@wikipedia
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 :
where
For non-smooth pipelines
the
Darcy friction factor can be estimated from
empirical Colebrook–White correlation which works for non-
laminar flow:
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\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 Churchill correlation provides a fair (< 2 % accuracy and improving towards laminar flow) estimation of Darcy friction factor
for all pipe flow regimes:
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anchor | Chirchil |
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alignment | left |
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| 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} |
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| \Theta_1 = \left[ 2.457 \, \ln \left( \left( \frac{7}{\rm Re} \right)^{0.9} + 0.27 \, \frac{\epsilon}{d} \right) \right]^{16} |
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| \Theta_2 = \left( \frac{37530}{\rm Re} \right)^{16} |
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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.
See also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Darcy–Weisbach equation / Darcy friction factor
[ Surface roughness ]
Reference
Moody’s Friction Factor Calculator @ gmallya.com