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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 \, \Delta Z}{c^*f \rho^*, L} \cdot \frac{left [ 
1 -+ \frac{(\rho/\rho_0)^2 \cdot -1}{1 - \exp(2 \left(,  -L/ L^* \right)}{2 \ln (c_0 \, \rho_0/\rho) + fL/d \cdot (1-, \exp \left(  - L/ L^* \right))/(L/L^*)}Delta Z)}
\right]



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



LaTeX Math Block
anchorstatic
alignmentleft
\rho = \rho_0 \, \exp (2с_0 \, \rho_0 \, L/L^* \Delta Z) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{Gq_0^2}{A^2} \cdot \frac{1 - \exp(- 2 \, c_0 \, \rho_0^2}0 \cdot, (\Delta 1Z) -} \exp(-L/L^*)){\Delta Z}}



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