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- Submitted: Aug 30 2011 01:53 PM
- Last Updated: Sep 13 2011 01:07 PM
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Download New Solution for the Colebrook-White Equation 1.1
11 Votes1 / λ^{1/2} = -2 Log [ 2.51 / (Re λ^{1/2}) + (k / d_{h}) / 3.7 ] where λ is the friction coefficient
Today the Colebrook-White equation is the currently accepted world standard form of the Darcy-Weisbach equation. Since it was published in 1937 there has been no direct solution to find the value of the friction coefficient. But there have been many approximations to get special solutions to specific flow types, for
special types of pipe materials, and some types of liquid to flow at specific temperatures etc. These “special” types of approximations were made because there was no solution to the complete equation.
There are many other complete approximations like “Swamee and Jain” , and the “Serghide” approximation, etc., but none of these are solutions to the equation. With a true solution, you can solve for the friction coefficient for air, gas, or liquid. Also for different temperatures, viscosities and pressures, and for all pipe types and even rectangular ducts!
Macro Enabled MS Excel spreadsheet. MS Excel 2007 or higher is required. Two files included.
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New File added 9/13/2011:
I am submitting a new Colebrook-White solution. This workbook is not protected, I will show users how to easily compute the Darcy friction factor for many different equations. My solution is so simple anyone that knows Excel can do it. My solution is the ultimate accuracy, and I will show you how I solved the most complex equations with out having to do any math, other that squaring a number. I laughed when I found this out of the box solution. Why didn't others see this simple solution?
Will professional pipe designer be hurt because now almost any designer can beat their accuracy? I don't know, but I want general users to be able to find these solutions with simple Excel functions. My solution does not need VBA, you can do these simple and accurate methods.
Excel workbook: The Ragknot solutons for Colebrook Equations.xlsm
What's New in Version 1.1 (See full changelog)
- 9/13/2011 - Added second workbook with VBA code included.
Disclaimer: All software provided "As-Is" with no warranty, expressed or implied, available. See our Terms of Use for more information.
Here is another equation. The main one is ...
1/Sqrt(f)=-2*Log(Rr/3.7+2.51/(Re*Sqrt(f))
Then change it to be equal to f
f=1/(-2*Log(Rr/3.7+2.51/(Re*Sqrt(f))))^2
Just enter the first equation in Excel, and use the right Rr and Re and in left f use 1.
Then copy that equation, but for the left f, just use Excel to point to the first equation.
And then copy the bottom equation to about 10 more cells, and the f will change to the previous f.
It usually stop changing at about 5 cells.
It you want to use different Rr and Re then enter the in cells, like B1 and B2, but in the equation just use $B$1 and $B$2
because the $ makes the numbers the same when copying them to cells that down change, but the f will change until it solution stops changing.
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When you see how easy this is, you will know the solution for a 5th or 6th equation.
It also includes a module that you can copy and paste into your own excel file(s).
I hope to hear from others that like it, or want to ask some questions.
Harrell