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InputsOutputs

Pipeline trajectory

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

along-pipe distribution of stabilised pressure 

LaTeX Math Inline
bodyp(l)

Pipeline cross-section area 

LaTeX Math Inline
bodyA(l)

along-pipe distribution of stabilised flow rate 

LaTeX Math Inline
bodyq(l)

Fluid density

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

along-pipe distribution of stabilised average flow velocity 

LaTeX Math Inline
bodyu(l)
 

Inner pipe wall roughness

LaTeX Math Inline
body\epsilon


Assumptions

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Stationary flow
Homogenous flow (no phase segregation)
Isothermal or quasi-isothermal conditions

Constant area

LaTeX Math Inline
bodyA(l)
along hole

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