Darcy Friction Loss via the Colebrook-White Equation

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It has been said that there's no solution to ColeBrook-White Equation.

Well, I say I have a solution. It is so simple that many say it is to easy to be a "solution". Some say a solution must be this or that, but I just say a solution is a proper answer to as many decimal places as you need. If you need only two of three decimal places then most approximation methods will work, but some won't.

I am going to use Excel to teach this, and 15 decimal places is the maximum for Excel, so I will have to settle for 15 places. If you needed 100 decimal places my procedure would work for if you had a PC program that would go that far.

I think the first part of training should be my "Funnel" solution. Let's look at a graph of what I call the funnel.

The left (vertical) axis shows an initial approximation for an equation. The bottom axis shows the steps. The graphs shows nine different initial guesses (step one) from 0 to 8. The funnel takes to the second step, which is just over 4. Even if you guessed 100, the funnel still guides you to about the same point as the other guesses at step 2. You can see that after step 2, the different paths all converge to the same answer. We will not have to construct a funnel for the accurate solution of the Colebrook-White equation. The funnel picture is just a way to understand that whatever your initial approximation is, the funnel will guide you to the right answer.

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In 1937 a two men named Colebrook and White published an engineering equation for pipe design. The equation was so complex that no one could do more than an approximation, but it because was accurate it became the world standard. But unfortunately today engineers have to buy complex and expensive computer programs to find the answers.

On July 4th (2011) I found a simple, easy solution, in 30 minutes. Many pipe companies are arguing now that it can not be true. Why would they say that? Well, because engineers would not have to buy their $1000 computer solutions.

Three pipe companies have now agreed with me, that engineers should know my easy solution to make designs accurate and cheaper, and easier. One company offered to buy my solution, but when they saw how easy it was, they said it would be wrong for them to sell it because a complex program is not required to solve it. I laughed and agreed with them.

The CheResource company is now helping me sharing it with the rest of the world for FREE. Eventually it will be seen that I am right, and those incorrect, but expensive programs will be lost.

Visit my engineering article here.
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http://www.cheresources.com/invision/blog/20/entry-144-a-new-simplified-accurate-method-for-colebrook-equations/

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It works well in Excel, but the method is so simple people can derive their own processing solution or procedure.



Harrell Geron
Civil Engineer
(Ragknot)