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Darcy friction factor 

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bodyf
 depends on flow regime, as well as shape Reynolds number and a shape and roughness 
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body\epsilon
of inner pipe walls.:

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f = f({\rm Re}, \epsilon)



For a smooth (

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body\epsilon = 0
) tubular pipeline Darcy friction factor 
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bodyf
 can be estimated from various empirical correlations

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\begin{cases}
f = 64/\mbox{Re}, & \forall &  \mbox{if  Re}<2,100
\\f = 0.03048 + k \cdot ( \mbox{Re} -2,100), &  \forall & 2,100 < \mbox{if  Re}<4,000 
\\f = f_{CW}( \mbox{Re}, \, \epsilon), & \forall & \mbox{if  Re}>4,000
\end{cases}

where

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