What is submerged body?

Short Answer:

A submerged body is a solid object that is completely or partially covered by a fluid, such as water or oil, in which it is immersed. The fluid exerts an upward buoyant force on the body that opposes its weight.

In simple words, a submerged body is one that remains fully under the surface of a liquid. The balance between the weight of the body and the buoyant force acting on it determines whether it stays at rest, sinks, or rises. Examples include submarines, underwater pipelines, and fish swimming below the water surface.

Detailed Explanation :

Submerged Body

A submerged body is a solid body that is completely immersed in a fluid so that every part of its surface is in contact with the fluid. The fluid can be either a liquid (like water) or a gas (like air). When a body is submerged, the fluid exerts a pressure force on all sides of the body. These pressure forces vary with depth because fluid pressure increases as we go deeper.

According to Archimedes’ Principle, any object submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by the body. This upward force is called the buoyant force or upthrust.

If the weight of the submerged body is exactly equal to the buoyant force, the body remains in equilibrium under the surface. If the weight is greater, the body sinks further, and if it is smaller, the body rises toward the surface.

Classification of Submerged Bodies

Submerged bodies can be classified into two main types depending on the depth of immersion:

  1. Partially Submerged Body:
    • A part of the body is above the fluid surface while the remaining portion is below it.
    • Example: A floating ship or boat.
  2. Completely Submerged Body:
    • The entire body is inside the fluid and does not touch the surface.
    • Example: A submarine operating below the water surface or a diver under the sea.

Forces Acting on a Submerged Body

When a body is submerged in a fluid, mainly two types of forces act on it:

  1. Weight of the Body (W):
    • Acts vertically downward through the center of gravity (G) of the body.
    • It depends on the density and volume of the body and is given by:

where,
= Density of the body,
= Acceleration due to gravity,
= Volume of the body.

  1. Buoyant Force (F_B):
    • Acts vertically upward through the center of buoyancy (B), which is the centroid of the displaced fluid volume.
    • Given by Archimedes’ Principle:

where,
= Density of the fluid.

The net force acting on the body determines its motion or stability in the fluid.

Conditions of Equilibrium for a Submerged Body

For a submerged body, equilibrium depends on the relationship between the weight of the body and the buoyant force.

  1. Neutral Equilibrium:
    • When the weight of the body (W) equals the buoyant force (F_B).
    • The body neither rises nor sinks; it remains at rest within the fluid.
    • Example: A submarine adjusted to neutral buoyancy.
  2. Stable Equilibrium:
    • When the center of gravity (G) lies below the center of buoyancy (B).
    • If the body is disturbed, it tends to return to its original position.
  3. Unstable Equilibrium:
    • When the center of gravity (G) lies above the center of buoyancy (B).
    • On disturbance, the body continues to tilt and may overturn.

Thus, for stability of a submerged body, the center of gravity should be below the center of buoyancy.

Mathematical Explanation

Let,

  •  = Density of the body
  •  = Density of the fluid
  •  = Volume of the body

Then,

  • Weight of body (W):
  • Buoyant force (F_B):

The behavior of the submerged body depends on the relation between   and  :

  1. If   → Body remains in equilibrium (neutral buoyancy).
  2. If   → Body sinks because its weight is greater than the buoyant force.
  3. If   → Body rises toward the surface because buoyant force exceeds its weight.

Examples of Submerged Bodies

  1. Submarine:
    • A classic example of a completely submerged body.
    • The submarine controls its depth using ballast tanks, which adjust its overall density.
  2. Hydrometer:
    • Though partially submerged, it operates on the same principle.
    • Used to measure fluid density.
  3. Diver Underwater:
    • A diver’s body behaves as a submerged body; air in the lungs affects buoyancy.
  4. Pipelines and Marine Structures:
    • Submerged oil or gas pipelines are designed to resist buoyant forces that could lift them.
  5. Underwater Mines or Equipment:
    • Designed to stay submerged using weights and proper balance between buoyant and gravitational forces.

Importance of Studying Submerged Bodies

  1. Marine Engineering:
    Helps in designing submarines, underwater vehicles, and ships with proper buoyancy control.
  2. Hydraulic Engineering:
    Used in analyzing submerged structures like gates, dams, and pipelines.
  3. Fluid Mechanics Applications:
    Essential for understanding fluid pressure, buoyancy, and equilibrium.
  4. Stability Studies:
    Ensures safety of underwater equipment and vessels by maintaining proper center of gravity.
  5. Environmental Studies:
    Helps in studying floating and submerged objects in oceans, such as research devices and buoys.

Example Calculation

A steel ball of volume   is completely submerged in water ( ), and the density of steel is  .

  • Weight (W):
  • Buoyant Force (F_B):

Since  , the ball sinks in water.

Conclusion

In conclusion, a submerged body is an object that is completely immersed in a fluid and experiences both buoyant force and gravitational force. The equilibrium and stability of the body depend on the relationship between its weight and the buoyant force. When the density of the body equals the density of the fluid, it remains neutrally buoyant. If its density is higher, it sinks, and if lower, it rises. Understanding submerged bodies is essential for marine, mechanical, and fluid engineers to design stable underwater systems and floating vessels.