...

See Surface roughness for more data on typical values for various materials and processing conditions.

Interpolated full-range model

...

The most popular full-range model of Darcy friction factor is:

...

...

Bellos full-range model

...

...

...

LaTeX Math Block anchor 1 alignment left f = \frac{64}{\rm Re} \cdot \Phi	LaTeX Math Block anchor Cheng alignment left \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)}
LaTeX Math Block anchor 1 alignment left a = \left[ 1+ \left( \frac{{\rm Re}}{2712} \right)^{8.4} \right]^{-1}	LaTeX Math Block anchor 1 alignment left b = \left[ 1+ \left( \frac{{\rm Re} \cdot \epsilon/d}{150} \right)^{1.8} \right]^{-1}

Cheng full-range model

...

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

\Phi = \left( \frac{{\rm Re}}{64} \right)^{1-a}
\cdot \left( 1.8 \cdot \ln \frac{{\rm Re}}{6.8} \right)^{-2 \,(1-a)\,b}
\cdot \left( 2.0 \cdot \ln \frac{3.7}{\epsilon/d} \right)^{-2 \,(1-a)\,(1-b)}

a = \left[ 1+ \left( \frac{{\rm Re}}{2720} \right)^9 \right]^{-1}

b = \left[ 1+ \left( \frac{{\rm Re} \cdot \epsilon/d}{160} \right)^2 \right]^{-1}

Churchill full-range model

...

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

cdot \

Phi

\Phi = \left[ 1+ \frac{\

left(\rm Re / 8 \

right)^{12} }{ \

left( \Theta_1 + \Theta_2 \

right)^{1.5} }  \

right]^{1/12}

\Theta_1 = \left[  2.457 \, \ln \left(  \left( \frac{7}{\rm Re} \right)^{0.9}  + 0.27 \, \frac{\epsilon}{d}  \right)   \right]^{16}

\Theta_2 = \left(  \frac{37530}{\rm Re} \right)^{16}

See also

...

Physics / Fluid Dynamics / Pipe Flow Dynamics / Darcy–Weisbach equation / Darcy friction factor 

[ Surface roughness ] [ Reduced Friction Factor (Φ) ]

Reference

...

Moody’s Friction Factor Calculator @ gmallya.com

...