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LaTeX Math Block

anchor	n
alignment	left

n = \frac{f \, L^*}{d}

LaTeX Math Block

anchor	L*
alignment	left

L^* = \frac{1}{2 \, G \, c^* \, \rho^*} = \frac{1}{2 \, G \, c_0 \, \rho_0}

LaTeX Math Block

anchor	rho_rho0
alignment	left

\rho_0/\rho = \frac{1+c^* p_0}{1+c^* p}

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LaTeX Math Inline

body	n \geq 1

which is equivalent to

LaTeX Math Inline

body	--uriencoded--L%5e* \geq 1d

and holds true for the most of practical tube diameters (< 1 m ), as the lowest practical values of

LaTeX Math Inline

body	--uriencoded--L%5e* \geq d

are

LaTeX Math Inline

body	--uriencoded--L%5e* \geq 7,000 \, %7B\rm m%7D

LaTeX Math Block

anchor	q0_G
alignment	left

q_0^2 = 
\frac{2 \, d \, A^2 \, G}{f \, L} \cdot \left [ 
\Delta1 Z + (\frac{(\rho/\rho_0)^2 -1) \cdot  \frac{ \Delta Z}{1 - \exp (2 \, c_0 \, \rho_0 \, G \Delta, ZL)}
 \right]

LaTeX Math Block

anchor	q0_G
alignment	left

\dot m^2 = \rho_0^2 \cdot \
=
\frac{2 \, d \, A^2  \, g}{f \, L} \cdot \left [ 
\Delta Z + ((\rho/\rho_0)^2 -1) \cdot  \frac{ \Delta Z}{1 - \exp(2 \, c_0 \, \rho_0 \, g \,  \Delta Z)}
\right]

LaTeX Math Block

anchor	q0_G
alignment	left

\dot m = \rho_0 \, q_0

LaTeX Math Block

anchor	static
alignment	left

\rho =
\rho_0 \, \exp(c_0 \, \rho_0 \, G \, L) \, \sqrt{1 - \frac{f \, q_0^2}{2 \, d \, A^2} \cdot \frac{1- \exp(-2 \, c _0 \, \rho_0 \, G \, L)}{G}} 
=\rho_0 \, \exp (с_0 \, \rho_0 \, g \, \Delta Z) \cdot \sqrt{ 1 - \frac{f8}{2d\pi^2} \cdot   \frac{f \, L}{d^5} \cdot q_0^2}{A^2} \cdot \frac{1 - \exp(- 2 \, c_0 \, \rho_0 \, g \, \Delta Z) } { g \, \Delta Z}}

LaTeX Math Block

anchor	1
alignment	left

p(L) = p_0 + \frac{1}{c_0} \, \left[ \frac{\rho}{/\rho_0} -1 \right]}{c_0}

Pressure Profile in GC-proxy static fluid column @model

LaTeX Math Block

anchor	static
alignment	left

\rho = \rho_0 \, \exp (L/L^*c_0 \, \rho_0 \, g \, \Delta Z)

LaTeX Math Block

anchor	static
alignment	left

p(L) =  p_0 + \frac{-1 + (\exp (c_0 \, \rho_0/\rho^*) \, g \cdot, \exp(L/L^*)}{c^*}  Delta Z) -1}{c_0}

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