Article on calculation on friction factor
Article on calculation on friction factor
(OP)
On several occasions I have come across a reference to an article written by S.W. Churchill regarding calculation of friction factors. I have the complete reference here:
Churchill, S.W. Friction-factor equation spans all fluid flow regimes. Chem. Eng. (New York) 84 (24), pp. 91–92. 1977.
I have for a while now been searching for that article but with no success. Maybe someone in this forum can tell me where I can get it.
Kind regards,
Hans Henrik Larsen
Copenhagen, Denmark
Churchill, S.W. Friction-factor equation spans all fluid flow regimes. Chem. Eng. (New York) 84 (24), pp. 91–92. 1977.
I have for a while now been searching for that article but with no success. Maybe someone in this forum can tell me where I can get it.
Kind regards,
Hans Henrik Larsen
Copenhagen, Denmark





RE: Article on calculation on friction factor
RE: Article on calculation on friction factor
Matt
RE: Article on calculation on friction factor
RE: Article on calculation on friction factor
RE: Article on calculation on friction factor
If you want to read the full article then MortenA's advice is the best.
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Article on calculation on friction factor
I allready have the formulas, but my scientific background tells me to read an article before I refer to it in calculations, reports etc. in case someone starts asking questions.
To MortenA:
I have mailed to DTU asking them for a copy of the article.
RE: Article on calculation on friction factor
You will find your requested article on pages 94 and 95 of this book:
Process Piping Systems (Chemical Engineering)
Hardcover: 482 pages
Publisher: Mcgraw-Hill (Tx) (June 1980)
Language: English
ISBN-10: 0070107068
ISBN-13: 978-0070107069
RE: Article on calculation on friction factor
In 2014, I analyzed 25 such explicit approximations to determine their relative accuracy compared to CW. I am not the first person to do such an analysis, but I may be the first person to use Mathcad for it. You can find the documents here: https://www.ptcusercommunity.com/docs/DOC-5465 For readers without Mathcad Prime 3.0, the .zip file includes Adobe Acrobat .pdf files. In my research, I came across many published papers and articles, but I don't recall finding Churchill's paper. I may have it, I just don't recall seeing it.
For my data set, I used 21 relative roughness curves (typical for most of the Moody Diagrams I own) and 45 Reynolds Numbers on each curve. This generated a matrix of 945 data points for comparison with CW. I calculated the relative error (RE) compared to CW for each of the 945 data points and reported the minimum and maximum values. I also calculated the mean squared error for all 945 data points, then added them up to create a single value (SumMSE) for each equation that I used to rank them for overall accuracy.
Churchill's 1973 equation has REs ranging from -0.61% to +3.34%, while Churchill's 1977 equation has REs ranging from -0.64% to +3.10%. The SumMSEs are 6.3*10^-5 and 6.1*10^-5, respectively. These aren't bad, considering the error bars on the original data used to create CW (IIRC, it was ±5%).
However, I found 15 explicit approximations to CW that are more accurate than Churchill's two equations. At least two are as simple as Churchill 1973 and more accurate than Churchill 1977, including Jain 1976 (SumMSE = 5.4*10^-5) and Haaland 1983 (SumMSE = 3.0*10^-5). Zigrang & Sylvester #1 and #2 (both 1982) are much more accurate and still less complex than Churchill 1977 (SumMSE = 1.2*10^-5 and 1.4*10^-7, respectively. By far the most accurate and by far the most complex of the explicit approximations is Goudar & Sonnad #2 (2008), which nowhere deviates from CW by more than about 10^-10%. Seriously. The SumMSE for Goudar & Sonnad #2 is a miniscule 3.6*10^-26.
This is a very long way of saying that there are many explicit approximations to CW that are better than either of Churchill's equations.
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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
RE: Article on calculation on friction factor
RE: Article on calculation on friction factor
thank you all for you replies. I eventually got the article from Danish Technical University here in Copenhagen.
RE: Article on calculation on friction factor
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"