GLOSSARY

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InputsOutputs

LaTeX Math Inline
bodyp_0

Intake pressure 

LaTeX Math Inline
bodyp(l)

Pressure distribution along the pipe

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 and 



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



Equations

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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(p)}{\rho(p)}



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



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


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