# Archimedes’ Principle and Helium Balloons

**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.

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