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LaTeX Math Inline
body--uriencoded--f_%7BCW%7D(\mbox%7BRe%7D, \epsilon)

Colebrook–White correlation

LaTeX Math Inline
body--uriencoded--\displaystyle k = \frac%7B f_%7BCW%7D( \mbox%7BRe%7D =4,000, \, \epsilon) -0.03048%7D%7B1,900%7D

interpolation multiplier between laminar and turbulent flow regimes

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Bellos full-range model

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LaTeX Math Block
anchor1
alignmentleft
f = \frac{64}{\rm Re} \cdot \Phi
LaTeX Math Block
anchor
Chirchil
Cheng
alignmentleft
\Phi = \left
[
(
1+ 
\frac{{\
left(\
rm Re
/ 8
}}{64} \right)^{
12} }{
1-a}
\cdot \left( 0.75 \
Theta_1 + \Theta_2
cdot \ln \frac{{\rm Re}}{5.37} \right)^{-2 \,(1
.5} } 
-a)\,b}
\cdot \left( 0.83 \cdot \ln \frac{3.41}{\epsilon/d} \right
]
)^{
1/12
-2 \,(1-a)\,(1-b)}
LaTeX Math Block
anchor1
alignmentleft
\Theta_1
a = \left[
2.457 \, \ln \left( 
1+ \left( \frac{
7}
{\rm Re}}{2712} \right)^{
0
8.
9
4}
+ 0.27 \, \frac{
\
epsilon}{d} \
right
) \right
]^{
16
-1}
LaTeX Math Block
anchor1
alignmentleft
\Theta_2 =
b = \left[ 1+ \left(
 \frac{
37530}
{\rm Re} \cdot \epsilon/d}{150} \right)^{1.8} \right]^{
16
-1}


Cheng full-range model

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LaTeX Math Block
anchor1
alignmentleft
f = \frac{64}{\rm Re} \cdot \Phi
LaTeX Math Block
anchorCheng
alignmentleft
\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)}
LaTeX Math Block
anchor1
alignmentleft
a = \left[ 1+ \left( \frac{{\rm Re}}{2720} \right)^9 \right]^{-1}
LaTeX Math Block
anchor1
alignmentleft
b = \left[ 1+ \left( \frac{{\rm Re} \cdot \epsilon/d}{160} \right)^2 \right]^{-1}

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Churchill full-range model

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LaTeX Math Block
anchor1
alignmentleft
f = \frac{64}{\rm Re} \cdot \Phi
LaTeX Math Block
anchor
Cheng
Chirchil
alignmentleft
\Phi = \left
(
[ 1+ \frac{
{
\left(\rm Re
}}{64}
 / 8 \right)^{
1-a} \cdot
12} }{ \left(
0.75
 \
cdot \ln \frac{{\rm Re}}{5.37}
Theta_1 + \Theta_2 \right)^{
-2 \,(1-a)\,b} \cdot \left( 0.83 \cdot \ln \frac{3.41}{\epsilon/d} \right)^{-2 \,(1-a)\,(1-b)
1.5} }  \right]^{1/12}
LaTeX Math Block
anchor1
alignmentleft
a
\Theta_1 = \left[
1+
 2.457 \, \ln \left(  \left( \frac{7}{\rm Re} \right)^{0.9}
{2712
  + 0.27 \, \frac{\epsilon}{d}  \right)
^8.4
   \right]^{
-1
16}
LaTeX Math Block
anchor1
alignmentleft
b
\Theta_2 = \left
[ 1+ \left(
(  \frac{37530}{\rm Re} \
cdot \epsilon/d}{150} \
right)
^1.8 \right]
^{
-1
16}


See also

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

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

Reference

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Moody’s Friction Factor Calculator @ gmallya.com

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