Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in a particular substance. Essentially, this is what Archimedes (c.287 BC – c.212 BC) observed when he stated that:
“Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”
In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged within the fluid, experiences an overall greater pressure at the bottom of the column than at the top.
This difference in pressure results in a net force that tends to accelerate an object upwards. The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and equivalent to the weight of the fluid that would otherwise occupy the column, i.e. the displaced fluid.
Of course, we can think of a fluid as being either a liquid, or a gas…
Up and Away
Air is 80% nitrogen.
Since helium weighs 0.1785 grams per litre, and nitrogen weighs 1.2506 grams per litre, 1.25 grams is a good approximation for the weight of a litre of air.
The height to which a balloon rises tends to be stable.
As a balloon rises, it tends to increase in volume with reducing atmospheric pressure.
But the balloon itself does not expand as much as the air on which it rides.
The average density of the balloon decreases less than that of the surrounding air.
The weight of the displaced air is reduced.
A rising balloon stops rising when it and the displaced air are equal in weight. Similarly, a sinking balloon tends to stop sinking.