Air density and Altitude

[thais]

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I am a bit confused about the correlation between altitude and air density. If someone could please clarify it for me it would be great 🙂

I know that air is more dense at lower altitudes, but I get lost when I try to justify this concept with Bernoulli's equation.

P + pv^2/2 + pgh = constant.

Thus, at higher altitudes we have a bigger h (because h here is positive going up, right?) then our density must decrease to compensate. (?) However, wouldn't the decrease in density have an effect on the "pv^2/2" decreasing it? But I though v had to increase. Thus, it is okay for density to decrease and v to increase?

Also, why can't we use the equation P = pgy (when y is positive going down)? Is it because the pressure is different at different altitudes, thus we can't compare the density for the two altitude points using this formula?

I hope my questions seem coherent. 😕

 

[thais]

I guess I find it confusing because the density factor shows up twice in the Bernoulli's equation.

 

[milski]

Bernoulli is not really applicable since the atmosphere is not a fluid flowing in a tube with constant flow.

mgy assumes constant density of the fluid. That is a reasonable approximation at low altitudes but gets more and more incorrect as density decreases.

 

[MedPR]

Are you trying to answer a specific question? I don't know why we would have to understand or know why air density increases or decreases. Just know that high altitudes = lower partial pressure of O2.

 

[thais]

Are you trying to answer a specific question? I don't know why we would have to understand or know why air density increases or decreases. Just know that high altitudes = lower partial pressure of O2.

yes. This question from GS1

3) Bernoulli's equation can be manipulated to the following:

L = (1/2)ρv2ACl

where L = is the lift force
ρ = is the air density
v = is the velocity of the plane
A = is the area of the wing
Cl = is the lift coefficient at the desired angle of attack.

A plane flies from low to high altitude. Which of the following is true?

A. At a given velocity, at the lower altitude the plane will experience greater lift.
B. At a given velocity, at the higher altitude the plane will experience greater lift.
C. The lift the plane experiences is not dependent on altitude.
D. At low altitudes Bernoulli's effect is not applicable.