Motivation

One of the key challenges in Pipe Flow Dynamics is to predict the along-hole temperature distribution during the stationary fluid transport.

In many practical cases the temperature distribution for the stationary fluid flow can be approximated by homogenous fluid flow model.

Pipeline Flow Temperature Model is addressing this problem with account of the varying pipeline trajectory, pipeline schematic and heat transfer with the matter around pipeline.

Inputs & Outputs

Inputs	Outputs
pipeline trajectory	along-pipe temperature distribution
pipeline cross-section area
fluid density and fluid viscosity
inflow temperature , inflow pressure , inflow rate
initial temperature of the medium around pipeline
specific heat capacity , thermal conductivity of the medium around pipeline
heat transfer coefficient based on pipeline schematic

Assumptions

Stationary fluid flow

Homogenous fluid flow

Equations

\bigg( 1 -  \frac{c(p) \, \rho_0^2 \, q_0^2}{A^2}   \bigg )  \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl}  - \frac{\rho_0^2 \, q_0^2 }{2 A^2 d} \frac{f(p)}{\rho(p)}

u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A(l)}

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

(see Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model )

Approximations

References

https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae

https://neutrium.net/fluid_flow/pressure-loss-in-pipe/