Pipes
Pipes are used in a wide range of engineering applications, from delivering water to homes to transporting chemicals for industry. The fundamental description of mixing within pipes was provided by Sir Geoffrey Taylor in the 1950s.
Taylor (1953) provided an integration of the laminar velocity profile in pipes to derive the spreading of matter as a result of differential advection. Taylor (1954) described the process of dispersion in highly turbulent flow in a simple uniform pipe using a similar integration of a turbulent velocity profile.
Both studies resulted in relationships between velocity and a diffusion coefficient, which could be used to describe the dispersion of soluble material. (Visit Wikipedia to learn more about Taylor dispersion.)
Today, Sir Taylor's basic analytical equilibrium approach remains the primary tool for modelling mixing in all 1D network models: rivers, urban drainage and water supply.
Professor Ian Guymer
The University of Sheffield
Ongoing research at the University of Sheffield focuses on expanding the advection-dispersion description of pollutant transport, for example in low turbulence transitional flows that are neither laminar nor fully turbulent (Hart et al., 2021).
Low velocity and unsteady flows are common in water supply network extremities. Water supply networks, in contrast to the dendritic nature of river and urban drainage networks, are designed with redundancy to ensure continuity of supply by incorporating loops.
Loops in pipe water supply networks can lead to pipe lengths where water experiences alternating flow directions, potentially trapping volumes in “tidal points” (WHO, 2004). The age, mixing and water quality within such volumes are unknown.
It is important to understand how mixing occurs in pipes under such complex conditions to ensure that safe drinking water quality standards are maintained.
Relevant articles
- Taylor, G. I. (1953). Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 219(1137), 186-203.
- Taylor, G. I. (1954). This dispersion of matter in turbulent flow through a pipe. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 223(1155), 446-468.
- Hart, J., Sonnenwald, F., Stovin, V., and Guymer, I. (2021). Longitudinal dispersion in unsteady pipe flows. Journal of Hydraulic Engineering.
- WHO (2004). Safe Piped Water: Managing Microbial Water Quality in Piped Distribution Systems. World Health Organisation. ISBN: 1-84339-039-6.