Buoyancy

What is Buoyancy?

Buoyancy is the upward force exerted by a fluid (like water or air) on an object submerged or partially submerged. This force arises because of the pressure difference in the fluid at different depths: pressure increases with depth, so the pressure on the bottom of the object is greater than the pressure on the top, resulting in a net upward force.

The Physics of Buoyancy

Archimedes' Principle

Archimedes’ principle is fundamental in understanding buoyancy and its effects on objects in fluids. It quantitatively measures the buoyant force and explains why objects float, sink, or remain neutrally buoyant.

It’s used to design and analyze the buoyancy of boats, ships, submarines, and even aerodynamics to understand how lighter-than-air vehicles like balloons or airships can float in the atmosphere. Archimedes’ principle also explains why dense objects like steel ships can float on water: if the ship’s design displaces enough water, the buoyant force will support the ship’s weight, allowing it to float.

Displacement of Fluid: When an object is immersed in a fluid, it pushes aside or displaces a fluid volume. The volume of fluid displaced is equivalent to the volume of the part of the object submerged in the liquid.
Buoyant Force: The buoyant force exerted on the object is equal to the weight of the displaced fluid. This force acts upward, opposing the object’s weight, which acts downward due to gravity.
Proportionality to Displaced Volume: The buoyant force is directly proportional to the volume of fluid displaced, which in turn depends on the density of the liquid and the volume of the object submerged. This means that objects in denser fluids experience a greater buoyant force.

Buoyant Force Formula

The buoyant force ( $F_b$ ) on an object submerged in a fluid is calculated using the formula:

$F_b=\rho \times V\times g$

where:

$\rho$ (rho) is the density of the fluid in which the object is submerged,
$V$ is the volume of the fluid displaced by the object, and
$g$ is the acceleration due to gravity.

The direction of the buoyant force is always upward, counteracting the weight of the object submerged in the fluid. This force is what allows objects to float or rise in a fluid. If the buoyant force equals the object’s weight, it floats or remains suspended at a certain depth. If the buoyant force exceeds the object’s weight, the object will rise to the surface and float. If less, the object will sink.

Factors Affecting Buoyancy

Density of the Fluid ( $\rho$ ): This indicates how much fluid mass is present in a given volume. A higher density means the fluid has more mass in the same volume, leading to a greater buoyant force.
Volume of Fluid Displaced ( $V$ ): This is equivalent to the volume of the part of the object that is submerged in the fluid. Larger objects displace more fluid, which increases the buoyant force.
Acceleration Due to Gravity ( $g$ ): Gravity is the force that pulls objects towards the center of the Earth. It affects the weight of the displaced fluid and, thus, the buoyant force. On Earth, $g$ is approximately $9.81 m/s^2$ .

Floating and Sinking

The buoyancy of an object in a fluid, leading to either floating or sinking, is primarily determined by the relative densities of the object and the fluid:

Floating: An object floats when its density is lower than that of the fluid it is in. Because of its lower density, the object displaces a volume of fluid whose weight is equal to the object’s weight before the object is completely submerged. At this point, the buoyant force (upward) balancing the object’s weight (downward) allows it to float. The object rises in the fluid until the upward buoyant force equals the downward gravitational force, reaching an equilibrium position. This is why, for example, an ice cube (which has a lower density than water) floats in water.
Sinking: Conversely, if an object’s density exceeds the fluid’s, it will sink. The object displaces a volume of fluid with a weight less than its weight before it is fully submerged, and thus, the buoyant force is not enough to counteract its weight. As a result, the object continues to descend until it reaches the bottom of the fluid container or another stable position where it can rest. A rock, for example, sinks in water because its density is higher than the water.

Buoyancy in Action

Ship Design: In shipbuilding, understanding buoyancy is essential to ensure a vessel can float and remain stable in water. Ships are designed to displace a volume of water with a weight equal to or greater than the ship’s total weight, including its cargo and passengers. A ship’s hull is shaped and constructed to displace a sufficient amount of water to generate the necessary buoyant force to keep it afloat. Even though ships are made of materials heavier than water, their design allows them to displace enough water to float.
Submarines and Buoyancy Control: Submarines have the unique ability to control their buoyancy, enabling them to float, submerge, and rise according to need. This is achieved through buoyancy control systems that adjust the submarine’s overall density. By taking water into ballast tanks, a submarine increases its weight and density, causing it to sink. Conversely, when it expels water from these tanks and fills them with air, its density decreases, making it less dense than the surrounding water, which allows it to rise.
Hot Air Balloons: Hot air balloons operate based on the principle of buoyancy. The air inside the balloon is heated, which reduces its density compared to the cooler outside air. As a result, the balloon displaces a volume of air heavier than the hot air inside, creating an upward buoyant force that allows the balloon to float and ascend. By controlling the temperature of the air inside the balloon, pilots can adjust its altitude and navigate.

Buoyancy Calculator

Instructions: Input the density of the fluid, the volume of fluid displaced, and gravity (9.81 Earth)

Density of Fluid (kg/m³):
Volume of Fluid Displaced (m³):
Acceleration Due to Gravity (m/s²):