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Low compressible fluids: LaTeX Math Inline |
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body | --uriencoded--c%5e* p \ll 1, \, \, c%5e* p_0 \ll 1 |
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| High compressible fluids: LaTeX Math Inline |
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body | --uriencoded--c%5e* p \gg 1, \, \, c%5e* p_0 \gg 1 |
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LaTeX Math Inline |
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body | --uriencoded--\displaystyle \rho_0/\rho = c%5e* \cdot (p_0-p) |
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| LaTeX Math Inline |
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body | \displaystyle \rho_0/\rho = p_0/p |
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Approximations
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which is equivalent to LaTeX Math Inline |
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body | --uriencoded--L%5e* \geq 1 |
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| to and holds true for the most of practical tube diameters (< 1 m ) |
LaTeX Math Block |
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| q_0^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{1 - (\rho/\rho_0)^2 \cdot \exp \left( -L/ L^* \right)}{2 \ln (\rho_0/\rho) + fL/d \cdot (1- \exp \left( - L/ L^* \right))/(L/L^*)} |
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LaTeX Math Block |
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| \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^*)} |
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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^* \rho^* \, G \, L) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{G \, \rho_0^2} \cdot ( 1 - \exp(-2 \, c^* \rho^* \, G \, L))} |
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LaTeX Math Block |
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anchor | static |
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alignment | left |
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| p(L) = \frac{1}{c^*} \cdot \left[
-1 + (1+c^* p_0) \cdot \exp (c^* \rho^* \, G \, L) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{G \rho_0^2} \cdot \big(1 - \exp (-2 \, c^* \rho^* \, G \, L) \big) }
\right] |
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Pressure Profile in GC-proxy static fluid column @model LaTeX Math Inline |
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body | \dot m = 0, \, q_0 = 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 (L/L^*) |
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LaTeX Math Block |
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anchor | static |
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alignment | left |
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| p(L) = \frac{-1 + (1+c^* \, p_0) \cdot \exp(L/L^*)}{c^*} |
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See also
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