GLOSSARY

Page tree

Versions Compared

Old Version 29

changes.mady.by.user Arthur Aslanyan (Nafta College)

Saved on

compared with

New Version 30

changes.mady.by.user Arthur Aslanyan (Nafta College)

Saved on

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

...

The base driving equations of a pipe flow isare:

Steady-state 1D inviscid fluid flowPipe Flow Mass Conservation
Equation of State (EOS)


LaTeX Math Block
anchorIY1I1
alignmentleft
\frac{d p}{d l} =
-\rho \, u \, \frac{d u}{d l}  + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}



LaTeX Math Block
anchorIY1I1
alignmentleft
j_m(l) = j_m = \rho(l) \cdot u = \rm const


Equation of State (EOS)Darcy–Weisbach


LaTeX Math Block
anchorIY1I1
alignmentleft
\rho = \rho(p, T)



LaTeX Math Block
anchorgradP
alignmentleft
f_{\rm cnt, l} =  -  f \cdot \frac{  \rho \, u^2 \, }{2 d}


where

LaTeX Math Inline
bodyl

distance along the fluid flow streamline

LaTeX Math Inline
body\theta(l)

inclinational deviation,  

LaTeX Math Inline
body\displaystyle \cos \theta = dz/dl

LaTeX Math Inline
bodyz(l)

elevation along the 1D flow trajectory 

LaTeX Math Inline
bodyT(l)

fluid temperature

LaTeX Math Inline
bodyp(l)

fluid pressure

LaTeX Math Inline
body\rho(l)

fluid density

LaTeX Math Inline
body--uriencoded--%7B\bf u%7D(l)

fluid velocity vector 

LaTeX Math Inline
bodyu(l)

superficial velocity of the pipe flow

LaTeX Math Inline
body--uriencoded--%7B\bf f%7D_%7B\rm cnt%7D(l)

volumetric density of all contact forces exerted on fluid body

LaTeX Math Inline
body--uriencoded--%7Bf%7Df_%7B\rm cnt, l%7D(l) = %7B\bf e%7D_u \cdot %7B\bf f%7D_%7B\rm cnt%7D

projection of 

LaTeX Math Inline
body--uriencoded--%7B\bf f%7D_%7B\rm cnt%7D
 onto the unit fluid velocity vector:  
LaTeX Math Inline
body--uriencoded-- %7B\bf e%7D_u = %7B %7C %7B\bf u%7D %7C%7D %5e%7B-1%7D \, %7B\bf u%7D

LaTeX Math Inline
bodyj_m

fluid mass flux

LaTeX Math Inline
body\dot m

mass flowrate

LaTeX Math Inline
bodyg

standard gravity constant

...