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

Inputs

Assumptions

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{\rho_0 \cdot q_0}{\rho(T(l), p(l))) \cdot A}

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

where

Approximations

Incompressible pipe flow 

Pressure Profile in Incompressible Isoviscous Stationary Quasi-Isothermal Pipe Flow @model

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

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

q(l) =q_0 = \rm const

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

where

\frac{dp}{dl} = \rho_0 \, g \, \frac{dz}{dl}  - \frac{j_m^2  f_0}{2 \, \rho_0 \, d}

The first term in the right side of 

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

See also