Error Analysis of Non-Iterative Friction Factor Formulas Relative to Colebrook-White Equation for The Calculation of Pressure Drop in Pipes

Abstract

Pressure drop in pipes can be calculated by using Darcy-Weisbach formula. In order to use this formula, Darcy friction factor should be known. The best approximation to Darcy friction factor for turbulent flow is given by Colebrook-White equation. This equation can only be solved by numerical root finding methods. There are several other approximate equations to Darcy friction factor with some relative error compared to Colebrook-White equation. In some of these equations the percentage error is so small that they can be used directly in place of Colebrook equation. In this study relative error of several equations are re-evaluated. katsayısının hesaplanması gereklidir. Türbülanslı akışlarda Darcy sürtünme katsayısının hesaplanmasında en geçerli yöntem Colebrook-White denklemidir, ancak bu denklem sayısal kök bulma yöntemleri kullanılarak çözülebilen bir denklemdir. Colebrook-White denklemine yaklaşım yapan ve direk olarak çözülebilen çeşitli denklemler mevcuttur. Bu denklemlerin bazılarının Colebrook-White denklemiyle kıyaslandığında hata yüzdeleri çok küçük olduğundan, direk olarak bu denklemin yerine kulanılmaları mümkündür. Yazımızda çeşitli Darcy sürtünme faktörü denklemlerinin Colebrook – White denklemine gore göreceli hatası irdelenmiştir

Keywords

• -

Error Analysis of Non-Iterative Friction Factor Formulas Relative to Colebrook-White Equation for The Calculation of Pressure Drop in Pipes

Abstract

Keywords

• Darcy-Weichbach basınç düşümü, Boru içi basınç düşümü, Colebrook denklemi

References

1. Barr, D.I.H., “Solutions of the Colebrook-White functions for resistance to uniform turbulent flows.”, Proc. Inst. Civil. Engrs. Part 2. 71,1981.
2. Chen, N.H., “An Explicit Equation for Friction factor in Pipe”, Ind. Eng. Chem. Fundam., Vol. 18, No. 3, 296-297, 1979.
3. Churchill, S.W., “Friction factor equations spans all fluid-flow ranges.”, Chem. Eng., 91,1977.
4. Colebrook, C.F. and White, C.M., “Experiments with Fluid friction roughened pipes.”,Proc. R.Soc.(A), 161,1937.
5. Haaland, S.E., “Simple and Explicit formulas for friction factor in turbulent pipe flow.”, Trans. ASME, JFE, 105, 1983.
6. Liou, C.P., “Limiations and proper use of the Hazen-Williams equations.”, J. Hydr., Eng., 124(9), 951-954, 1998.
7. Manadilli, G., “Replace implicit equations with sigmoidal functions.”, Chem.Eng. Journal, 104(8), 1997.
8. McKeon, B.J., Swanson, C.J., Zagarola, M.V., Donnelly, R.J. and Smits, A.J.,“Friction factors for smooth pipe flow.”, J.Fluid Mechanics, Vol.541, 41-44, 2004.

9. Moody, L.F., “Friction factors for pipe flows.”, Trans. ASME, 66,641,1944.
10. Nikuradse, J. “Stroemungsgesetze in rauhen Rohren.” Ver. Dtsch. Ing. Forsch., 361, 1933.
11. Romeo, E., Royo, C., and Monzon, A., ‘‘Improved explicit equations for estimation of the friction factor in rough and smooth pipes.’’ Chem. Eng. J., 86, 369–374, 2002.
12. Round, G.F., “An explicit approximation for the friction factor-Reynolds number relation for rough and smooth pipes.”, Can. J. Chem. Eng., 58,122-123,1980.
13. Schlichting, H., “Boundary-Layer Theory” ,McGraw–Hill, New York, 1979.
14. Swamee, P.K. and Jain, A.K., “Explicit equation for pipe flow problems.”, J.Hydr. Div., ASCE, 102(5), 657-664, 1976.
15. U.S. Bureau of Reclamation., “Friction factors for large conduit flowing full.” Engineering Monograph, No. 7, U.S. Dept. of Interior, Washington, D.C, 1965.
16. Von Bernuth, R. D., and Wilson, T., “Friction factors for small diameter plastic pipes.” J. Hydraul. Eng., 115(2), 183–192, 1989.
17. Wesseling, J., and Homma, F., “Hydraulic resistance of drain pipes.” Neth. J. Agric. Sci., 15, 183–197, 1967.
18. Wood, D.J., “An Explicit friction factor relationship.”, Civil Eng., 60-61,1966.
19. Zagarola, M. V., ‘‘Mean-flow Scaling of Turbulent Pipe Flow,’’ Ph.D.thesis, Princeton University, USA, 1996.
20. Zigrang, D.J. and Sylvester, N.D., “Explicit approximations to the Colebrook’s friction factor.”, AICHE J. 28, 3, 514, 1982.
21. Goudar, C.T. and Sonnad, J.R. , “Comparison of the iterative approximations of the Colebrook- White equation”, Hydrocarbon Processing, August 2008, pp 79-83
22. Serghides, T.K., “Estimate friction factor accurately”, Chem. Eng. 91, 1984, pp. 63-64
23. White, Frank M., “Fluid Mechanics”, Fourth Edition, McGrawHill, 1998, ISBN 0-07-069716-7