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| LaTeX Math Block |
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| n = \frac{f \, L^*}{d}
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| | LaTeX Math Block |
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| L^* = \frac{1}{2 \, G \, c^* \, \rho^*} = \frac{1}{2 \, G \, c_0 \, \rho_0}
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| | LaTeX Math Block |
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| anchor | rho_rho0 |
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| alignment | left |
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| \rho_0/\rho = \frac{1+c^* p_0}{1+c^* p}
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|
...
which is equivalent to | LaTeX Math Inline |
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| body | --uriencoded--L%5e* \geq 1d |
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|
and holds true for the most of practical tube diameters (< 1 m ), as the lowest practical values of | LaTeX Math Inline |
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| body | --uriencoded--L%5e* \geq d |
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are | LaTeX Math Inline |
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| body | --uriencoded--L%5e* \geq 7,000 \, %7B\rm m%7D |
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| LaTeX Math Block |
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| q_0^2 =
\frac{2 \, d \, A^2 \, G}{f} \cdot \left [
1 + \frac{(\rho/\rho_0)^2-1}{1- \exp (2 \, c_0 \, \rho_0 \, G \, L)}
\right]
=
\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] |
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| LaTeX Math Block |
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| \dot m^2m = \frac{A^2}{c^*rho_0 \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^*)}, q_0 |
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| LaTeX Math Block |
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| anchor | static |
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| alignment | left |
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| \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}}
= | | LaTeX Math Block |
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| anchor | static |
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| alignment | left |
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| \rho = \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}} |
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| LaTeX Math Block |
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| p(L) = p_0 + \frac{1}{c^*} \cdot \left[
-1 + (\\rho/\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] -1}{c_0} |
|
| Pressure Profile in GC-proxy static fluid column @model |
| LaTeX Math Block |
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| anchor | static |
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| alignment | left |
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| \rho = \rho_0 \, \exp (L/L^*c_0 \, \rho_0 \, g \, \Delta Z) |
|
| LaTeX Math Block |
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| anchor | static |
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| alignment | left |
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| p(L) = p_0 + \frac{-1 + (\exp (c_0 \, \rho_0/\rho^*) \, g \cdot, \exp(L/L^*)}{c^*} Delta Z) -1}{c_0} |
|
See also
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