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

[tglester]

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

 

[Q_Goest]

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.

 

[tglester]

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.

 

[tglester]

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.