[Thomas Gaudich]

regarding your formula:

f = 1/ [ 4 * log10((e/3.7D) + ((2.51/Re*sqrt(f))))]^2

it seems be incorrect. my transformation was:

(1/sqrt(f))^2=(-2log10((e/3.7D) + ((2.51/Re*sqrt(f)))))^2 <=>

1/f=[-2 * log10((e/3.7D) + ((2.51/Re*sqrt(f))))]^2 <=>


f=1/[-2 * log10((e/3.7D) + ((2.51/Re*sqrt(f))))]^2 or

f = 1/ 4 *[ log10((e/3.7D) + ((2.51/Re*sqrt(f))))]^2

if i'm wrong, please correct me, it's been a while since i worked with these formulas. The solving method you've proposed works with these formulas. There's however another way to solve this, using the Goalseek tool in Microsoft Excel. The way i do it is:

first i transform the colebrook formula in:

1=-2*sqrt((f))*log10((e/3.7D) + ((2.51/Re*sqrt(f))))

then, in cell A, i write the formula

=-2*sqrt((f))*log10((e/3.7D) + ((2.51/Re*sqrt(f))))

and in cell B i put a starting number for f

then, with goalseek, make excel calculate the formula in A to value 1 by changing the B cell