What is the most accurate explicit solution for the Colebrook equation?

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The discussion centers on updating explicit equations for the Colebrook equation, particularly the Goudar-Sonnad equation, which the author has struggled to verify for accuracy. Testing at specific parameters revealed discrepancies between Goudar's results and those from an iterative solution, suggesting the latter is more accurate. The Colebrook equation predates the Moody diagram, which serves as a graphical representation but may not match perfectly. User Defined Functions (UDFs) developed for Excel provide iterative solutions with high accuracy. The Goudar-Sonnad equation's accuracy has been confirmed with a correction to its parameters, establishing it as the most reliable explicit form evaluated.
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I authored the articles, http//www.cheresources.com/colebrook1.shtml with parts 2 and 3 in 2004. I'm requesting assistance in updating the explicit equations portions of that series. My problem is that I have been unable to verify the accuracy of the Goudar - Sonnad equation. I have attempted to enter the equations in an Excel spreadsheet but the results are not to the stated accuracy.
Specifically, I have tried to test Goudar against Serghide at the point of maximum error in Serghide, which is at Rel Roughness of 0 and Reynolds Number of 171,000. As I have entered the formulas, I get a result from Goudar of f = .0162416. An iterative solution would yield f = .0161281. Back substitution of these results into the original Colebrook equation would suggest that the iterative solution is more accurate.
I'd appreciate any comments or assistance
 
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Hi tglester, welcome to the board. How close is the Colebrook equation to the Moody diagram? I don't think they match exactly. I've always assumed the Moody diagram was the basis for the equations that are created, but I'm not sure. Do you know?

There's another reference http://www.eng-tips.com/faqs.cfm?fid=1236" that you may find interesting.
 
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Q_Goest said:
Hi tglester, welcome to the board. How close is the Colebrook equation to the Moody diagram? I don't think they match exactly. I've always assumed the Moody diagram was the basis for the equations that are created, but I'm not sure. Do you know?

There's another reference http://www.eng-tips.com/faqs.cfm?fid=1236" that you may find interesting.
The Colebrook equation came first, 1937 I believe. The Moody diagram (1944) is a graphic representation of the Colebrook equation and is as accurate as you can read it; which may be a problem depending on the accuracy you seek.
Explicit forms of Colebrook are generally "curve fits" to the original implicit forms of Colebrook. Iterative solutions to Colebrook are just that. I developed User Defined Functions (UDF's) that are iterative's which can be used in Excel spreadsheets. While the need for accuracy can be questioned, the the UDF's I developed are accurate to six significant digits.
 
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The problem with Goudar-Sonnad has been solved. I had a version of Goudar-Sonnad that gave the d parameter as: d=ln(10) x Re/5.2. I believe the source was Wikipedia which now correctly lists this as: d=ln(10) x Re/5.02. With this corrected equation, I have verified that Goudar-Sonnad is the most accurate of all the explicit forms that I have evaluated.
 

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