Talha's Physics Academy
Fluid Mechanics - Buoyancy in Liquids and Gases
Q. Define Buoyancy. Describe the characteristics of buoyancy in liquids and gases.
Buoyancy
"Buoyancy is the upward force exerted by a fluid on an immersed or submerged object. It results from the hydrostatic pressure difference between the top and bottom surfaces of the object caused by the weight of the displaced fluid. The magnitude of the buoyant force is precisely equal to the weight of the fluid displaced by the object."
Figure: Upward buoyant force acting on an immersed object due to fluid displacement.
Formula for Buoyant Force
$F_b = \rho_{\text{fluid}} \cdot V \cdot g$
Where:
- $\rho_{\text{fluid}}$ (Density of Fluid): The density of the liquid or gas in which the object is submerged.
- $V$ (Volume of Displaced Fluid): The volume of fluid displaced by the immersed portion of the object.
- $g$ (Acceleration due to Gravity): The acceleration experienced due to Earth's gravitational field ($\approx 9.8 \, \text{m/s}^2$).
Law of Floatation
"A floating object displaces a weight of fluid exactly equal to its own total weight."
Characteristics of Buoyancy in Gases and Liquids
1. Buoyant Force in Gases
Archimedes' principle applies equally to gases (such as air): an object surrounded by air is buoyed up by a force equal to the weight of the displaced air. At normal atmospheric pressure and room temperature, $1 \, \text{m}^3$ of air has a mass of about $1.2 \, \text{kg}$, yielding a weight of approximately $12 \, \text{N}$.
- Sinking in Air: If the mass of a $1 \, \text{m}^3$ object is greater than $1.2 \, \text{kg}$, its weight exceeds the buoyant force, causing it to fall to the ground when released.
- Rising in Air: If an object of this size has a mass less than $1.2 \, \text{kg}$, the upward buoyant force exceeds its weight, causing it to rise in the air. This is why weather and helium/hydrogen-filled balloons ascend. As the balloon rises into higher altitudes where air is less dense, less weight of air is displaced per given volume.
- Ceasing Ascent: When the weight of the displaced air equals the total weight of the balloon, the upward buoyant force matches the balloon's weight, and its upward motion ceases.
2. Buoyant Force in Liquids
The behavior of a submerged object in a liquid depends on the relative magnitude of its weight compared to the upward buoyant force:
- Sinking: If the downward weight of the submerged object is greater than the upward buoyant force ($W > F_b$), the object sinks to the bottom.
- Neutral Buoyancy: If the weight of the object equals the buoyant force acting upwards ($W = F_b$), it remains suspended at any level in the fluid without sinking or rising, much like a fish in water.
- Floating / Rising: If the buoyant force is greater than the weight of a completely submerged object ($F_b > W$), it rises to the surface and floats. For example, when a ship is launched into the sea, it sinks into the water until the weight of the displaced water exactly equals its own weight. As cargo is loaded onto the ship, it sinks deeper into the water, displacing a greater volume of liquid to maintain equilibrium.
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