A review of non iterative friction factor correlations for the calculation of pressure drop in pipes

Abstract

Pressure drop in pipes can be calculated by using the Darcy-Weisbach formula. In order to use this formula, the Darcy friction factor should be known. The best approximation to the Darcy friction factor for turbulent flow is given by the Colebrook-White equation. This equation can only be solved by numerical root finding methods. There are several other approximate correlations to the Darcy friction factor with some relative error compared to the Colebrook-White equation. It was found that in some of these correlations, the percentage error is so small that they can be used directly in place of the Colebrook equation. In this study, a review of several friction factor correlations is performed. Relative error of these correlations is re-evaluated against the Reynolds number for a different value of relative pipe roughness. Also statistical analyses will be given for each correlation.

Keywords

• Colebrook equation, Darcy –Weisbach pressure drop formula, friction factor

References

1. Barr DIH (1981). Solutions of the Colebrook-White functions for resistance to uniform turbulent flows. Proc Inst Civil Eng 71, 529-536.
2. Brkic D (2011). An explicit approximation of the Colebrook equation for fluid flow friction factor. Petrol Sci Tech 29, 1596-1602.
3. Buzzelli D (2008). Calculating friction in one step. Mach Des, 80, 54–55.
4. Chen NH (1979). An explicit equation for friction factor in Pipe. Ind. Eng Chem Fund 18, 296-297.
5. Churchill, SW (1973). Empirical expressions for the shear stress in turbulent flow in commercial pipe. AIChE J 19, 375-376.
6. Churchill SW (1977). Friction factor equation spans all fluid-flow ranges. Chem Eng 84, 91-92.
7. Colebrook CF, White CM (1937). Experiments with fluid friction roughened pipes. Proc R Soc (A), 161.
8. Clamond D (2009). Efficient resolution of the Colebrook equation. Ind Eng Chem Res 48, 3665–3671.

9. Eck B (1973). Technische Stromungslehre. Springer, New York.
10. Fang X, Xua Y, Zhou Z (2011). New correlations of single- phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations. Nucl Eng Des 241, 897-902.
11. Genić S, Arandjelović I, Kolendić P, Jsrić M, Budimir N (2011). A review of explicit approximations of Colebrook’s equation. FME Trans 39, 67-71.
12. Ghanbari A, Farshad F, Rieke HH (2011). Newly developed friction factor correlation for pipe flow and flow assurance. J Chem Eng Mat Sci 2, 83-86.
13. Goudar CT, Sonnad JR (2008). Comparison of the iterative approximations of the Colebrook-White equation. Hydrocarb Process 87, 79-83
14. Haaland SE (1983). Simple and Explicit formulas for friction factor in turbulent pipe flow. J Fluid Eng ASME 105, 89–90.
15. Jain AK (1976). Accurate explicit equation for friction factor. J Hydraul Div Am Soc Civ Eng 102, 674–677.
16. Manadilli G (1997). Replace implicit equations with signomial functions. Chem Eng 104, 129-132.
17. Moody LF (1947). An approximate formula for pipe friction factors. Trans ASME 69, 1005-1006.
18. Papaevangelou G, Evangelides C, Tzimopoulos C (2010). A new explicit relation for friction coefficient in the Darcy-Weisbach equation. Proceedings of the Tenth Conference on Protection and Restoration of the Environment 166,1-7pp, PRE10 July 6-09 2010 Corfu, Greece.
19. Romeo E, Royo C, Monzón A (2002). Improved explicit equations for estimation of the friction factor in rough and smooth pipes. Chem Eng J 86, 369-374.
20. Round, GF (1980). An explicit approximation for the friction factor-Reynolds number relation for rough and smooth pipes. Can J Chem Eng 58, 122-123.
21. Samadianfard S (2012). Gene expression programming analysis of implicit Colebrook-White equation in turbulent flow friction factor calculation. J Petrol Sci Eng 92, 48-55.
22. Serghides TK (1984). Estimate friction factor accurately. Chem Eng 91, 63-64.
23. Shacham M (1980). An explicit equation for friction factor in pipe. Ind Eng Chem Fund 19, 228 - 229.
24. Sonnad JR, Goudar CT (2006). Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook-White equation. J Hydraul Eng 132, 863-867.
25. Swamee PK, Jain AK (1976). Explicit equation for pipe flow problems. J Hydr Div ASCE 102, 657-664.
26. Tsal RJ (1989). Altshul-Tsal friction factor equation. Heating Piping Air Conditioning 8, 30-45.
27. Winning HK, Coole T (2013). Explicit friction factor accuracy and computational efficiency for turbulent flow in pipes. Flow Turbulence Combust 90, 1-27.
28. White F (2001). Fluid Mechanics. Fourth edition. Published by McGraw-Hill, New York ISBN 0-07- 069716-7.
29. Wood DJ (1966). An explicit friction factor relationship. Civil Eng 60-61.
30. Zigrang DJ, Sylvester ND (1982). Explicit approximations to the Colebrook’s friction factor. AICHE J 28, 514-515.