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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


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PressureProfile
q_0G
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q^2
q_0^2 = \frac{2 d A^2 G}{f} \cdot \left[ 

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



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 \cos \theta \neq 0



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



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 \cos \theta = 0




The equation 

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for horizontal pipelines can be re-written explicitly in terms of pressure:

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