Variation of Density with Elevation

[cruckshank]

Hi, I've been given a list of heights and corresponding densities of air at these heights. I'm trying to find an expression for the variation of density with height. From the data, it looks like the density would be equal to some kind of logarithmic relationship? However, I'm not too sure how to actually establish the equation for this.

Thanks in advance!

 

[Nidum]

https://en.wikipedia.org/wiki/International_Standard_Atmosphere

https://en.wikipedia.org/wiki/Density_of_air#Altitude

 

[cruckshank]

https://en.wikipedia.org/wiki/International_Standard_Atmosphere

But g isn't constant in this case?

 

[SteamKing]

Hi, I've been given a list of heights and corresponding densities of air at these heights. I'm trying to find an expression for the variation of density with height. From the data, it looks like the density would be equal to some kind of logarithmic relationship? However, I'm not too sure how to actually establish the equation for this.

Thanks in advance!

Probably, a more apt equation for you problem is the barometric formula:

https://en.wikipedia.org/wiki/Barometric_formula

Here, the formulation depends only on the value of g at sea level.

If you do need to know the variation of g with altitude, there is this:

https://en.wikipedia.org/wiki/Gravity_of_Earth

 

[Chestermiller]

Much more important than the variation of g with altitude is the variation of temperature with altitude. In applying the barotropic formula to determine the variation of pressure and density with altitude, it is critical to include the temperature dependence.