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Darcy friction factor depends on flow regime, as well as shape and roughness of inner pipe walls.

For a smooth () tubular pipeline Darcy friction factor can be estimated from various empirical correlations :

f = 64 \, \rm Re^{-1}

Laminar fluid flow

нет стабильных корреляций

Laminar-turbulent transition fluid flow

f = 0.32 \, \rm Re^{-0.25}

Turbulent fluid flow

f = 0.184 \, \rm Re^{-0.2}

Strong-turbulent fluid flow

where

	Reynolds number
	Inner diameter of a pipe
	dynamic fluid viscosity as function of pressure and temperature along the pipe

For non-smooth pipelines the Darcy friction factor can be estimated from empirical Colebrook–White correlation which works for non-laminar flow:

\frac{1}{\sqrt{f}} = -2 \, \log \Bigg( \frac{\epsilon}{3.7 \, d}  + \frac{2.51}{{\rm Re} \sqrt{f}} \Bigg)

For many practical applications the Chirchill correlation provides a fair (< 2 % accuracy) estimation of Darcy friction factor for all pipe flow regimes:

f = \frac{64}{\rm Re} \, \Bigg [ 1+ \frac{\big(\rm Re / 8 \big)^{12} }{ \big( \Theta_1 + \Theta_2 \big)^{1.5} }  \Bigg]^{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}

Typical surface roughness of a factory steel pipelines is = 0.05 mm which may increase significantly under mineral sedimentation or erosive impact of the flowing fluids.

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