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
T_0 | Intake temperature | T(l) | Along-pipe temperature profile |
p_0 | Intake pressure |
\rho(T, p) | |
q_0 | Intake flowrate |
\mu(T, p) | |
z(l) | Pipeline trajectory TVDss | A | Pipe cross-section area |
\theta (l) | Pipeline trajectory inclination, \displaystyle \cos \theta (l) = \frac{dz}{dl} | \epsilon | Inner pipe wall roughness |
Assumptions
Stationary flow | Homogenous flow | Isothermal or Quasi-isothermal conditions | Constant cross-section pipe area A along hole |
Equations
Pressure profile along the pipe | ||
---|---|---|
|
where
\displaystyle j_m = \frac{ \dot m }{ A} | mass flux |
\displaystyle \dot m = \frac{dm }{ dt} | mass flowrate |
\displaystyle q_0 = \frac{dV_0}{dt} = \frac{ \dot m }{ \rho_0} | Intake volumetric flowrate |
\rho_0 = \rho(T_0, p_0) | Intake fluid density |
\Delta z(l) = z(l)-z(0) | elevation drop along pipe trajectory |
f(T,p) = f({\rm Re}(T,p), \, \epsilon) | Darcy friction factor |
\displaystyle {\rm Re}(T,p) = \frac{u(l) \cdot d}{\nu(l)} = \frac{j_m \cdot d}{\mu(T,p)} | Reynolds number in Pipe Flow |
\mu(T,p) | dynamic viscosity as function of fluid temperature T and pressure p |
\displaystyle d = \sqrt{ \frac{4 A}{\pi}} | characteristic linear dimension of the pipe |
The equation (1) can also be written in the following form:
Pressure profile along the pipe | ||
---|---|---|
|
where
\Phi = \frac{1}{64} \cdot {\rm Re} \cdot f | Reduced Friction Factor |
See also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Homogeneous Steady-State Pipe Flow @model
[ Darcy friction factor ] [ Darcy friction factor @model ] [ Reynolds number in Pipe Flow ]
[ Mass Rate in L-Proxy Pipe Flow @model ]
[ Homogenous Pipe Flow Temperature Profile @model ]