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LaTeX Math Inline
bodyn \geq 1
 which is equivalent to
LaTeX Math Inline
body--uriencoded--L%5e* \geq 1
 and holds true for the most of practical tube diameters (< 1 m )


LaTeX Math Block
anchorq0_G
alignmentleft
q_0^2 = \frac{2 \, d \, A^2 }{f \, L} \cdot \left [ 
\Delta Z + ((\rho/\rho_0)^2 -1) \cdot  \frac{ \Delta Z}{1 - \exp(2 \, c_0 \, \rho_0 \, \Delta Z)}
\right]



LaTeX Math Block
anchorq0_G
alignmentleft
\dot m^2 = \frac{A^2}{c^*rho_0^2 \rho^*} \cdot \frac{2 \rho_0^2, -d \rho^2, A^2 }{f \cdot, L} \expcdot \left(  -L/ L^* \right)}{2 \ln [ 
\Delta Z + ((\rho_0/\rho_0) + fL/d \cdot (1^2 -1) \cdot  \frac{ \Delta Z}{1 - \exp(2 \left(, c_0 - L/ L^* \right))/(L/L^*)}\, \rho_0 \, \Delta Z)}
\right]



LaTeX Math Block
anchorstatic
alignmentleft
\rho = \rho_0 \, \exp (с_0 \, \rho_0 \, \Delta Z) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{q_0^2}{A^2} \cdot \frac{1 - \exp(- 2 \, c_0 \, \rho_0 \, \Delta Z) } {\Delta Z}}



LaTeX Math Block
anchor1
alignmentleft
p(L) = p_0 + \frac{1}{c^*c_0} \cdot, \left[ 
-1 + (\rho_0/\rho^*) \cdot \exp (2 \, L/L^*) \cdot \sqrt{  1 - \frac{f}{2d}  \cdot \frac{j_m^2\rho}{G \rho_0^20} \cdot \left(1 - \exp (-L/L^*) \right) }
-1 \right]


Pressure Profile in GC-proxy static fluid column @model


LaTeX Math Block
anchorstatic
alignmentleft
\rho = \rho_0 \, \exp (L/L^*)



LaTeX Math Block
anchorstatic
alignmentleft
p(L) = \frac{-1 + (\rho_0/\rho^*) \cdot \exp(L/L^*)}{c^*}   


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