This is an old one, See new training web page
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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