https://www.toppr.com/ask/question/archimedes-principle-does-not-apply-to-gases/
https://byjus.com/question-answer/archimedes-principle-cannot-be-applied-to-gases-true-false-1/
These two pages say that Archimedes' Principle is valid for gases.
If that is so then:
Doing a quick internet search tells me that density of air is about $1.2kg/m^3$.
I have an object of density less than that of air.
Why don't I see it flying, accelerating up to start floating at the top of the air surface, as predicted by the law of floatation:
$$\frac{Volume Of Object Immersed}{Entire Volume Of Object} = \frac{Density Of Solid}{
Density Of Fluid}$$
Since density of object is less than that of air, RHS of the equation is less than 1 and therefore volume immersed must be less than the volume not immersed, that is, object floats.
Is the Archimedes' principle valid for fluids of incompressible category, and thus it is not valid for gases?
The book that I am using to learn Archimedes' Principle doesn't mention anything about the fluid being ideal ,non ideal, non Compressible etc.
It just talks about a fluid.
What's the problem here?
Best Answer
According to a wikipedia article the least dense solid known to exist is graphene aerogel with a density of 1.6 kg/m$^3$. So it seems there are no solids that will float in air of density 1.2 kg/m$^3$. The only thing that can rise in air is another gas of lower density than air.
But you generally can't "see" another gas rising in air unless that gas is enclosed in some visible solid, such that the density of the combination of the visible solid and gas is less than air. That's the case of a balloon filled with a gas lighter than air (e.g., helium).
Hope this helps.