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Pressure profile along the pipe


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L = \frac{1}{2 \, G \, c^*  \rho^*}  \cdot \ln \frac{G \, \rho^2-F}{G \, \rho_0^2-F}
-\frac{d}{f} \cdot \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}



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 \cos \theta \neq 0



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L = \frac{\rho_01}{j_m^2 \cdot f/(2d)} 
\left[ (p_0-p) + \frac{c^*}{2 p_0} \left( p2F\, c^* \rho^*} \cdot (\rho_0^2 - p^2 \rightrho^2) \right]
 - \frac{2d}{f} \cdot \ln \frac{\rho_0}{\rho}



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 \cos \theta = 0


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titleDerivation


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



The 

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

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L = (\rho^*/F)  \cdot (p_0-p) \cdot (1+ 0.5 \, c^* \cdot (p+p_0))


See also

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