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\mbox{Nu}_D= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}_D^{1/6}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2



Churchill and Chu 



All All flow regimes in regimes in pipelines

LaTeX Math Inline
body--uriencoded--\mbox%7BRa%7D_D \leq 10%5e%7B12%7D


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\mbox{Nu}_L= 0.68 + \frac{0.663 \, \mbox{Ra}^{1/4}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{4/9}}



Churchill and Chu



Laminar flowsflow

LaTeX Math Inline
body--uriencoded--\mbox%7BRa%7D \leq 10%5e9


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\mbox{Nu}_L= \left[ 0.6 + \frac{0.387 \, \mbox{Ra}^{1/6}}{ \left[ 1+ (0.559/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2


Churchill and Chu



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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} }



Mills



Laminar flow in pipeline with diameter 

LaTeX Math Inline
bodyD
 and length 
LaTeX Math Inline
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 

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



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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



Transitional flow and turbulent flow in rough pipeline

LaTeX Math Inline
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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{\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 


All flow regimes in pipelines

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

Accuracy 

LaTeX Math Inline
body--uriencoded--\sim 20 \%25

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