Motivation

One of the key challenges in Pipe Flow Dynamics is to predict the pressure distribution along the pipe during the stationary 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.

Inputs & Outputs

Assumptions

Equations

\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({\rm Re}, \, \epsilon)}{\rho(p)}

u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A}

q(l) = \frac{\rho_0 \cdot q_0}{\rho(p)}

where

See Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model.

Approximations

Incompressible pipe flow 

LaTeX Math Inline
body \rho(p) = \rho_0

with constant friction 

LaTeX Math Inline
body --uriencoded--f(%7B\rm Re%7D, \, \epsilon) = f_0

p(l) = p_0 + \rho \, g \, z(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 \, l

\frac{dp}{dl} = \rho \, g \cos \theta(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 

u(l) = u_0 = \frac{q_0}{A} = \rm const

q(l) =q_0 = \rm const

where

The first term in 

In most practical applications in water producing or water injecting wells the water can be considered as incompressible and friction factor  an be assumed constant

References