My sincerest compliments go to Quark for the extensive and hard work he has put into this subject and which represents so much positive input to the learning and background of all Forum members. I am only disappointed in by the lack of “Stars” next to his name which would indicate the gratitude of the many readers who obviously will profit from this work.
The fluid flow pioneering work done by such people as Prandtl, Reynolds, Froude, Darcy, Weisbach, Colebrook, et al has been of continuing interest to me as well as perhaps to many others. Allow me to share some interesting information from the information I’ve gathered through the years:
I have never succeeded in obtaining or reading Colebrook’s famous 1937 or 1939 papers on his findings and I wonder if anyone has a copy they can share. I have always been under the impression that he and White developed their findings based on the original data from Nikuradse. I stand corrected if they actually derived the equation from theoretical relationships – as Quark mentions. In any event, the whole subject of fluid flow and its description by the friction factor and related equations is a fascinating one that has always intrigued me. I have developed a better and deeper understanding of the science – as well as an appreciation of the findings – by carefully reading and researching the history of how it all came about.
My favorite expert historian on the subject is Prof. Glenn O. Brown of Oklahoma State University. His writings on the subject are extensive and extremely interesting in their historical content and findings. For a few of his insights go to:
And read his interesting papers (in either English or Portuguese) and also download and read his fascinating Adobe paper on the History of the Darcy-Weisbach Equation. Pay special attention to the part on how Colebrook and White’s findings found their way into Hunter Rouse’s (What a name!) expert hands and what he did with the information. Contrary to popular belief, it was Rouse, not Lewis Moody, who constructed the first graphical depiction of the friction factor. After this exciting first act, the intrigue follows. Lewis F. Moody (late of Princeton) enters the performance as a Johnny-come-lately and upstages Hunter Rouse and all his efforts. As I understand it, Hunter never spoke to Lewis again. Hunter presumably went into seclusion and fluid flow History forgot him. You’ve gotta luv it…Hollywood couldn’t do it better.
Putting the romantic history aside, the current state of affairs with the friction factor is that present-day application of extensive and critical natural gas pipelines have led to the discovery of major areas of inaccuracy in the Colebrook-White equation. If one can appreciate the history, I suspect that we all could understand why this would come about.
To quote just one of several engineering abstracts – “A continuously increasing demand for higher pipeline transport capacity combined with increased computer simulation capacity has pursued the research for a more accurate description of the pressure loss due to friction in gas pipelines – particularly sub-sea natural gas pipelines. From research work performed by various parties it is well known that the methods for calculating the friction loss as used today are inaccurate and subject to uncertainty, especially for high Reynolds number flow.”
Also, from
:
Elling Sletfjerding
1996
“ABSTRAKT
The accuracy of the Colebrook-White equation for friction factor calculations for high Reynolds number flow in gas pipelines is investigated. The friction factor is essential to the deliverability of a natural gas transmission line. Using second order analysis of the fully developed turbulent flow it is shown that the friction factor may be overestimated with as much as 15 % using the Colebrook-White equation. This is due to Reynolds number dependence of the slope of the logarithmic velocity profile in turbulent pipe flow.”
I know there are a lot of concerned and interested sharp engineers out there (like Katmar, for one) who have a professional and personal interest in following up on this subject and I would draw their attention to the above in the event it can be of any assistance. I also have labored under the dark cloud of not knowing to what degree of accuracy I can subject Colebrook-White and what is the relevancy of seeking other equations that are measured to their standard of “accuracy”.
All this fortifies what I stated originally: Quark’s contribution should be of great interest because it allows us to better understand and employ the concept of frictional losses in fluid flow. By easing the pain and the effort to attain usable frictional values, he is allowing us all to keep abreast with what we are doing in our engineering efforts and always seeking better methods to achieve better results.
Thank you, Quark. May your tribe increase.
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