Keywords: water distribution networks, uncertainty, informational entropy, design optimisation, hydraulic reliability, fire-fighting, pressure-dependent modelling, energy dissipation.

There is a considerable amount of uncertainty associated with the design and operation of water distribution systems. These include: long-term projections of the growth in demand; the spatial distribution of the nodal demands coupled with diurnal and seasonal consumption patterns; variations in electricity/energy tariffs; bursts and component failures; possible changes in pipe diameters and roughness with age. Following a pipe failure/removal or large localised increase in demand, flows in pipe networks are rerouted in complex ways which are generally difficult to predict prior to a full simulation of the network concerned. This can cause difficulties and further uncertainty at the design stage, because of the general inability to identify the critical elements of the network.

It would appear that the entropy-constrained approach to the design optimization of water distribution systems has the potential to generate designs which have a high degree of hydraulic predictability in the sense that, in general, the higher the entropy value, the greater the likelihood that the hydraulic properties of the design achieved will be intuitively obvious. In effect, it appears, that entropy can be used at the design stage to place the critical nodes and links at intuitively more obvious locations and, in consequence, reduce the need to explicitly consider certain critical operating conditions.

This point is illustrated in this paper using results for two networks. Using pressure-dependent modelling to simulate critical operating conditions including fire-fighting and pipe failure, the key nodes and distribution mains are identified. The determination of the critical links and nodes is based on several measures including the pressure-dependent rate of flow delivery; nodal hydraulic reliability; and the deterioration in the hydraulic performance of the network. A new hydraulic performance indicator is introduced, based on the rate at which a water distribution network dissipates energy relative to the amount of water supplied. The ability to predetermine the most likely critical nodes and links of a water distribution system may find applications in certain reliability analysis and optimal design formulations [1].

Acknowledgment

The authors are grateful to the UK Engineering and Physical Sciences Research Council for its financial support for the PRAAWDS component of this research under Grant GR/NO2672. Professor Andrew Templeman's contribution to the development of PRAAWDS is gratefully acknowledged.

1

Xu, C., Goulter, I., "Reliability-based optimal design of water distribution networks", J. Water Resources Planning and Management, ASCE, 125(6), 352-362, 1999. doi:10.1061/(ASCE)0733-9496(1999)125:6(352)

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