GLOSSARY

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Inputs & Outputs

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p
InputsOutputs

LaTeX Math Inline
body

T_0

Intake pressure temperature 

LaTeX Math Inline
bodyp(l)

Pressure distribution along the pipe

LaTeX Math Inline
bodyp_0

Intake pressure 


LaTeX Math Inline
bodyu(l)

LaTeX Math Inline
bodyq_0

Intake flowrate 

LaTeX Math Inline
bodyu(l)

Flow velocity distribution along the pipe

LaTeX Math Inline
body\theta (l)

Pipeline trajectory inclination 



LaTeX Math Inline
body--uriencoded--%7B\bf r%7D(l)

Pipeline trajectory



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



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LaTeX Math Block
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\bigg( 1 -  \frac{c(p) \, \rho_0^2 \, q_0^2}{A^2}   \bigg )  \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl}  - \frac{\rho_0^2 \, q_0^2 }{2 A^2 d} \frac{f({\rm Re}, \, \epsilon)}{\rho(p)}



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q(l) = \frac{\rho_0 \cdot q_0}{\rho(p)}



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u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A}



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anchorp0
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p(l=0) = p_0



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anchorp0
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q(l=0) = q_0



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\rho(T_0, p_0) = \rho_0


where

LaTeX Math Inline
body--uriencoded--f(%7B\rm Re%7D, \, \epsilon)

Darcy friction factor

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bu(l) \cdot d%7D%7B\nu(l)%7D = \frac%7B4 \rho_0 q_0%7D%7B\pi d%7D \frac%7B1%7D%7B\mu(T, p)%7D

Reynolds number

LaTeX Math Inline
body--uriencoded--\displaystyle d = \sqrt%7B \frac%7B4 A%7D%7B\pi%7D%7D

characteristic linear dimension of the pipe

(or exactly a pipe diameter in case of a circular pipe)

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