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

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In summary, tglester has authored the articles Colebrook1.shtml with parts 2 and 3 in 2004. tglester is requesting assistance in updating the explicit equations portions of that series. tglester's problem is that he has been unable to verify the accuracy of the Goudar-Sonnad equation. tglester has attempted to enter the equations in an Excel spreadsheet but the results are not to the stated accuracy. Specifically, tglester has 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 tglester has entered the formulas, he has gotten
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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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  • #3
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.
 

What is Colebrook's equation and what is its significance in fluid mechanics?

Colebrook's equation is an explicit solution used to determine the friction factor in fluid flow. It is significant because it allows for the calculation of pressure drop in pipes and channels, which is crucial in the design of many engineering systems.

Can Colebrook's equation be solved analytically or does it require numerical methods?

Colebrook's equation cannot be solved analytically, meaning there is no closed-form solution. It requires the use of numerical methods, such as iterations or root-finding algorithms, to obtain a solution.

What are the main limitations of Colebrook's equation?

The main limitations of Colebrook's equation are that it is only valid for smooth pipes with turbulent flow, and requires the use of a reference roughness value. It also does not account for the effects of changing temperature, viscosity, or compressibility.

How accurate is Colebrook's equation compared to experimental data?

Colebrook's equation has been shown to have good accuracy compared to experimental data, with an average error of less than 5% for most applications. However, it may not be as accurate for extreme flow conditions or non-circular pipes.

Are there any alternative explicit solutions to Colebrook's equation?

Yes, there are alternative explicit solutions to Colebrook's equation, such as the Swamee-Jain equation and the Haaland equation. These equations have been developed to improve upon the accuracy of Colebrook's equation for certain flow conditions.

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