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@wikipedia


Motivation

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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

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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

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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
body

\rho

p_0

Gas 

density

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

c_0 at Logging reference point

M

Compressibility

LaTeX Math Inline
body

z_0 LaTeX Math Inlinebody

g

Standard gravity constant

LaTeX Math Inline
body

p_0

T

Gas 

pressure at Logging reference point 



LaTeX Math Inline
body

z_0

LaTeX Math Inline
bodyR

Gas constant

LaTeX Math Inline
bodyM

Gas molar mass

R

Gas constant


Expand
titleDerivation


Panel
borderColorwheat
bgColormintcream
borderWidth7

Following Ideal Gas Equation of State:

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




See also

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

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