Motivation
...
One of the key challenges in Pipe Flow Dynamics is to predict the pressure distribution along the pipe during the stationary fluid transport.
...
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
...
| LaTeX Math Block |
|---|
| \left( 1 - \frac{\rho_s^20^2 \, q_s^20^2}{A^2} \cdot \frac{c(p)}{\rho} \right) \frac{dp}{dl} = \rho \, g \, \cos \theta(l) - \frac{\rho_s^20^2 \, q_s^20^2 }{2 A^2 d} \frac{f({\rm Re}, \, \epsilon)}{\rho} |
|
| LaTeX Math Block |
|---|
| p(l=0) = p_s0 |
|
| LaTeX Math Block |
|---|
| u(l) = \frac{\rho_s0 \cdot q_s0}{\rho(T(l), p(l))) \cdot A} |
|
| LaTeX Math Block |
|---|
| q(l) = \frac{\rho_s0 \cdot q_s0}{\rho(T(l),p(l))} |
|
where
| fluid flow rate at pipe intake |
| LaTeX Math Inline |
|---|
| body | \rho_s 0 = \rho(T_s0, p_s0) |
|---|
|
| fluid density at intake temperature and pressure |
| Fluid Compressibility |
| LaTeX Math Inline |
|---|
| body | --uriencoded--f(%7B\rm Re%7D, \, \epsilon) |
|---|
|
| Darcy friction factor |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bu(l) \cdot d%7D%7B\nu(l)%7D = \frac%7B4 \rho_s 0 q_s%7D%7B0%7D%7B\pi d%7D \frac%7B1%7D%7B\mu(T, p)%7D |
|---|
|
| Reynolds number |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle d = \sqrt%7B \frac%7B4 A%7D%7B\pi%7D%7D |
|---|
|
| characteristic linear dimension of the pipe (or exactly a pipe diameter in case of a circular pipe) |
...
...
