When an object is immersed in a liquid, it experiences an upward force known as upthrust or buoyant force. This force makes objects appear lighter in water and is the reason why ships float and balloons rise. But what determines the magnitude of this force?
In this topic, we will explore the concept of upthrust, its formula, the factors affecting it, and its real-world applications in an easy-to-understand manner.
What Is Upthrust?
Definition of Upthrust
Upthrust, also known as buoyant force, is the force exerted by a liquid that opposes the weight of an object submerged in it. It acts vertically upward and is responsible for the floating or sinking of objects in a fluid.
This phenomenon is governed by Archimedes’ Principle, which states:
A body partially or fully submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by the body.
Formula for Upthrust
The upthrust or buoyant force ( F_b ) is given by the equation:
where:
- F_b = Upthrust or buoyant force (Newtons, N)
- rho = Density of the liquid (kg/m³)
- g = Acceleration due to gravity (9.81 m/s²)
- V = Volume of the displaced liquid (m³)
This formula shows that the greater the volume of displaced liquid, the greater the upthrust.
Factors Affecting Upthrust
Several factors determine the magnitude of upthrust:
1. Density of the Liquid ( rho )
The higher the density of the liquid, the stronger the upthrust. For example, seawater provides more upthrust than freshwater because it has a higher density due to dissolved salts.
2. Volume of Displaced Liquid ( V )
An object with a larger submerged volume displaces more liquid and experiences a greater upthrust. This explains why large ships, despite being heavy, can float.
3. Acceleration Due to Gravity ( g )
The value of gravity affects upthrust. On Earth, it is 9.81 m/s², but on the Moon, where gravity is weaker, objects experience less upthrust in a liquid.
4. Shape and Orientation of the Object
A flat or wide object displaces more water and experiences more upthrust than a compact, dense object of the same mass. This is why a flat wooden plank floats, but a dense metal ball sinks.
Archimedes’ Principle and Upthrust
Understanding Archimedes’ Principle
Archimedes’ Principle forms the basis of upthrust and explains why some objects float while others sink.
If the upthrust is greater than the object’s weight, the object floats.
If the upthrust is equal to the object’s weight, the object remains suspended.
If the upthrust is less than the object’s weight, the object sinks.
Floating and Sinking Objects
| Object | Density Compared to Liquid | Behavior |
|---|---|---|
| Wood | Less dense | Floats |
| Ice | Less dense | Floats |
| Iron | More dense | Sinks |
| Submarine | Adjustable density | Can float or sink |
Examples of Upthrust in Everyday Life
1. Floating of Ships
Ships are designed with a hollow hull that allows them to displace enough water to generate sufficient upthrust. Even though they are made of metal, they float because of their large volume and air-filled spaces.
2. Icebergs Floating on Water
Icebergs float because ice is less dense than water. However, nearly 90% of an iceberg is submerged, with only a small portion visible above the surface.
3. Swimming and Buoyancy
When a person swims, they experience upthrust, which helps them stay afloat. The more water displaced, the easier it is to float. This is why people with higher body fat float more easily than those with more muscle mass.
4. Hot Air Balloons
Hot air balloons rise due to the buoyancy of warm air, which is similar to upthrust in liquids. Hot air is less dense than cold air, creating an upward force that lifts the balloon.
5. Submarines and Buoyancy Control
Submarines adjust their buoyancy by controlling the amount of water in their ballast tanks. By taking in water, they increase their density and sink. By releasing water and filling the tanks with air, they decrease their density and rise.
Mathematical Example of Upthrust Calculation
Example 1: Determining the Upthrust on a Wooden Block
A wooden block with a volume of 0.02 m³ is floating on water. If the density of water is 1000 kg/m³, what is the upthrust acting on the block?
Solution:
Using the formula:
The upthrust acting on the block is 196.2 N.
Applications of Upthrust in Science and Engineering
1. Designing Floating Structures
Engineers use Archimedes’ Principle to design bridges, floating docks, and oil platforms to ensure they displace enough water to remain stable.
2. Marine and Naval Architecture
The design of boats, ships, and submarines depends on understanding upthrust and fluid displacement.
3. Hydrometers in Liquid Measurement
A hydrometer is a device that floats in liquid to measure density. It is widely used in chemical and food industries to check the quality of liquids like milk, alcohol, and fuel.
4. Fluid Mechanics in Engineering
Upthrust is important in fluid dynamics, influencing the design of pipes, pumps, and turbines used in water distribution and energy generation.
- Upthrust is the upward force exerted by a liquid on an immersed object.
- It is given by the formula F_b = rho g V and depends on liquid density, volume displaced, and gravity.
- Archimedes’ Principle explains how objects float, sink, or remain suspended in a liquid.
- Real-life examples include floating ships, icebergs, swimming, and submarines.
- Upthrust is essential in engineering, marine design, and industrial applications.
Understanding upthrust and buoyancy is crucial for designing efficient systems in transportation, engineering, and environmental sciences.