Page tree

Versions Compared

Key

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


LaTeX Math Block
anchorO4JELdotm
alignmentleft
\dot m(t,l) = \dot m = \rm const

where

LaTeX Math Inline
body\dot m

mass flowrate along the pipe


The physical meaning of Pipe Flow Mass Conservation is that total mass passing through cross-section area of a pipe at any location of its trajectory is staying constant as there is no mass exchange of the fluid through the walls.

Equation 

LaTeX Math Block Reference
anchordotm
 can be also written as:

LaTeX Math Block
anchorSHK81
alignmentleft
\dot m(t,l) = \rho(p) \cdot q(t,l) = \rm const

where

LaTeX Math Inline
body\dot m

mass flowrate along the pipe

LaTeX Math Inline
body\rho(T, p)

fluid density 

LaTeX Math Inline
bodyp(t,l)

fluid pressure distribution along the pipe

LaTeX Math Inline
bodyq(t,l)

volumetric flowrate of the pipe flow

Alternative forms

...


In case of a 
 Pipe Flow with constant cross-section area 

LaTeX Math Inline
bodyA(l) = A = \rm const
it also leads to conservation of mass flux: 

LaTeX Math Block
anchorIY1I1jm
alignmentleft
j_m(t,l) = j_m = \frac{\dot m}{A} = \rm const

...

LaTeX Math Inline
body j_m

mass flux along the pipe


Equation 

LaTeX Math Block Reference
anchorjm
 can be also written as:

LaTeX Math Block
anchorERYKY
alignmentleft
j_m = \rho \cdot u = \rm const

where

LaTeX Math Inline
bodyu

superficial velocity of the pipe flow


See also

...

Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Pipe Flow / Pipe Flow Dynamics / Pipe Flow Simulation 

...