Formulas for Friction Factor in Transitional Regimes
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 9
Abstract
This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse’s experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows.
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References
Barr, D. I. H. (1977). “Discussion of ‘Accurate explicit equation for friction factor’.” J. Hydr. Div., 103(HY3), 334–337.
Bradshaw, P. (2000). “A note on ‘Critical roughness height’ and ‘Transitional roughness.’” Phys. Fluids, 12(6), 1611–1614.
Brownlie, W. R. (1981). “Reexamination of Nikuradse roughness data.” J. Hydr. Div., 107(1), 115–119.
Cheng, N. S., and Chiew, Y. M. (1998). “Modified logarithmic law for velocity distribution subjected to upward seepage.” J. Hydraul. Eng., 124(12), 1235–1241.
Colebrook, C. F. (1939). “Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws.” Proc.-Inst. Civ. Eng., 12, 393–422.
Haaland, S. E. (1983). “Simple and explicit formulas for the friction factor in turbulent pipe-flow.” J. Fluids Eng., 105(1), 89–90.
Hinze, J. O. (1975). Turbulence, McGraw-Hill, New York.
Jimenez, J. (2004). “Turbulent flows over rough walls.” Annu. Rev. Fluid Mech., 36, 173–196.
Ligrani, P. M., and Moffat, R. J. (1986). “Structure of transitionally rough and fully rough turbulent boundary-layers.” J. Fluid Mech., 162, 69–98.
Montes, S. (1998). Hydraulics of open channel flow, ASCE Press, Reston, Va.
Nikuradse, J. (1933). “Stromungsgesetze in Rauhen Rohren.” Forschung auf dem Gebiete des Ingenieurwesens, Forschungsheft 361, VDI Verlag, Berlin, Germany (in German) (English translation: Laws of flow in rough pipes, NACA TM 1292, 1950).
Schlichting, H. (1979). Boundary-layer theory, McGraw-Hill, New York.
Swamee, P. K., and Jain, A. K. (1976). “Explicit equations for pipe-flow problems.” J. Hydr. Div., 102(HY5), 657–664.
White, F. M. (1991). Viscous fluid flow, McGraw-Hill, New York.
Yalin, M. S., and Da Silva, A. M. A. F. (2001). Fluvial processes, IAHR, Delft, The Netherlands.
Yen, B. C. (2002). “Open channel flow resistance.” J. Hydraul. Eng., 128(1), 20–39.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 9 • September 2008
Pages: 1357 - 1362
Copyright
© 2008 ASCE.
History
Received: Oct 12, 2006
Accepted: Sep 25, 2007
Published online: Sep 1, 2008
Published in print: Sep 2008
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