Two Methods for the Computation of Commercial Pipe Friction Factors
Publication: Journal of Hydraulic Engineering
Volume 131, Issue 8
Abstract
Two methods are proposed for the computation of friction factors of commercial pipes. The first method applies the mean value of the zero velocity point (MZVP) to a theoretical friction factor equation, and the other directly computes the mean friction factor (MFF) by averaging the friction factor of both the smooth and rough walls while considering their relative contribution. The MFF method is preferred, because it is simple but covers all the flow characteristics of commercial pipes. Both MFF and MZVP methods consider two parts of a wall with different roughness heights: One part is rough and the other is smooth. A regression analysis was performed to determine optimum values of the roughness height and probability of encountering each part, using several sets of field data, including galvanized iron, wrought iron, cast iron, concrete, riveted steel, and concrete. The analysis showed that both the roughness height and the relative contribution of the rough part are strongly dependent on the pipe diameter. The MFF method gave an average error of less than 3%, whereas the traditional Colebrook–White equation gave an average error of more than 11% when compared with Colebrook’s data.
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Acknowledgments
The writers wish to express their thanks to Dr. A. Borthwick for reviewing a draft of the paper. The present study has been supported by Ajou University, which provided the financial support to equip the laboratory facility in 1995. Some of the data analysis has been conducted by Y.S. Wun, specifically for the field data collected by Colebrook (1938) and von Bernuth and Wilson (1989), and by M. I. Moon for the field data collected by the U.S. Bureau of Reclamation (1965). The majority of the work was conducted at Louisiana State University during the period of sabbatical leave of the first writer in 2002. The writers also express their gratitude to the anonymous reviewers for providing constructive reviews of the paper.
References
Bagarello, V., Ferro, V., Provenzano, G., and Pumo, D. (1995). “Experimental study on flow resistance law for small-diameter plastic pipes.” J. Irrig. Drain. Eng., 121(5), 313–316.
Barr, D. I. H. (1976). “Discussion on technical note 128.” Proc. Inst. Civ. Eng., Part 2, 61, 489–497.
Boussinesq, J. (1877). “Essay on the theory of flowing water.” French Acad. Sci., 23, 1–860.
Colebrook, C. F. (1938). “Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws.” J. Inst. Civ. Eng., London, 11, 133–156.
Colebrook, C. F., and White, C. M. (1937). “Experiments with fluid friction in roughened pipes.” Proc. Royal Society, Series A Math. & Phys. Sci., 161(904), 367–381.
Darcy, H. (1857). “Recherches experimentales relatives au movement de l’eaudans les tuyaux,” Paris, France.
Jain, A. K., Mohan, D. M., and Khanna, P. (1978). “Modified Hazen-Williams formula.” J. Env. Eng. Div., ASCE, 104(EE1), 137–146.
Kamand, F. Z. (1988). “Hydraulic friction factors for pipe flow.” J. Irrig. Drain. Eng., 114(2), 311–323.
Moody, L. F. (1944). “Friction factors for pipe flow.” Trans. Am. Soc. Mech. Engrs., 66, 671–684.
Nikuradse, J. (1933). “Stroemungsgesetze in rauhen Rohren.” Ver. Dtsch. Ing. Forsch., 361.
Prandtl, L. (1925). “Bericht ber Untersuchungen zur ausgebildeten Turbulenz.” Angew. Math. Mech., 5(2), 136.
Reynolds, O. (1895). “On the dynamical theory of incompressible viscous fluids and the determination of the criterion.” Philosophical Transactions, Royal Society, Series A1, 186, 123.
Singh, V. P. (1996). Kinematic wave modeling in water resources: Surface water hydrology, Wiley, New York.
Swamee, P. K., and Jain, A. K. (1976). “Explicit equations for pipe-flow problems.” J. Hydraul. Div., 102(5), 657–664.
U.S. Bureau of Reclamation. (1965). “Friction factors for large conduit flowing full.” Engineering Monograph, No. 7, U.S. Dept. of Interior, Washington, D.C.
von Bernuth, R. D., and Wilson, T. (1989). “Friction factors for small diameter plastic pipes.” J. Hydraul. Eng., 115(2), 183–192.
Weisbach, J. (1845). Lehrsbuch der Ingeniur und Maschinenmechanik (Textbook of Engineering Mechanics), Brunswick, Germany.
Wesseling, J., and Homma, F. (1967). “Hydraulic resistance of drain pipes.” Neth. J. Agric. Sci., 15, 183–197.
Williams, G. S., and Hazen, A. (1933). Hydraulic tables, Wiley, New York.
Yen, B. (2002). “Open channel flow resistance.”J. Hydraul. Eng., 128(1), 20–37.
Yoo, D. H., and Singh, V. P. (2004). “Explicit design of commercial pipes with no secondary losses.” J. Irrig. Drain. Eng., 130(5), 437–440.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 131 • Issue 8 • August 2005
Pages: 694 - 704
Copyright
© 2005 ASCE.
History
Received: Oct 29, 2002
Accepted: Dec 21, 2004
Published online: Aug 1, 2005
Published in print: Aug 2005
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