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LaTeX Math Inline
bodyT_0

Intake temperature 

LaTeX Math Inline
bodyT(l)

Along-pipe temperature profile 

LaTeX Math Inline
bodyp_0

Intake pressure 

LaTeX Math Inline
body\rho(T, p)

LaTeX Math Inline
bodyq_0

Intake flowrate 

LaTeX Math Inline
body\mu(T, p)

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
bodyA

Pipe cross-section area  
LaTeX Math Inline
body\theta


Pipeline trajectory inclination,

LaTeX Math Inline
body--uriencoded--\displaystyle \cos \theta = \frac%7Bdz%7D%7Bdl%7D = \rm const

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness

Assumptions

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Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole

LaTeX Math Inline
body\theta (l) = \theta = \rm const

LaTeX Math Inline
bodyf(l) = f = \rm const

LaTeX Math Inline
body--uriencoded--\rho = \rho%5e* \cdot ( 1 + c%5e* \cdot p)

LaTeX Math Inline
bodyA(l) = A = \rm const

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