Physics of Fluids: Buoyancy and Archimedes’ Principle

Buoyancy is defined as the overall ability of a fluid, which includes both liquids and gases, to make an object float or rise.
The Buoyant Force, also known as upthrust, refers to the force acting upward on an object that is wholly or partly immersed in a fluid.
This force acts in the opposite direction to gravity, meaning it counteracts the object's weight and reduces the actual weight of the object when it is underwater.
A fluid is any substance that flows. This category encompasses liquids, such as water and oil, as well as gases like air.
Displaced fluid refers to the specific amount of fluid that is pushed aside or moved away when an object is placed within it.

Archimedes’ Principle states that when an object is totally or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced by that object.
This principle is most frequently applied to the behavior of objects in water to explain phenomena such as floating, sinking, and why objects appear lighter when submerged.
While commonly associated with water, the principle also applies to objects in the air, such as balloons.
The upward force exerted is exactly equal to the weight of the displaced fluid, not the volume or mass of the submerged object itself.
The magnitude of the upward force increases as more fluid is displaced; thus, displacing a greater volume of fluid results in a greater buoyant force.

The buoyant force can be calculated using the following formula derived from Archimedes' Principle:

$F_b = \rho_f \, g \, V_d$

In this equation, the variables represent:
- $F_b$ : The buoyant force, measured in Newtons ( $N$ ).
- $\rho_f$ : The density of the fluid, measured in kilograms per cubic meter ( $kg/m^3$ ).
- $g$ : The acceleration due to gravity, which is a constant approximately equal to $9.8 \, m/s^2$ .
- $V_d$ : The volume of the fluid displaced, measured in cubic meters ( $m^3$ ).
The buoyant force acts upward through a specific point called the center of buoyancy, which is the geometric center of the displaced fluid.

Buoyancy is caused by the difference in fluid pressure acting on the various surfaces of an object.
There are three primary factors that determine or affect buoyancy:
1. Density of the object.
2. Density of the fluid.
3. Volume of the fluid displaced.

Positive Buoyancy:
- This occurs when the weight of the object is less than the weight of the displaced fluid (\text{Weight of object} < \text{Weight of displaced fluid}).
- Result: The object rises and stays partially above the surface (floats).
- Named examples include cork and wood.
Negative Buoyancy:
- This occurs when the weight of the object is greater than the weight of the displaced fluid (\text{Weight of object} > \text{Weight of displaced fluid}).
- Result: The object moves down to the bottom (sinks).
- A named example is iron.
Neutral Buoyancy:
- This occurs when the weight of the object is exactly equal to the weight of the displaced fluid ( $\text{Weight of object} = \text{Weight of displaced fluid}$ ).
- Result: The object stays suspended wherever it is placed within the fluid (it neither sinks nor rises).
- A named example is a watermelon.

Weight Transportation:
- Ships and boats utilize buoyancy to carry heavy cargo across water.
- Submarines control their buoyancy to submerge or surface.
Swimming and Safety:
- Humans utilize buoyancy to swim, and flotation devices are designed to provide extra positive buoyancy to keep individuals above water.
Biological Examples:
- Fish use buoyancy to navigate different depths without constant swimming.
- Ducks and water birds have features that allow them to float easily on the surface.
Aviation:
- Hot air balloons and airships (dirigibles) apply buoyant forces in the atmosphere to rise and travel.

Do humans float or sink?
- A human will float if they can displace a weight of water equal to or greater than their own body weight. This is often influenced by lung capacity (air adds volume without much weight) and body composition.
What type of buoyancy do fish apply?
- Fish typically apply neutral buoyancy. This allows them to stay at a specific depth in the water column without sinking to the bottom or floating to the surface involuntarily.
Does adding more water help an object float?
- No, adding more water to the container does not change the buoyant force. Buoyancy depends on the weight of the fluid displaced by the object, not the total amount of fluid present in the environment.
Why do ships float?
- Ships float because their design ensures the upthrust of the water (buoyant force) is equal to the total mass/weight of the ship. This is achieved by having a large volume (displacing a lot of water) and maintaining an average density lower than that of water."