Braess's paradox and power-law nonlinearities in networks

Bruce Calvert; Grant Keady

doi:10.1017/s0334270000007256

Braess's paradox and power-law nonlinearities in networks

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000007256 ◽

1993 ◽

Vol 35 (1) ◽

pp. 1-22 ◽

Cited By ~ 27

Author(s):

Bruce Calvert ◽

Grant Keady

Keyword(s):

Water Supply ◽

Potential Function ◽

Power Law ◽

Equilibrium Flow ◽

Pipe Network ◽

Pipe Networks ◽

Braess’S Paradox ◽

Supply Pipe ◽

The Difference ◽

Increasing Function

AbstractWe study flows in physical networks with a potential function defined over the nodes and a flow defined over the arcs. The networks have the further property that the flow on an arc a is a given increasing function of the difference in potential between its initial and terminal node. An example is the equilibrium flow in water-supply pipe networks where the potential is the head and the Hazen-Williams rule gives the flow as a numerical factor ka times the head difference to a power s > 0 (and s ≅ 0.54). In the pipe-network problem with Hazen-Williams nonlinearities, having the same s > 0 on each arc, given the consumptions and supplies, the power usage is a decreasing function of the conductivity factors ka. There is also a converse to this. Approximately stated, it is: if every relationship between flow and head difference is not a power law, with the same s on each arc, given at least 6 pipes, one can arrange (lengths of) them so that Braess's paradox occurs, i.e. one can increase the conductivity of an individual pipe yet require more power to maintain the same consumptions.

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Analysis of Causes for Pipe Explosion of Urban Water Supply Pipe Network

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.864-867.2039 ◽

2013 ◽

Vol 864-867 ◽

pp. 2039-2042

Author(s):

Gao Jie Hang ◽

Lei Zhang ◽

He Zhang

Keyword(s):

Human Factors ◽

Water Supply ◽

Urban Water ◽

Urban Water Supply ◽

Pipe Network ◽

Pipe Networks ◽

Natural Factors ◽

Supply Pipe

There is a great many reasons for pipe explosion of urban water supply pipe networks. Three major aspects of water supply pipe explosion causes were analyzed comprehensively in this paper: natural factors, pipeline factors and human factors, to raise awareness about the causes of pipe explosion.

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Development of the Urban Water Balance Model by Linking Water Distribution and Sewer Networks

Korean Society of Hazard Mitigation ◽

10.9798/kosham.2020.20.6.369 ◽

2020 ◽

Vol 20 (6) ◽

pp. 369-377

Author(s):

Gunhui Chung ◽

Won Soo Ohk

Keyword(s):

Water Supply ◽

Water Distribution ◽

Low Impact Development ◽

Distribution Networks ◽

Water Circulation ◽

Urban Water ◽

Pipe Network ◽

Sewage Pipe ◽

Pipe Networks ◽

Supply Pipe

Due to urban overcrowding, the population density of residential areas and water use per unit are increasing. Therefore, it is necessary to study the flow of water supplied to cities and to improve the healthy circulation of urban water. This study used Modelica, a non-causal analytical program. Using Open Modelica, the researchers constructed a model linking water distribution and sewerage, as the basis of a balanced urban water model. Using the programmer's toolkit provided by EPA-NET and EPA-SWMM, which are commonly used to simulate the existing water supply and sewage pipe networks, Open Modelica-based water distribution networks and sewage pipe networks can be connected and simulated based on the customer block. A model was built so that 90% of the hourly water consumption supplied to the water supply pipe network can be automatically introduced into the sewage pipe network. If a matching table is constructed to connect the nodes of the water supply pipe network and the sewer pipe network, the nodes will reflect in the graphical user interface (GUI) developed in Open Modelica. It was developed to enable modification of links, pumps, tanks, and valves. The 48-hour water supply was simulated using the developed model, and it was confirmed that water supply and sewage networks were successfully connected. In the future, we plan to develop a more expanded and realistic urban water circulation model by considering additional urban water circulation factors, such as sewage treatment, water reuse, rainwater use, storm runoff, and low-impact development facilities. Through this study, it was confirmed that Modelica can simulate changes in the system over time. Since it is a formula-based non-causal simulation language, it is possible to establish and reuse relationships between blocks through block-by-block development of urban water circulation elements. It is expected to contribute to the visualization and concretization of future urban water circulation models.

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