# How do density and buoyancy relate?

Aug 7, 2014

Buoyant force is directly proportional to the density of the fluid in which an object is immersed.

Buoyancy is the tendency to rise or float in a fluid. The upward force exerted on objects submerged in fluids is called the buoyant force.

The formula for buoyant force is

F=ρVg = mg

where ρ is the density, $V$ is the volume, and $m$ is the mass of the displaced fluid. $g$ is the acceleration due to gravity (9.81 m·s⁻²).

So the denser the fluid is, the greater the buoyancy and the buoyant force.

Example:

An average 25-year-old adult male with a mass of 70 kg has a density of
1.06 kg/dm³.

His volume is

$V$ = 70 kg × $\left(1 \text{dm³")/(1.06"kg}\right)$ = 66 dm³

Since the density of water is 1.00 kg/dm³, the person displaces 66 kg of water.

The buoyant force of the water is not enough to keep him afloat.

The density of water in the Dead sea is 1.24 kg/dm³. The person immersed in this water will displace

66 dm³× $\left(1.24 \text{kg")/(1"dm³}\right)$ = 82 kg of water.

The buoyant force of the water enables him to float in the Dead Sea with ease.

This video shows a classic experiment, the Cartesian diver, when the depth of the diver depends on the buoyant force acting on it. Changing the density of the diver (by changing pressure) will change the buoyant force.

video from: Noel Pauller