User:Harrell Geron/sandbox

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The main Colebrook equation written in Excel is... 1/SQRT(f)= -2*LOG(e/(3.7*Dh) + 2.51/(Re*SQRT(f))) but compute e/Dh as the relative roughness and call it Rr. And re-write 2.51/(Re*SQRT(f)) as 2.51/Re*1/SQRT(f) just so we can see that both sides have 1/SQRT(f). Then let's change 1/SQRT(f) as X so the equation is... X=-2*LOG(Rr/3.7+2.51/Re*X). Since the right X is in a LOG computation it will allow an easy computation. You can guess any positive number for the first X. If you use 1000, it might make one extra loop. Seven is the average loops needed to get 15 correct digits. A guess less then 10 might save one loop. Just compute -2*LOG(Rr/3.7+2.51/Re*X)' and use the answer for the next X. Each loop will give a closer solution by about 1,2 or 3 more correct digits. When the X stops changing, compute f as 1/(X)^2. Checking the f in both sides of the Colebrook equation you will see both sides of the equation is the X you figured!

Web site with some poor approximations ... en.wikipedia.org/wiki/Darcy_friction_factor_formulae