f = \frac{64}{\rm Re} \cdot \Phi

\Phi = \left( \frac{{\rm Re}}{64} \right)^{1-a}
\cdot \left( 0.75 \cdot \ln \frac{{\rm Re}}{5.37} \right)^{-2 \,(1-a)\,b}
\cdot \left( 0.83 \cdot \ln \frac{3.41}{\epsilon/d} \right)^{-2 \,(1-a)\,(1-b)}

a = \left[ 1+ \left( \frac{{\rm Re}}{2712} \right)^8^{8.4} \right]^{-1}

b = \left[ 1+ \left( \frac{{\rm Re} \cdot \epsilon/d}{150} \right)^1^{1.8} \right]^{-1}