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LaTeX Math Block
anchordpdl
alignmentleft
\left(   \frac{dp}{dl} \right)_f = - \frac{ j_m^2}{2 d}  \cdot \frac{f(l)}{\rho(l)}

where

LaTeX Math Inline
bodyl

pipe length 

LaTeX Math Inline
bodyj_m = \dot m / A

mass flux

LaTeX Math Inline
body \dot m (l) = \dot m = \rm const

mass flowrate 

LaTeX Math Inline
bodyd

pipe
diameter
 diameter

LaTeX Math Inline
body--uriencoded--A = 0.25 \, \pi \, d%5e2

pipe
cross
 cross-section area

LaTeX Math Inline
body--uriencoded--f= f(%7B\rm Re%7D, \epsilon)

Darcy friction factor

LaTeX Math Inline
body\epsilon

inner pipe walls roughness

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bj_m \, d%7D%7B\mu%7D

Reynolds number 

LaTeX Math Inline
body\mu(T, p)

dynamic viscosity as function of fluid temperature 

LaTeX Math Inline
bodyT
 and pressure 
LaTeX Math Inline
bodyp


The accurate calculations require
solving of a self-consistent equation of Pressure Profile in Homogeneous Quasi-Isothermal Steady-State Pipe Flow @model.

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