[Tom Hill]

You could merely look up the applicable Darcy friction factors on the Moody Diagram without having the calculation them. The moody diagram is readily available is most hydraulics textbooks. I believe it was first published by Lewis F. Moody in ASME Transactions, November 1944 in his article entitled "Friction Factors for Pipe Flow". I use the one copied in Crane TP410.

If you still wish to calculate the Darcy friction factor using the Colebrook-White equation, then I suggest putting it into a spreadsheet. It is an implicit iterative calculation requiring an initial guess (usually around 0.02), and then solving successive iterations until the desired convergence is achieved. I personally find that about 4 or 5 iterations is sufficient. However, I set up my spreadsheets to run about 8 to 10 iterations just to make sure.

Original Colebrook White formula as published:

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

Note that "f" occurs on both sides of the equation.
Revise terms to solve for f:

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

Use an initial guess on the right hand side (rhs) of f=0.02,
then solve for new f on the left hand side (lhs).
Take resulting new f from lhs and plug back into rhs.
solve again for new f on lhs. Do this over and over until
consecutive values of f are identical to 5 decimal places.

Good Luck...