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excellent approximation
I use the following as an initial guess in a Newton iteration to the Colebrook-White eqn for hydraulically smooth pipes:
f = 0.0079284 + 0.5966*Re^(-0.35703) + 6.3776*Re^(-0.71406)
The formula gives f correct to two significant digits over the range of [10^3, 10^6]. The Newton solver finds the remaining accuracy to many more digits in fewer than 5 iterations if I need the precision.
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