What Is Buoyancy?

Have you ever wondered why some objects float while others sink? This phenomenon is governed by a fascinating physical principle called buoyancy. From the way ships stay afloat to how fish maneuver underwater, buoyancy plays a crucial role in our daily lives and in nature. In this article, we will explore the buoyancy definition, buoyancy meaning in physics, its governing laws, the force of buoyancy formula, and the concept of the centre of buoyancy. Additionally, we will discuss buoyancy in biology, and its significance in physics. By the end of this article, you’ll have a deeper appreciation for the power of buoyancy and its role in shaping the world around us.

What Is Buoyancy?

Let’s start with the buoyancy definition. Buoyancy is the upward force exerted by a fluid (liquid or gas) on an object immersed in it (Fig.1). This force acts against gravity and determines whether an object will float, sink, or remain suspended in the fluid. The concept of buoyancy was first explained by Archimedes, an ancient Greek mathematician, in what we now call the buoyancy law or Archimedes’ Principle.

Figure 1- Buoyancy: The Upward Force in Fluids[1]

Buoyancy Meaning in Physics

The buoyant force ( ​) is the upward force exerted by a fluid on an object submerged in it. It can be derived using pressure differences (Fig.2) in a fluid and Archimedes’ principle.

Figure 2- Proofing the Buoyancy law by using the pressure differences[2]

Buoyancy is caused by differences in pressure acting on opposite sides of an object immersed in a static fluid. A typical situation:

• The pressure on the bottom of an object is greater than the top (since pressure increases with depth).
• The force on the bottom pushes up and the force on the top pushes down (since force is normal to the surface).
• The direction of the net force due to the fluid is upward.

Step 1: Understanding Pressure in a Fluid

Fluid pressure increases with depth according to the equation:

where:

• P = pressure at depth h,
• P0​= atmospheric pressure at the surface,
• ρ = fluid density,
• g = gravitational acceleration,
• h = depth in the fluid.

Step 2: Pressure Difference on the Object

Consider an object submerged in a fluid with height h:

Top surface at depth ​ has pressure:

Bottom surface at depth ​ has pressure:

Step 3: Net Upward Force (Buoyant Force)

The force exerted by a fluid on a surface is:

where 𝐴 is the area of the object’s surface.

The net upward force (buoyant force) is the difference between the forces on the bottom and top:

Since the volume of the submerged part of the object is

If we substitute V into  , the buoyant force can be written as follows:

This equation confirms Archimedes’ principle, which states that the buoyant force is equal to the weight of the displaced fluid. Buoyancy plays a crucial role in buoyancy-driven flow, where fluid motion is caused by density variations, often due to temperature differences. Worth mentioning the to simplify buoyancy-driven flow calculations, the Boussinesq assumption is often applied

Buoyancy Law: Archimedes’ Principle

The buoyancy law is formally stated as Archimedes’ Principle: “A body wholly or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.” This principle is the foundation for understanding why boats float, why some objects sink, and why helium balloons rise in the air. The Fig.3 shows an experiment which effectively explains how buoyant force is equal to the weight of the displaced liquid.

Figure 3- Archimedes’ Principle: The Relationship between Buoyant Force and Displaced Water[1]

Force of Buoyancy Formula

The buoyant force on an object (See Fig.3) equals the weight of the fluid it displaces. In equation form, Archimedes’ principle is

Where  is the buoyant force and  is the weight of the fluid displaced by the object. is Density of the fluid, and  is volume of displaced fluid.

Considering the buoyancy force in some CFD is very crucial and have widely applications. For instance, during Nucleate Boiling CFD Simulation (Fig.4) which is a vital heat transfer process where vapor bubbles form, grow, and detach from a heated surface submerged in liquid. As these bubbles grow, they detach and rise through the liquid due to the buoyancy force.

Figure 4– Nucleate Boiling CFD Simulation, ANSYS Fluent Training

Apparent Weight and Buoyancy Formula

The difference between the buoyant force and the actual weight of an object is called the apparent weight of the object. The apparent weight is always less than the actual weight of the object (Fig.5). When an object is submerged in a fluid, its apparent weight is reduced due to the buoyant force acting on it. In fact, the apparent weight is the weight of the object in the fluid.

Figure 5 – Apparent Weight vs. actual weight[3]

The relationship between the real weight, buoyant force, and apparent weight is given by the following formula:

Where:

• = Apparent weight of the object in the fluid
• W= Actual weight of the object in air. W=mg, where m is mass and g is gravitational acceleration)
• is the buoyant force

Types of Buoyancy

Generally, there are three types of buoyancy (Fig.6):

1. Negative Buoyancy:  An object is negatively buoyant when it is denser than the fluid it displaces. The object will sink because its weight is greater than the buoyant force.
2. Neutral Buoyancy: An object is neutrally buoyant when its density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink or rise. An object that has neutral buoyancy will neither sink nor rise.

• Positive Buoyancy: An object is positively buoyant when it is lighter than the fluid it displaces. The object will float because the buoyant force is greater than the object’s weight.

Figure 6- Three types of buoyancy[4]

The buoyancy of water is the upward force exerted by water on objects submerged in it. Learn to simulate and optimize the movement of hybrid buoyancy-driven underwater gliders using dynamic mesh CFD simulation in ANSYS Fluent, focusing on buoyancy, hydrodynamics, and extended range capabilities (Fig.7). This training is ideal for improving underwater glider performance for oceanographic research, environmental monitoring, and marine engineering applications.

Figure 7– Underwater Glider Movement Using Dynamic Mesh CFD Simulation, ANSYS Fluent Training

The Centre of Buoyancy

The canter of buoyancy is the centroid of the displaced fluid volume and represents the point where the buoyant force acts upward, opposing gravity. In contrast, the center of gravity is the point where the object’s weight is concentrated and acts downward. While the center of buoyancy depends on the shape and volume of the submerged portion, the center of gravity is determined by the object’s overall mass distribution. Fig.8 depicts why the canter of buoyancy is different than the center of gravity.

• When an object is partially submerged, the displaced fluid volume is asymmetrical, leading to a difference between the two centers.
• When an object is fully submerged, the displaced volume is symmetric, often causing the centers to coincide, provided the object has uniform density.

Figure 8- The difference between the centers of buoyancy and gravity

Metacenter Point and Stability

The metacenter (M) is a crucial point (Fig.9) in fluid mechanics and naval architecture, determining the stability of floating objects. It is defined as the intersection of two lines:

1. A vertical line passing through the center of buoyancy (B), which is the centroid of the displaced fluid volume.
2. A vertical line (imaginary vertical line) passing through the geometric center of the body.

Figure 9- Illustration of Metacenter Point[5]

It should be noted that when a floating body tilts, the center of buoyancy shifts as the submerged volume changes (Fig.10).

Figure 10- Centre of Buoyancy

The stability of a floating body is determined by the metacentric height (GM), which is the vertical distance between the center of gravity (G) and the metacenter (M):

• Stable Equilibrium: If M is above G, the buoyant force creates a restoring moment, bringing the body back to equilibrium (Fig.11-a).
• Unstable Equilibrium: If M is below G, the buoyant force causes further tilting, making the body unstable (Fig.11-b).
• Neutral Equilibrium: If M coincides with G, the body remains in its tilted position without returning or capsizing (Fig.12).

For practical applications, increasing the metacentric height improves stability but may cause uncomfortable oscillations. Naval architects carefully design ships and floating structures to ensure an optimal balance between stability and maneuverability.

Figure 11- Stable Equilibrium (a) vs. Unstable Equilibrium (b)[6]

Figure 12- Neutral Equilibrium[5]

For practical applications, to understand the Metacenter point and stability conception, you can use the “Two-phase Bubbly Flow CFD Simulation, ANSYS Fluent Training” (Fig.13). This CFDL products teaches how to simulate gas bubbles rising through liquid, highlighting the interaction between buoyancy and drag forces that cause the bubble to deform from a sphere shape.

Figure 13– Two-phase Bubbly Flow CFD Simulation, ANSYS Fluent Training

Conclusion

Buoyancy is a fundamental concept that explains why some objects float while others sink, based on the buoyancy definition. It is the upward force exerted by a fluid, explained by the buoyancy law or Archimedes’ Principle. The force of buoyancy formula quantifies this force, helping us understand the buoyancy of water and other fluids. By exploring the buoyancy meaning in physics and the center of buoyancy, we can analyze the stability of submerged objects. Whether calculating forces or simulating buoyancy-driven flows, these concepts are crucial for various applications in science and engineering.

FAQs

1. What is the buoyancy definition?

Buoyancy is the upward force exerted by a fluid on an object immersed in it, which opposes the object’s weight and determines whether the object will float, sink, or remain suspended.

2. What is the buoyancy law?

The buoyancy law, also known as Archimedes’ Principle, states that an object wholly or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

3. What is the canter of buoyancy?

The center of buoyancy is the centroid of the displaced fluid volume and represents the point where the buoyant force acts upward, opposing gravity.

4. What does buoyancy meaning in physics refer to?

In physics, buoyancy refers to the upward force exerted by a fluid on an object submerged in it, which counteracts the object’s weight and determines its movement in the fluid.

5. How is the buoyancy formula applied in CFD simulations?

The buoyancy formula is crucial in CFD simulations, especially in applications like buoyancy-driven flows, where the buoyant force plays a key role in fluid movement and heat transfer processes.