GLOSSARY

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InputsOutputs

LaTeX Math Inline
bodyT_s

Intake temperature 

LaTeX Math Inline
bodyp(l)

Pressure distribution along the pipe

LaTeX Math Inline
bodyp_s

Intake pressure 

LaTeX Math Inline
bodyq(l)

Flowrate distribution along the pipe

LaTeX Math Inline
bodyq_s

Intake flowrate 

LaTeX Math Inline
bodyu(l)

Flow velocity distribution along the pipe

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
body\theta (l)


Pipeline trajectory inclination,

LaTeX Math Inline
body--uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D



LaTeX Math Inline
bodyT(l)

Along-pipe temperature profile 



LaTeX Math Inline
body\rho(T, p)

Fluid density 



LaTeX Math Inline
body\mu(T, p)

Fluid viscosity 



LaTeX Math Inline
bodyA

Pipe cross-section area  

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness



Assumptions

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Stationary fluid flowHomogenous fluid flowIsothermal or Quasi-isothermal conditions
Constant cross-section pipe area
LaTeX Math Inline
bodyA
along hole

Incompressible fluid  

LaTeX Math Inline
body\rho(T, p)=\rho_s = \rm const

Isoviscous  

LaTeX Math Inline
body\mu(T, p) = \mu_s = \rm const

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole


Equations


Pressure profilePressure gradient profileFluid velocityFluid rate


LaTeX Math Block
anchorPPconst
alignmentleft
p(l) = p_s + \rho_s \, g \, z(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s \, l



LaTeX Math Block
anchorgradP
alignmentleft
\frac{dp}{dl} = \rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s



LaTeX Math Block
anchor1
alignmentleft
q(l) =q_s = \rm const



LaTeX Math Block
anchor1
alignmentleft
u(l) = u_s = \frac{q_s}{A} = \rm const


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