Volume 4, Issue 2, March 2019, Page: 28-34
An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator
Chung-Yueh Ho, Tempace HVAC&R Consultancy Firm, Taiwan
Cheng-Ta Ho, Tempace HVAC&R Consultancy Firm, Taiwan
Received: Jun. 18, 2019;       Accepted: Sep. 12, 2019;       Published: Sep. 26, 2019
DOI: 10.11648/j.ajmie.20190402.11      View  482      Downloads  104
ASHRAE Handbooks are the worldwide reference books for HVAC engineers. When we tried to develop a duct software, we also followed the steps shown in 2013 ASHRAE Handbook. Accidently we found that some friction loss data of a duct design example seemed contrary to the data obtained from duct friction chart. Then we go back to adopt Darcy’s and Colebrook’s equations that have been used to solve duct/pipe friction loss for decades. However, the calculation process needs to use complicated computer program. After doing huge trial and error processes by computerized program, we obtained one integrated equation that can be used to calculate duct/pipe friction loss by hand calculator. We own an HVAC&R consultancy firm and have the opportunity to contact many real duct/pipe projects. This empirical equation has been successfully applied to dozens of actual duct and pipe design projects. For Reynolds Number (Re) is greater than 10,000 (i.e. turbulent flow), our analysis shows the friction losses obtained from this integrated equation are within ±2.0% of those obtained from Darcy’s and Colebrook’s equations. The accuracy (±2.0%) is good enough for engineers doing realistic duct/pipe designs. Hence, this one-step equation can be the handy alternative for Darcy’s and Colebrook’s equations. For the practical duct/pipe designs, engineers can calculate friction loss easily, no need to use iterative method.
Darcy Equation, Colebrook Equation, Moody Chart, Friction Loss Chart
To cite this article
Chung-Yueh Ho, Cheng-Ta Ho, An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator, American Journal of Mechanical and Industrial Engineering. Vol. 4, No. 2, 2019, pp. 28-34. doi: 10.11648/j.ajmie.20190402.11
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Brown, G. O. “The History of the Darcy-Weisbach Equation for pipe Flow Resistance” Environmental and Water Resources History. American Society of Civil Engineers. Pp. 34-43. ISBN978-0-7844-0650-2, 2003.
Colebrook, C. F.: Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws, Journal of the Institution of Civil Engineers, England, Vol. 11, No.4, 1939.
Moody, L. F.: Friction factors for pipe flow Transactions of the ASME. Vol. 66, No.8, 1944.
ASHRAE Handbook 2017, Figure 10 (p21.9) in Chapter 21.
ASHRAE Handbook 2017, Figure 4 in Chapter 22.
ASHRAE Handbook 2013, Example 7 (p21.22) in Chapter 21.
Moody, L. F.: An approximate formula for pipe friction factors, Transactions of the ASME, Vol. 69, 1947.
Zigrang, D. J. and Sylvester, N. D.: Explicit approximations to the solution of Colebrook’s friction factor equation, AIChE Journal, Vol. 28, No.3, 1982.
Haaland, S. E.: Simple and explicit formulas for the friction factor in turbulent pipe flow, Transactions of the ASME, Journal of Fluids Engineering, Vol. 105, No.1, 1983.
Romeo, Royo, and Monzon, “Improved explicit equations for estimation of friction factor in rough and smooth pipes” 2002.
Lester, T. “Solving for Friction Factor.” ASHRAE Journal July, 2003.
Avci and Karagoz, “A novel Explicit Equation for friction factor in smooth and rough pipes”, ASME J. Fluids Eng., 131, 2009.
More, A. A. “Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes”. Chemical Engineering Science. 61 (16), 2006.
Fang, X, Xua, Y. and Zhou Z., “New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations”, Nuclear Engineering and Design, Vol. 241, No. 3, 2011.
Brkic, Dejan, Review of explicit approximations to the Colebrook relation for the flow friction, Journal of Petroleum Science and Engineering, 77 (1), Elsevier, 2011.
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