What is center of buoyancy?

Short Answer:

The center of buoyancy is the point through which the buoyant force acts on a body when it is immersed in a fluid. It is the center of gravity of the displaced fluid volume. In other words, it is the point where the total upward thrust (buoyant force) on the body is considered to act.

In simple terms, when an object floats or is submerged in a fluid, the upward buoyant force acts vertically upward through the center of buoyancy. Its position depends on the shape of the body and the amount of fluid displaced.

Detailed Explanation :

Center of Buoyancy

The center of buoyancy (B) is an important concept in fluid mechanics and naval architecture. It is defined as the center of gravity of the displaced fluid when a body is immersed in a liquid or gas. When a floating or submerged body displaces a certain volume of fluid, the upward buoyant force acts through this point.

The center of buoyancy is not a fixed point—it changes with the orientation and position of the body in the fluid. It determines the stability of floating bodies such as ships, boats, submarines, and buoys.

Mathematically, the buoyant force acts vertically upward through the center of buoyancy and is equal to the weight of the displaced fluid, according to Archimedes’ principle.

Definition and Concept

When a body is immersed in a fluid, it pushes away or displaces a certain volume of fluid. The weight of this displaced fluid acts vertically downward through its center of gravity, while an equal and opposite buoyant force acts vertically upward through the center of buoyancy of the displaced volume.

Hence,

The center of buoyancy is the centroid of the volume of the displaced fluid.

If the body is in equilibrium, the line of action of the buoyant force passes through both the center of buoyancy (B) and the center of gravity (G) of the body. The relative position of these two points determines whether the body is stable, neutral, or unstable when floating.

Location of Center of Buoyancy

  1. For a fully submerged body:
    • The center of buoyancy coincides with the centroid of the displaced volume of the fluid.
    • Its position remains fixed with respect to the body.
  2. For a floating body:
    • The center of buoyancy lies below the waterline (the plane separating the immersed and non-immersed parts).
    • As the body tilts or moves, the center of buoyancy shifts due to the change in shape and position of the displaced fluid volume.

Example:
For a floating ship, if it tilts to one side, the shape of the displaced water changes, and the center of buoyancy moves toward the tilted side to maintain balance.

Relation between Center of Buoyancy and Stability

The stability of a floating body depends largely on the relative positions of the center of buoyancy (B) and the center of gravity (G).

  1. Stable Equilibrium:
    • If the center of buoyancy moves to the same side as the tilt and the line of action of the buoyant force passes through the metacenter (M) above the center of gravity (G), the body returns to its original position.
    • This is known as stable equilibrium.
    • Example: A well-designed ship that returns upright after tilting.
  2. Unstable Equilibrium:
    • If the metacenter (M) lies below the center of gravity (G), the body continues to tilt and may overturn.
    • Example: A poorly loaded ship that capsizes easily.
  3. Neutral Equilibrium:
    • When the metacenter (M) coincides with the center of gravity (G), the body remains in its new position after tilting.

Hence, the position of the center of buoyancy and its movement play a crucial role in determining whether a floating body is stable or unstable.

Mathematical Expression

If   is the volume of the fluid displaced, the buoyant force acting on the body is given by:

where,

  •  = Buoyant force,
  •  = Density of fluid,
  •  = Acceleration due to gravity,
  •  = Volume of fluid displaced.

This buoyant force acts vertically upward through the center of buoyancy (B), located at the centroid of the displaced volume.

Example to Understand Center of Buoyancy

Let’s consider a wooden block floating in water:

  • The block pushes down a portion of water.
  • The weight of the displaced water is equal to the weight of the block (for floating condition).
  • The point through which the upward buoyant force acts is called the center of buoyancy (B).
  • If the block tilts, the displaced water’s shape changes, causing B to shift. This shift helps the block regain balance if the metacenter is above the center of gravity.

Numerical Example:
Suppose a wooden block displaces 0.02 m³ of water. The density of water is 1000 kg/m³.

Thus, the buoyant force acting through the center of buoyancy is 196.2 N.

Factors Affecting the Position of Center of Buoyancy

  1. Shape of the Body:
    • A wider or flatter base increases the volume of displaced fluid, changing the location of the center of buoyancy.
  2. Inclination or Tilt of the Body:
    • When the body tilts, the center of buoyancy shifts laterally to the new centroid of the displaced fluid.
  3. Density of Fluid:
    • Does not directly affect the position but influences the amount of fluid displaced.
  4. Immersion Depth:
    • The deeper the immersion, the higher the buoyant force and the lower the position of the center of buoyancy relative to the body.

Applications of Center of Buoyancy

  1. Ship and Submarine Design:
    • Engineers ensure that the center of buoyancy is correctly located to provide stability and prevent overturning.
  2. Marine Engineering:
    • Helps determine the draft and tilt of floating structures.
  3. Hydraulic and Naval Architecture:
    • Used in analyzing the equilibrium and stability of floating bodies.
  4. Floating Devices:
    • Design of buoys, pontoons, and floating docks relies on proper positioning of the center of buoyancy.
  5. Airships and Balloons:
    • The principle also applies to gases, determining stability in the air.
Conclusion

In conclusion, the center of buoyancy is the point through which the buoyant force acts on a submerged or floating body. It corresponds to the center of gravity of the displaced fluid volume. The position of the center of buoyancy, along with the center of gravity, determines the stability of the body in the fluid. A properly designed structure maintains its balance by ensuring that the center of buoyancy shifts appropriately during tilting, allowing the body to regain equilibrium. This concept is vital in naval, marine, and mechanical engineering applications.