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Motivation

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One of the key challenges in Pipe Flow Dynamics is to predict the pressure distribution along the pipe during the steady-state fluid transport.

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LaTeX Math Inline
bodyp(l)

Pressure distribution along the pipe

LaTeX Math Inline
bodyq(l)

Flowrate distribution along the pipe

LaTeX Math Inline
bodyu(l)

Flow velocity distribution along the pipe

Inputs

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LaTeX Math Inline
bodyT_0

Intake temperature 

LaTeX Math Inline
bodyT(l)

Along-pipe temperature profile 

LaTeX Math Inline
bodyp_0

Intake pressure 

LaTeX Math Inline
body\rho(T, p)

LaTeX Math Inline
bodyq_0

Intake flowrate 

LaTeX Math Inline
body\mu(T, p)

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
bodyA

Pipe cross-section area  
LaTeX Math Inline
body\theta (l)


Pipeline trajectory inclination,

LaTeX Math Inline
body--uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness

Assumptions

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Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole


Equations

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Pressure profile along the pipe


LaTeX Math Block
anchorPressureProfile
alignmentleft
L =\int_{\rho_0}^{\rho} \frac{\rho \, dp}{G \, \rho^2 - F} -\frac{j_m^2}{2} \, \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}


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References

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Show If
grouparax


Panel
bgColorpapayawhip
titleARAX




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