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  


Inner pipe wall roughness

Assumptions


Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area along hole


Equations



\left[\rho(p) -  j_m^2 \cdot c(p)   \right]  \frac{dp}{dl} = \rho^2(p) \, g \, \cos \theta(l)  - \frac{ j_m^2 }{2 d} \cdot  f({\rm Re}, \, \epsilon)



p(l=0) = p_0




u(l) = \frac{j_m}{\rho(l)}



q(l) =A \cdot u(l)


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

Characteristic linear dimension of the pipe

(or exactly a pipe diameter in case of a circular pipe)




See Derivation of Pressure Profile in Steady-State Homogeneous Pipe Flow @model.



Approximations



Pressure Profile in G-Proxy Pipe Flow @modelquardrature

Pressure Profile in GF-Proxy Pipe Flow @modelquardrature

Pressure Profile in GFC-Proxy Pipe Flow @modelalgebraic equation

Pressure Profile in FC0-Proxy Pipe Flow @modeclosed-form expression


See also


Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Quasi-Isothermal Stationary Pipe Flow @model

Darcy friction factor ] [ Darcy friction factor @model ] [ Reynolds number in Pipe Flow ]

Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model ]

Temperature Profile in Homogenous Pipe Flow @model ]

Fluid Compressibility ] Fluid Compressibility @model ]


References




PipeFlowSimulator.xls
Pressure loss in pipe @ neutrium.net 
R. Shankar, Pipe Flow Calculations, Clarkson University [PDF]
Pressure loss in chokes @ Studopedia