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{\rm Nu}=3.66 + \frac{ 0.065 \cdot {\rm Re} \cdot {\rm Pr} \cdot {D/L} }{ 1 + 0.04 \cdot ({\rm Re} \cdot {\rm Pr} \cdot {D/L})^{2/3} }




Laminar flow in pipeline with diameter 

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bodyD
 and length 
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bodyL
.


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anchorNu
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{\rm Nu}=0.023 \cdot \mbox{Re}_D^{3/4} \cdot \mbox{Pr}^n



Dittus-Boelter



Turbulent flow  in pipeline 

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body--uriencoded--\mbox%7BRe%7D \geq 10,000



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anchorNu
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{\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr}  }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) }


Gnielinski



Laminar-turbulent transition and turbulent flow in rough pipeline

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body--uriencoded--%7B\displaystyle 3000\leq \mathrm %7BRe%7D\leq 5\cdot 10%5e%7B6%7D%7D

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body--uriencoded--0.5\leq \mathrm %7BPr%7D \leq 2000
 

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bodyf
 is Darcy friction factor


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anchorNu
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{\rm Nu}=0.3 + \frac{0.62 \, \mbox{Re}^{1/2} \, \mbox{Pr}^{1/3} }
{\left[ 1+ (0.4/\mbox{Pr})^{2/3} \right]^{1/4}}
\left[ 1 + \left( \frac{\mbox{Re}}{282000} \right)^{5/8}\right]^{4/5}


Churchill–Bernstein 



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body--uriencoded--\mbox %7BRe%7D \cdot \mbox %7BPr%7D \geq 0.2

Accuracy 

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body--uriencoded--\sim 20 \%25

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