Buoyant Force

Buoyancy is simply defined as the ability of an object to float in a fluid (liquids and gases). When an object with a mass is submerged in any fluid, an upward force exerted by the fluid is experienced by the object that tends to push the object upwards. This upwards acting force that pushes the immersed body towards the surface of the fluid is termed buoyant force. This buoyant force is due to the pressure differences on the top and bottom surfaces of the immersed object. The object will experience an upwards buoyant force if the object is immersed completely or even partially. An object, when immersed in a fluid, will always feel lighter than it actually is because of the buoyant force, also otherwise known as upthrust. The following are the factors that influence the force of buoyancy.

• The density of the fluid involved
• The total volume of the fluid displaced
• Local acceleration due to gravity (g)

The buoyant force is given by F_b = ρVg

where

• F_b = the buoyant force
• ρ = the density of the fluid
• V = the volume of the displaced fluid
• g = the acceleration due to gravity

Buoyancy can be commonly experienced by humans when they are swimming. As the swimmer tries to go deeper into the water, there seems to be a force that is trying to push them back to the surface. However, there seems to be no issue when swimming on the surface of the water body. This is because the pressure acting upwards on the swimmer is greater than the pressure acting on top of the swimmer (atmospheric pressure), keeping him afloat. As the swimmer dives and goes deeper, the force from pressure exerted downward on the top of the swimmer will be less than the force from pressure exerted upward on the bottom of the swimmer. Pressure increases as the swimmer goes deeper because there are many layers of water on top of them. This pressure can be very dangerous and even fatal at times if the swimmer is not careful. This is why it is suggested that swimmers do not ever dive deeper than 60 feet in any water body.

Archimedes’ Principle

First discovered by Archimedes of Syracuse in 212 BC, Archimedes’ principle has been the foundation for further research and developments in the study of hydrostatics. For fluids, in terms of force, Archimedes’ principle is stated as “an object, when immersed partially or completely in a fluid, is buoyed up by force equal to the weight of the fluid displaced by the object”. Even though Archimedes’ principle does not consider the surface tension of the fluid, the idea that buoyancy = weight of displaced fluid holds true because the surface tension will modify only the amount of water displaced. If the surrounding fluid has uniform density, the weight of the displaced fluid is directly proportional to the volume of the displaced fluid. The principle further establishes that the force of buoyancy acting upwards on an object is equal to the weight of the fluid displaced by the object. Therefore, when objects with the same mass are immersed in a fluid, the object with more volume displaces relatively more water.

Examples of Buoyancy

Buoyancy is an important part of hydrostatics, and the appropriate calculation of it allows us to make objects float on fluids. Some real-life examples where buoyancy can be observed are discussed below.

• Submarines: Submarines have huge tanks called ballast tanks that can be filled with water when required. When a submarine is floating on the surface and has to dive deep into the ocean, the ballast tanks are opened, and it fills up with seawater while air is released outside through vents. When the ballast tanks are filled up and the submarine's overall density is more than the density of the surrounding seawater, the submarine starts to dive. A particular depth level can be maintained by the submarine by altering the amount of water in the ballast tanks. Conversely, if submarines need to resurface, water is released from the ballast tanks and filled up with air, lowering the density of the submarine, and the force of buoyancy pushes it back to the surface.
• Ships: Even though ships are made of heavy materials like steel, iron etc., which are significantly denser than water, ships can float thanks to their carefully designed shape. The hull of a ship is a hollow cavity with air inside it. Because of this, the total density of the ship tends to be lower than that of the density of the water displaced by it. This is why when the hull is damaged, water seeps into it and thereby sinking the ship.