Abstract
Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles' log-wake law for which the wake component is purely empirical. This research innovates Coles' wake law with another log-function, and thus combines the log- and the wake-laws into a single (complete) log-law, for which the von Kármán constant (0.39) is the only fit parameter. Specifically, the symmetrical velocity distribution about the centreline requires a symmetrical eddy viscosity model which is approximated by a quartic polynomial, leading to a complete log-law including the effects of the bottom and top walls as well as their interactions. The complete log-law is confirmed with data from both smooth and rough pipes; it also results in an accurate and explicit friction law for smooth pipe flow. Furthermore, the complete log-law is preliminarily tested with data from channels and boundary layers; the quartic eddy viscosity may be extended for ice-covered river flow in future studies.
Original language | English (US) |
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Pages (from-to) | 27-39 |
Number of pages | 13 |
Journal | Journal of Hydraulic Research |
Volume | 55 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2 2017 |
Keywords
- Eddy viscosity
- friction factor
- log-law
- pipe flow
- velocity distribution
- wall-bounded flow
ASJC Scopus subject areas
- Civil and Structural Engineering
- Water Science and Technology