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_s^2 \, q_s^2}{A^2}   \bigg )  \frac{dp}{dl} = \rho \, g \, \frac{dz}{dl}  - \frac{\rho_s^2 \, q_s^2 }{2 A^2 d} \frac{f({\rm Re}, \, \epsilon)}{\rho}

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

u(l) = \frac{\rho_s \cdot q_s}{\rho \cdot A}

p(l=0) = p_s

q(l=0) = q_s

\rho(T_s, p_s) = \rho_s

where

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

Approximations

Incompressible pipe flow 

LaTeX Math Inline
body \rho(T, p) = \rho_s

with constant viscosity 

LaTeX Math Inline
body \mu(T, p) = \mu_s

p(l) = p_s + \rho_s \, g \, z(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s \, l

\frac{dp}{dl} = \rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s

q(l) =q_s = \rm const

u(l) = u_s = \frac{q_s}{A} = \rm const

where

\frac{dp}{dl} = \rho_s \, g \, \frac{dz}{dl}  - \frac{\rho_s \, q_s^2 }{2 A^2 d} f_s

The first term in the right side of 

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

References