Buoyancy. Archimedes' Principle

In these revision notes for Buoyancy. Archimedes' Principle, we cover the following key points:

• The meaning of buoyancy
• What caused the buoyancy phenomenon?
• How to calculate the buoyant force?
• What does Archimedes' Principle say on buoyancy?
• How to calculate the maximum load a floating object can hold without sinking?
• How does air buoyancy act on flying objects?
• What is the difference between buoyancy in liquids and gases?

Buoyancy. Archimedes' Principle Revision Notes

Buoyancy is the lifting ability of fluids on objects immersed in them. In this sense, we can define buoyancy as an opposing force to gravity caused by the resistance of fluid against any molecular shift caused by the downward tendency of objects' motion. This resistance comes due to the medium's inertia (here, medium is represented by the fluid).

Buoyant force is the upward force exerted by a fluid on an object that is completely or partially immersed in it.

Buoyant force is symbolically expressed as F_b and like all the other forces, it is measured in Newton.

There are three possible positions of an object inside a liquid.

1. The object is sunk. This means F_g > F_b
2. The object is at rest, completely immersed in liquid. This means F_g = F_b
3. The object is forced to stay immersed in liquid but when released, it moves up and floats on liquid surface. In this case, we have initially F_g < F_b1 but when the equilibrium is reached (when floating), F_g = F_b2 where F_b2 is the new (reduced) buoyant force.

The equation of buoyant force for objects in a liquid is

By measuring the volume of the displaced water, Archimedes calculated indirectly the volume of immersed objects in water. Then, he used the equation of density (density = mass / volume) to find the density of unknown objects. Thus, Archimedes' Principle says:

"The buoyant force acting on an object immersed in a liquid is numerically equal to the weight of the displaced liquid."

Mathematically, we can write the Archimedes principle as

or

Archimedes' Principle is very important in daily life as its applications include a wide range of situation, where the most notorious is the ships construction. Thus, we can use Archimedes' Principle to calculate how much weight a boat or ship can hold without sinking.

We can obtain three important ratios based on the Archimedes' Principle, which give the percentage of the immersed part of a floating object:

where F_b1 is the buoyant force acting on a floating object and F_b2 is the new buoyant force acting on the same object when it is forced to immerse completely in liquid.

We can say the same words for buoyancy in gases as well. The only difference is that in gases there is no floating; we consider the object completely immersed in gas (especially in air). The third case mentioned above when buoyancy in liquids was explain (i.e. when density of object is smaller than the density of gas), is discussed only to see whether the object is moving up or not. Thus, the three cases explained in the buoyancy of liquids adapted for buoyancy in gases are:

1. When F_b < W_object the object falls down on the ground. In this case, ρ_gas < ρ_object
2. When F_b = W_object the object stays unmoveable, suspended in gas. In this case, ρ_gas = ρ_object
3. When F_b > W_object the object rises up. In this case, ρ_gas > ρ_object