Variation of Density with Elevation

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Discussion Overview

The discussion revolves around the variation of air density with elevation, focusing on establishing a mathematical expression based on provided data. Participants explore different relationships and formulas that might describe this variation, including the potential use of logarithmic relationships and the barometric formula.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the density of air might follow a logarithmic relationship with height but expresses uncertainty about how to derive the equation.
  • Another participant references the International Standard Atmosphere and the density of air at altitude, implying that established models exist for this relationship.
  • A later reply questions the assumption that gravitational acceleration (g) is constant in this context, indicating a potential complication in the analysis.
  • One participant proposes that the barometric formula may be more suitable for the problem, noting that it primarily depends on the value of g at sea level.
  • Another participant emphasizes the importance of considering temperature variation with altitude when applying the barotropic formula to determine pressure and density changes.

Areas of Agreement / Disagreement

Participants express differing views on the factors influencing air density with elevation, particularly regarding the roles of gravitational variation and temperature. No consensus is reached on a single model or equation to describe the relationship.

Contextual Notes

Participants highlight the need to consider both gravitational and temperature variations with altitude, indicating that the discussion may be limited by assumptions about these factors. The mathematical steps to derive a specific equation remain unresolved.

cruckshank
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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!
 
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cruckshank said:
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
 
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.
 
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