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LaTeX Math Inline
body--uriencoded--\displaystyle j_m = \frac%7B \dot m %7D%7B A%7D= \rm const

mass flux

LaTeX Math Inline
body--uriencoded--\displaystyle \dot m = \frac%7Bdm %7D%7B dt%7D= \rm const

mass flowrate

LaTeX Math Inline
body--uriencoded--\displaystyle q_0 = \frac%7BdV_0%7D%7Bdt%7D = \frac%7B \dot m %7D%7B \rho_0%7D

Intake volumetric flowrate

LaTeX Math Inline
body\rho_0 = \rho(T_0, p_0)

Intake fluid density 

LaTeX Math Inline
body\Delta z(l) = z(l)-z(0)

elevation drop along pipe trajectory

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

Darcy friction factor 

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Re%7D(T,p) = \frac%7Bu(l) \cdot d%7D%7B\nu(l)%7D = \frac%7Bj_m \cdot d%7D%7B\mu(T,p)%7D

Reynolds number in Pipe Flow

LaTeX Math Inline
body\mu(T,p\rho)

dynamic viscosity as function of fluid temperature 

LaTeX Math Inline
bodyT
 and pressure density 
LaTeX Math Inline
bodyp\rho

LaTeX Math Inline
body--uriencoded--\displaystyle c(T,p) = \frac%7B1%7D%7B\rho%7D \left( \frac%7B\partial \rho%7D%7B\partial p%7D \right)_T

fluid compressibility

LaTeX Math Inline
body--uriencoded--\displaystyle d = \sqrt%7B \frac%7B4 A%7D%7B\pi%7D%7D= \rm const

characteristic linear dimension of the pipe

(or exactly a pipe diameter in case of a circular pipe)

LaTeX Math Inline
bodyG = g \, \cos \theta= \rm const

gravity acceleration along pipe 

LaTeX Math Inline
body--uriencoded--F(T, p) = j_m%5e2 \cdot f(T,p)/(2d)


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