non-differentiable pressure-flow relationships, it is more difficult. A simple solution of measuring all flows and pressures is clearly not a practical proposition, so consequently, any advanced operational control of water distribution network needs to rely on mathematical modelling of the system. The role of the mathematical modelling will then be to relate a limited number of real measurements (and pseudomeasurements representing consumption estimates) through the pressure-flow relationships of network elements and to derive a consistent state vector. There is an important issue of deciding which are the most informative measurements, that need to be taken in the physical system. Techniques have been developed to relate the position and the accuracy of the meter to the benefit that can be derived from this measurement in the process of mathematical modelling [1]. The focus of this paper is the mathematical modelling itself. No two water networks are identical but for the purpose of network modelling one can disregard detail and focus on their essential features. The aim of water distribution networks is to transport water from one or more sources to consumers distributed over a certain area. The networks