Buoyancy and Archimedes’ Principle §

Overview §

Buoyancy, a fundamental concept in fluid dynamics, is the upward force exerted by a fluid that opposes the weight of an immersed object. This phenomenon is central to understanding why objects float or sink in fluids.

Archimedes’ Principle §

The Greek mathematician and inventor Archimedes discovered a principle that forms the basis for understanding buoyancy. Archimedes’ Principle states:

An object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

This principle applies to all fluids – gases as well as liquids.

Mathematical Expression §

Mathematically, Archimedes’ Principle can be expressed using the formula:

$F_b=\rho \cdot g\cdot V$

Where:

• $F_b$ = Buoyant Force
• $\rho$ = Density of the fluid
• $g$ = Acceleration due to gravity
• $V$ = Volume of fluid displaced

Applications §

1. Ship Design: Understanding buoyancy is crucial in designing ships and submarines. These vessels must have the right balance between weight and volume to float and maneuver efficiently.
2. Aerostatics: Hot air balloons rely on buoyancy. Heating the air inside the balloon decreases its density compared to the surrounding air, providing lift.
3. Hydrostatic Weighing: Used in determining body composition and density by measuring a person’s mass while submerged in water.

Historical Context §

Archimedes reportedly discovered this principle while taking a bath. He noticed that the water level rose as he got in, which led him to understand the relationship between the volume of the displaced water and the buoyant force.

Examples in Everyday Life §

• An ice cube floating in a glass of water.
• A steel ship floating in the sea despite steel being denser than water.

Test Questions §

1. STARTI [Basic] Question: What does Archimedes’ Principle state about buoyancy? Back: Archimedes’ Principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. ENDI
2. STARTI [Basic] Question: Calculate the buoyant force on an object that displaces 0.5 cubic meters of water. Assume the density of water is 1000 kg/m³ and $g=9.8$ m/s². Back: Using the formula $F_b=\rho \cdot g\cdot V$, the buoyant force is $1000\cdot 9.8\cdot 0.5=4900$ N. ENDI
3. STARTI [Basic] Question: Explain why a steel ship floats despite steel being denser than water. Back: A steel ship floats because its overall density, including the air inside it, is less than the density of water. The ship displaces a volume of water that weighs more than the ship, thus it floats. ENDI

Fluid Dynamics | Physics Principles | Historical Discoveries in Physics