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

where

LaTeX Math Inline
body\dot m

mass flowrate along the pipe

LaTeX Math Inline
body\rho

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

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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: 

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