An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator

Chung-Yueh Ho; Cheng-Ta Ho

doi:doi:10.11648/j.ajmie.20190402.11

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An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator

Chung-Yueh Ho, Cheng-Ta Ho

Published in American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 2)

Received: 18 June 2019 Accepted: 12 September 2019 Published: 26 September 2019

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Abstract

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.

Published in	American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 2)
DOI	10.11648/j.ajmie.20190402.11
Page(s)	28-34
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Darcy Equation, Colebrook Equation, Moody Chart, Friction Loss Chart

References

[1]	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.
[2]	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.
[3]	Moody, L. F.: Friction factors for pipe flow Transactions of the ASME. Vol. 66, No.8, 1944.
[4]	ASHRAE Handbook 2017, Figure 10 (p21.9) in Chapter 21.
[5]	ASHRAE Handbook 2017, Figure 4 in Chapter 22.
[6]	ASHRAE Handbook 2013, Example 7 (p21.22) in Chapter 21.
[7]	Moody, L. F.: An approximate formula for pipe friction factors, Transactions of the ASME, Vol. 69, 1947.
[8]	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.
[9]	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.
[10]	Romeo, Royo, and Monzon, “Improved explicit equations for estimation of friction factor in rough and smooth pipes” 2002.
[11]	Lester, T. “Solving for Friction Factor.” ASHRAE Journal July, 2003.
[12]	Avci and Karagoz, “A novel Explicit Equation for friction factor in smooth and rough pipes”, ASME J. Fluids Eng., 131, 2009.
[13]	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.
[14]	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.
[15]	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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APA Style

Chung-Yueh Ho, Cheng-Ta Ho. (2019). An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. American Journal of Mechanical and Industrial Engineering, 4(2), 28-34. https://doi.org/10.11648/j.ajmie.20190402.11

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ACS Style

Chung-Yueh Ho; Cheng-Ta Ho. An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. Am. J. Mech. Ind. Eng. 2019, 4(2), 28-34. doi: 10.11648/j.ajmie.20190402.11

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AMA Style

Chung-Yueh Ho, Cheng-Ta Ho. An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. Am J Mech Ind Eng. 2019;4(2):28-34. doi: 10.11648/j.ajmie.20190402.11

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@article{10.11648/j.ajmie.20190402.11,
  author = {Chung-Yueh Ho and Cheng-Ta Ho},
  title = {An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {2},
  pages = {28-34},
  doi = {10.11648/j.ajmie.20190402.11},
  url = {https://doi.org/10.11648/j.ajmie.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190402.11},
  abstract = {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.},
 year = {2019}
}

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TY - JOUR
T1 - An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator
AU - Chung-Yueh Ho
AU - Cheng-Ta Ho
Y1 - 2019/09/26
PY - 2019
N1 - https://doi.org/10.11648/j.ajmie.20190402.11
DO - 10.11648/j.ajmie.20190402.11
T2 - American Journal of Mechanical and Industrial Engineering
JF - American Journal of Mechanical and Industrial Engineering
JO - American Journal of Mechanical and Industrial Engineering
SP - 28
EP - 34
PB - Science Publishing Group
SN - 2575-6060
UR - https://doi.org/10.11648/j.ajmie.20190402.11
AB - 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.
VL - 4
IS - 2
ER -

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Author Information

Chung-Yueh Ho

Tempace HVAC&R Consultancy Firm, Taiwan
Cheng-Ta Ho

Tempace HVAC&R Consultancy Firm, Taiwan

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Plain Text BibTeX RIS

APA Style

Chung-Yueh Ho, Cheng-Ta Ho. (2019). An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. American Journal of Mechanical and Industrial Engineering, 4(2), 28-34. https://doi.org/10.11648/j.ajmie.20190402.11

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ACS Style

Chung-Yueh Ho; Cheng-Ta Ho. An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. Am. J. Mech. Ind. Eng. 2019, 4(2), 28-34. doi: 10.11648/j.ajmie.20190402.11

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AMA Style

Chung-Yueh Ho, Cheng-Ta Ho. An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator. Am J Mech Ind Eng. 2019;4(2):28-34. doi: 10.11648/j.ajmie.20190402.11

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@article{10.11648/j.ajmie.20190402.11,
  author = {Chung-Yueh Ho and Cheng-Ta Ho},
  title = {An Integrated One-step Equation for Solving Duct/Pipe Friction Loss by Hand Calculator},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {2},
  pages = {28-34},
  doi = {10.11648/j.ajmie.20190402.11},
  url = {https://doi.org/10.11648/j.ajmie.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190402.11},
  abstract = {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.},
 year = {2019}
}

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