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InputsOutputs

Pipeline trajectory

LaTeX Math Inline
body{\bf r} = {\bf r}(l) = \{ x(l), \, y(l), \, z(l) \}

along-pipe  stabilized pressure distribution 

LaTeX Math Inline
bodyp(l)

Pipe cross-section area 

LaTeX Math Inline
bodyA

along-pipe stabilized flowrate distribution 

LaTeX Math Inline
bodyq(l)

Along-pipe temperature profile 

LaTeX Math Inline
bodyT(l)

along-pipe stabiliszed average flow velocity distribution 

LaTeX Math Inline
bodyu(l)
 

Fluid density

LaTeX Math Inline
body\rho(T, p)
and fluid viscosity 
LaTeX Math Inline
body\mu(T, p)


Intake pressure 

LaTeX Math Inline
bodyp_0
, 


Intake rate 

LaTeX Math Inline
bodyq_0


Inner pipe wall roughness

LaTeX Math Inline
body\epsilon


Assumptions

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Stationary fluid flowHomogenous fluid flowIsothermal or Quasi-isothermal conditions
Homogenous fluid flow

Constant cross-section pipe area

LaTeX Math Inline
bodyA

(l)

along hole



Equations

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LaTeX Math Block
anchor9QRCZ
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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)}



LaTeX Math Block
anchor1
alignmentleft
u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A(l)}



LaTeX Math Block
anchor1
alignmentleft
q(l) = \frac{\rho_0 \cdot q_0}{\rho(p)}


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