# 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.

Gold Member
cruckshank
But g isn't constant in this case?

Staff Emeritus
Homework Helper
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.

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

Mentor
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.

Nidum