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titleDerivation


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See Derivation of Pressure Profile in GF-Proxy Pipe Flow @model



Alternative forms

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 Volumetric Flowrate in inclined pipe

LaTeX Math Inline
body\cos \theta \neq 0


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anchorq_0G
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q_0^2 = \frac{2 d A^2 G}{f} \cdot \left[ 

1 + \frac{ (\rho/\rho_0)^2 -1}{1- (\rho_0/\rho)^{\frac{2}{n-1}} \cdot 
\exp \left( \frac{fL/d}{ n-1}  \right)}
\right]


Volumetric Flowrate in horizontal pipe

LaTeX Math Inline
body\cos \theta = 0


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anchorq0_G0
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q_0^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{1 - (\rho/\rho_0)^2}{2 \ln (\rho_0/\rho) + fL/d}


where


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n = \frac{f \, L^*}{2 \, d}



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L^* = \frac{1}{G \, c^* \, \rho^*}



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\rho_0/\rho = \frac{1+c^* p_0}{1+c^* p}


with the following asymptotes:

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