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 | Fluid temperature at inlet point ( l=0) | T(l) | Along-pipe temperature profile |
p_0 | Fluid pressure at inlet point ( l=0) | \rho(T, p) | Fluid density |
q_0 | Fluid flowrate at inlet point ( l=0) | \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
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where
\displaystyle j_m =\frac{ \rho_0 \, q_0}{A} | |
q_0 = q(l=0) | Fluid flowrate at inlet point ( l=0) |
\rho_0 = \rho(T_0, p_0) | Fluid density at inlet point ( l=0) |
\rho(l) = \rho(T(l), p(l)) | Fluid density at any point l |
с(p) | Fluid Compressibility |
f({\rm Re}, \, \epsilon) | Darcy friction factor |
\displaystyle {\rm Re} = \frac{j_m \cdot d}{\mu(T, p)} | Reynolds number in Pipe Flow |
\displaystyle d = \sqrt{ \frac{4 A}{\pi}} | Characteristic linear dimension of the pipe |
Approximations
Pressure Profile in G-Proxy Pipe Flow @model | \theta(l) = \theta_0 = \rm const, |
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Pressure Profile in GF-Proxy Pipe Flow @model | \theta(l) = \theta_0 = \rm const, f(T, p)=f_0 = \rm const |
Pressure Profile in GFC-Proxy Pipe Flow @model | \theta(l) = \theta_0 = \rm const, f(T, p)=f_0 = \rm const, \rho(T, p) = \rho(T) \cdot (1+ c^*(T) \cdot p/p_0) |
Pressure Profile in FC0-Proxy Pipe Flow @mode | \rho(p)=\rho_0 = \rm const, f(T, p)=f_0 = \rm const |
See also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Quasi-Isothermal Stationary Pipe Flow @model
[ Darcy friction factor ] [ Darcy friction factor @model ] [ Reynolds number in Pipe Flow ]
[ Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model ]
[ Temperature Profile in Homogenous Pipe Flow @model ]
[ Fluid Compressibility ] [ Fluid Compressibility @model ]
References