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One of the key challenges in Pipe Flow Dynamics is to predict the along-hole pressure distribution during the stationary fluid transport.

The 

In many practical cases the stationary pressure distribution can be approximated by Isothermal or Quasi-isothermal homogenous fluid flow model.

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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)

Pipeline Pipe cross-section area 

LaTeX Math Inline
bodyA(l)

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)


inflow Intake pressure 

LaTeX Math Inline
bodyp_0
, 


Intake inflow rate 

LaTeX Math Inline
bodyq_0


Inner pipe wall roughness

LaTeX Math Inline
body\epsilon


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