Article on calculation on friction factor 1

[iTools]

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

 

[MortenA]

You could go to DTU library, and find chemical engineering magazine (Mc Hill back then i would think) and get a copy? I know its kind of old school but since you live in the cOpenhagen area it should be fairly close?

 

[mbt22]

The journal still exists, and offers reprints for sale on their website www.chemengonline.com.

Matt

 

[MortenA]

yes, but not online from '84

 

[MortenA]

and he lives near a technical university with a (public) library that has every year since 1944

 

[katmar]

If you are just looking to get the formulas then have a look at the FAQs 1236 and 1237 by quark. Click on the FAQ tab at the top of this page. These equations have become part of mainstream engineering and you will find them in the newer fluid mechanics texts as well- Rennels and Hudson certainly has it.

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"

 

[iTools]

To 'katmar':

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.

 

[grandnobi]

Hans Hendrik, Chemical Engineering Magazine has published a book on piping engineering containing numerous interesting articles from the 70-ties.
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

 

[fel3]

There is an entire cottage industry producing explicit approximations to the Colebrook-White Equation (CW):

https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae

It appears to be a buyer's market.

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.


==========
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[georgeverghese]

You can also find the Churchill equation in Perry's Chem Engg Handbook -chapter on Fluid Flow

 

[iTools]

Dear all,

thank you all for you replies. I eventually got the article from Danish Technical University here in Copenhagen.

 

[katmar]

The most important reason for using Churchill's equation is the avoidance of discontinuities. See

http://www.eng-tips.com/viewthread.cfm?qid=149386.

Depending on your application, this can trump all the others.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"