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@wikipedia


Motivation



Ideal Gas Static Vertical Pressure Variation


Output


LaTeX Math Inline
bodyp(z)

Fluid pressure 

LaTeX Math Inline
bodyp
 


Input


LaTeX Math Inline
bodyz

LaTeX Math Inline
body\rho_0

Fluid density at Logging reference point 

LaTeX Math Inline
bodyz_0

LaTeX Math Inline
bodyz_0

Logging reference point (usually at surface)

LaTeX Math Inline
bodyc_0

Fluid Compressibility at Logging reference point 

LaTeX Math Inline
bodyz_0

LaTeX Math Inline
bodyg

Standard gravity constant


Equation


LaTeX Math Block
anchorV9I53
alignmentleft
p(z) = p_0 \cdot \exp \left[ - \frac{\rho_0 \, g}{p_0} \cdot (z-z_0) \right]

where

LaTeX Math Inline
bodyz


LaTeX Math Inline
bodyp_0

Gas pressure at Logging reference point 

LaTeX Math Inline
bodyz_0

LaTeX Math Inline
bodyz_0

Logging reference point (usually at surface)
LaTeX Math Inline
body\rho_0


Gas density at Logging reference point 

LaTeX Math Inline
bodyz_0

LaTeX Math Inline
bodyg

Standard gravity constant
LaTeX Math Inline
bodyc_0


Gas Compressibility at Logging reference point 

LaTeX Math Inline
bodyz_0

Alternative form


LaTeX Math Block
anchorZ32TR
alignmentleft
p(z) = p_0 \cdot \exp \left[ - \frac{M }{R \, T} \cdot (z-z_0) \right]

where

LaTeX Math Inline
bodyz

LaTeX Math Inline
bodyp_0

Gas pressure at Logging reference point 

LaTeX Math Inline
bodyz_0

LaTeX Math Inline
bodyz_0

Logging reference point (usually at surface)

LaTeX Math Inline
bodyM

LaTeX Math Inline
bodyg

Standard gravity constant

LaTeX Math Inline
bodyT



LaTeX Math Inline
bodyR

Gas constant


Expand
titleDerivation


Panel
borderColorwheat
bgColormintcream
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Following Ideal Gas Equation of State:

LaTeX Math Block
anchorIG
alignmentleft
\frac{\rho_0}{p_0} =\frac{M}{R \, T}

 



See also


Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics

Fluid Dynamics ]