Moody (1947)Moody, L. F. An approximate formula for pipe friction factors. Transactions ASME, v.69, p.1005-1011, 1947.
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4 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 10-2
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(2) |
Wood (1966)Wood, D. J. An explicit friction factor relationship. Civil Engineering, v.36, p.60-61, 1966.
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4 × 103 ≤ Re ≤ 5 × 107 10-5 ≤ Ɛ/D ≤ 4 × 10-2
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(3) |
Churchill (1973)Churchill, S. W. Empirical expressions for the shear stress in turbulent flow in commercial pipe. AIChE Journal, v.19, p.375-376, 1973. https://doi.org/10.1002/aic.690190228
https://doi.org/10.1002/aic.690190228...
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Not specified |
(4) |
Eck (1973)Eck, B. Technische Stromungslehre. New York: Springer, 1973. 324p.
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0 ≤ Ɛ/D ≤ 10-2
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(5) |
Jain (1976)Jain, A. K. Accurate explicit equation for friction factor. Journal of the Hydraulics Division, v.102, p.674-677, 1976.
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5 × 103 ≤ Re ≤ 107
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(6) |
Swamee & Jain (1976)Swamee, P. K.; Jain, A. K. Explicit equations for pipe flow problems. Journal of the Hydraulics Division, v.102, p.657-664, 1976.
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5 × 103 ≤ Re ≤ 108 10-6 ≤ Ɛ/D ≤ 5 × 10-2
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(7) |
Chen (1979)Chen, N. H. An explicit equation for friction factor in pipes. Industrial & Engineering Chemistry Fundamentals, v.18, p.296-297, 1979. https://doi.org/10.1021/i160071a019
https://doi.org/10.1021/i160071a019...
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4 × 103 ≤ Re ≤ 4 × 108 10-7 ≤ Ɛ/D ≤ 5 × 10-2
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(8) |
Round (1980)Round, G. F. An explicit approximation for the friction factor-Reynolds number relation for rough and smooth pipes. The Canadian Journal of Chemical Engineering, v.58, p.122-123, 1980. https://doi.org/10.1002/cjce.5450580119
https://doi.org/10.1002/cjce.5450580119...
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4 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(9) |
Shacham (1980)Shacham, M. Comment on "Explicit equation for friction factor in pipe". Industrial & Engineering Chemistry Fundamentals, v.19, p.228-229, 1980. https://doi.org/10.1021/i160074a019
https://doi.org/10.1021/i160074a019...
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4 × 103 ≤ Re ≤ 4 × 108
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(10) |
Barr (1981)Barr, D. I. H. Solutions of the Colebrook-White function for resistance to uniform turbulent flow. Proceedings of the Institution of Civil Engineers, v.71, p.529-536, 1981.
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Not specified |
(11) |
Zigrang & Sylvester (1982)Zigrang, D. J.; Sylvester, N. D. Explicit approximations to the solution of Colebrook’s friction factor equation. AIChE Journal, v.28, p.514-515, 1982. https://doi.org/10.1002/aic.690280323
https://doi.org/10.1002/aic.690280323...
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4 × 103 ≤ Re ≤ 108 4 × 10-5 ≤ Ɛ/D ≤ 5 × 10-2
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(12) |
Haaland (1983)Haaland, S. E. Simple and explicit formulas for friction factor in turbulent pipe flow. Journal of Fluids Engineering, v.105, p.89-90, 1983. https://doi.org/10.1115/1.3240948
https://doi.org/10.1115/1.3240948...
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4 × 103 ≤ Re ≤ 108 10-6 ≤ Ɛ/D ≤ 5 × 10-2
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(13) |
Tsal (1989)Tsal, R. J. Altshul-Tsal friction factor equation. Heating, Piping and Air Conditioning, v.8, p.30-45, 1989.
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If A ≥ 0.018 than f = A If A < 0.018 than f = 0.0028 + 0.85A |
4 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(14) |
Robaina (1992)Robaina, D. A. Análise de equações explícitas para o cálculo do coeficiente “f” da fórmula universal de perda de carga. Ciência Rural, v.22, p.157-159, 1992. https://doi.org/10.1590/S0103-84781992000200006
https://doi.org/10.1590/S0103-8478199200...
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4 × 103 ≤ Re ≤ 4 × 107 10-5 ≤ Ɛ/D ≤ 10-2
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(15) |
Manadilli (1997)Manadilli, G. Replace implicit equations with signomial functions. Chemical Engineering, v.104, p.129-129, 1997.
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5.235 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(16) |
Sousa et al. (1999)Sousa, J.; Cunha, M. da C.; Marques, A. S. An explicit solution of the Colebrook-White equation through simulated annealing. Water Industry Systems: Modelling and Optimization Applications, v.2, p.347-355, 1999.
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Not specified |
(17) |
Romeo et al. (2002)Romeo, E.; Royo, C.; Monzón, A. Improved explicit equation for estimation of the friction factor in rough and smooth pipes. Chemical Engineering Journal, v.86, p.369-374, 2002. https://doi.org/10.1016/S1385-8947(01)00254-6
https://doi.org/10.1016/S1385-8947(01)00...
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3 × 103 ≤ Re ≤ 1.5 × 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(18) |
Sonnad & Goudar (2006)Sonnad, J. R.; Goudar, C. T. Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook-White equation. Journal of Hydraulic Engineering, v.132, p.863-867, 2006. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(863)
https://doi.org/10.1061/(ASCE)0733-9429(...
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4 × 103 ≤ Re ≤ 108 10-6 ≤ Ɛ/D ≤ 5 × 10-2
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(19) |
Rao & Kumar (2007)Rao, A. R.; Kumar, B. Friction factor for turbulent pipe flow. Bangalore: Division of Mechanical Science, Civil Engineering Indian Institute of Science Bangalore, 2007. 16p.
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Not specified |
(20) |
Buzzelli (2008)Buzzelli, D. Calculating friction in one step. Machine Design, v.80, p.54-55, 2008.
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3 × 103 ≤ Re ≤ 1.5 × 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(21) |
Vantankhah & Kouchakzadeh (2008)Vatankhah, A. R.; Kouchakzadeh, S. Discussion of “Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook-White equation” by Jagadeesh R. Sonnad and Chetan T. Goudar. Journal Hydraulic Engineering, v.134, p.1-9, 2008. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:8(1187)
https://doi.org/10.1061/(ASCE)0733-9429(...
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4 × 103 ≤ Re ≤ 108 10-6 ≤ Ɛ/D ≤ 5 × 10-2
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(22) |
Avci & Karagoz (2009)Avci, A.; Karagoz, I. A novel explicit equation for friction factor in smooth and rough pipes. Journal of Fluids Engineering, v.131, p.1-2, 2009. https://doi.org/10.1115/1.3129132
https://doi.org/10.1115/1.3129132...
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Not specified |
(23) |
Papaevangelou et al. (2010)Papaevangelou, G.; Evangelides, C.; Tzimopoulos, C. A new explicit equation for the friction coefficient in the Darcy-Weisbach equation. In: Proceedings of the Tenth Conference on Protection and Restoration of the Environment, v.166, p.6-9, 2010.
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104 ≤ Re ≤ 107 10-5 ≤ Ɛ/D ≤ 10-3
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(24) |
Brkić (2011a)Brkić, D. New explicit correlations for turbulent flow friction factor. Nuclear Engineering and Design, v.241, p.4055-4059, 2011a. https://doi.org/10.1016/j.nucengdes.2011.07.042
https://doi.org/10.1016/j.nucengdes.2011...
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Not specified |
(25) |
Fang et al. (2011)Fang, X.; Xu, Y.; Zhou, Z. New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing singlephase friction factor correlations. Nuclear Engineering and Design, v.241, p.897-902, 2011. https://doi.org/10.1016/j.nucengdes.2010.12.019
https://doi.org/10.1016/j.nucengdes.2010...
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3 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(26) |
Ghanbari et al. (2011)Ghanbari, A.; Farshad, F.; Rieke, H. Newly developed friction factor correlation for pipe flow and flow assurance. Journal of Chemical Engineering and Materials Science, v.2, p.83-86, 2011.
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2.1 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(27) |
Shaikh et al. (2015)Shaikh, M. M.; Massan S. ur R.; Wagan, A. I. A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases. International Journal of Heat and Mass Transfer, v.88, p.538-543, 2015. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.006
https://doi.org/10.1016/j.ijheatmasstran...
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104 ≤ Re ≤ 108 10-4 ≤ Ɛ/D ≤ 5 × 10-2
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(28) |
Brkić (2016)Brkić, D. A note on explicit approximations to Colebrook’s friction factor in rough pipes under highly turbulent cases. International Journal of Heat and Mass Transfer, v.93, p.513-515, 2016. https://doi.org/10.1016/j.ijheatmasstransfer.2015.08.109
https://doi.org/10.1016/j.ijheatmasstran...
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106 < Re < 108 10-2 < Ɛ/D < 5 × 10-2
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(29) |
Offor & Alabi (2016)Offor, U. H.; Alabi, S. B. An accurate and computationally efficient friction factor model. Advances in Chemical Engineering and Science, v.6, p.237-245, 2016. https://doi.org/10.4236/aces.2016.63024
https://doi.org/10.4236/aces.2016.63024...
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4 × 103 ≤ Re ≤ 108 0 ≤ Ɛ/D ≤ 5 × 10-2
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(30) |