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

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Discussion Overview

The discussion revolves around the accuracy of explicit solutions for the Colebrook equation, particularly focusing on the Goudar-Sonnad equation and its comparison with other formulations. Participants explore the implications of these equations in practical applications, including their use in Excel for calculations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in verifying the accuracy of the Goudar-Sonnad equation, noting discrepancies when compared to the Serghide equation at specific conditions.
  • Another participant questions the relationship between the Colebrook equation and the Moody diagram, suggesting that the diagram may not match the equation exactly.
  • A participant mentions that explicit forms of the Colebrook equation are generally curve fits to the original implicit forms and discusses the development of User Defined Functions (UDFs) for iterative solutions in Excel.
  • One participant claims to have resolved an issue with the Goudar-Sonnad equation by correcting a parameter, asserting that the revised equation is the most accurate among those evaluated.

Areas of Agreement / Disagreement

Participants express differing views on the accuracy of various explicit solutions for the Colebrook equation, with some asserting the superiority of the Goudar-Sonnad equation while others remain uncertain about its verification. The relationship between the Colebrook equation and the Moody diagram is also questioned, indicating a lack of consensus.

Contextual Notes

Participants reference specific conditions under which the equations are evaluated, such as Reynolds number and relative roughness, but do not resolve the accuracy of the equations discussed. There are also mentions of potential limitations in the accuracy of graphical representations like the Moody diagram.

tglester
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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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