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--uriencoded--displaystyle \cos \theta = \frac%7Bdz%7D%7Bdl%7D = \rm const

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)

Fluid density 

LaTeX Math Inline
bodyq_0

Intake flowrate 

LaTeX Math Inline
body\mu(T, p)

Fluid viscosity 

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

\

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness

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Stationary flowIsothermal or Quasi-isothermal flow

LaTeX Math Inline
body--uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial t%7D = 0 \rightarrow p(t,l) = p(l)

LaTeX Math Inline
body--uriencoded--\displaystyle \frac%7B\partial T%7D%7B\partial t%7D =0 \rightarrow T(t,l) = T(l)

Homogenous flow

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole

LaTeX Math Inline
body--uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial \tau_x%7D =\frac%7B\partial p%7D%7B\partial \tau_y%7D =0 \rightarrow p(\tau_x,\tau_y,l) = p(l)

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

Constant inclination

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



Equations

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Pressure profile along the pipe


LaTeX Math Block
anchorPressureProfile
alignmentleft
L = L(p) = \int_{p_0}^{p} \frac{ \rho(p) - j_m^2 \, c(p) }{G \, \rho^2(p) - F(\rho(p))} \, dp



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