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# Motivation

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

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

Pipeline Flow Pressure Model is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.

# Outputs

 $//$ Pressure distribution along the pipe $//$ Flowrate distribution along the pipe $//$ Flow velocity distribution along the pipe

# Inputs

 $//$ Fluid temperature at inlet point ($//$) $//$ Along-pipe temperature profile $//$ Fluid pressure at inlet point ($//$) $//$ Fluid density $//$ Fluid flowrate  at inlet point ($//$) $//$ $//$ Pipeline trajectory TVDss $//$ Pipe cross-section area $//$ Pipeline trajectory inclination, $//$ $//$ Inner pipe wall roughness

# Assumptions

 Steady-State flow Quasi-isothermal flow $//$ $//$ Homogenous flow Constant cross-section pipe area $//$ along hole $//$ $//$

# Equations

 (1)
 (2)

 (3)
 (4)

where

 $//$ mass flux $//$ Fluid flowrate at inlet point ($//$) $//$ Fluid density at inlet point ($//$) $//$ Fluid density at any point $//$ $//$ Fluid Compressibility $//$ Darcy friction factor $//$ Reynolds number in Pipe Flow $//$ dynamic viscosity as function of fluid temperature $//$ and density $//$ $//$ Characteristic linear dimension of the pipe(or exactly a pipe diameter in case of a circular pipe)

# Alternative forms

 (5)

where

 $//$ gravity losses which represent  pressure losses for upward flow and pressure gain for downward flow $//$ kinematic losses, which grow contribution at high velocities $//$ and high fluid compressibility (like turbulent gas flow) $//$ friction losses which are always negative along the flow direction

Approximations

Pressure Profile in G-Proxy Pipe Flow @model Pressure Profile in GF-Proxy Pipe Flow @model quadrature $//$ quadrature $//$, $//$ algebraic equation $//$, $//$$//$ quadrature $//$, $//$ closed-form expression $//$, $//$ (isothermal) closed-form expression $//$, $//$ (no flow)