Buoyancy

Buoyancy

When a body is partially or fully immersed in a fluid, it displaces a certain amount of fluid. The displaced fluid exerts an upward force on the body. The upward force exerted by a fluid that opposes the weight of an immersed object in a fluid is called upthrust or buoyant force and the phenomenon is called buoyancy.

Archimedes principle:

It states that when a body is partially or wholly immersed in a fl uid, it experiences an upward thrust equal to the weight of the fluid displaced by it and its upthrust acts through the centre of gravity of the liquid displaced.

upthrust or buoyant force = weight of liquid displaced.

Law of floatation

It is well-known that boats, ships, and some wooden objects move on the upper part of the water, we say they fl oat. Floatation can be defined as the tendency of an object to rise up to the upper levels of the fluid or to stay on the surface of the fluid.

The law of floatation states that a body will float in a liquid if the weight of the liquid displaced by the immersed part of the body equals the weight of the body. For example, a wooden object weighs 300 kg (about 3000 N) floats in water displaces 300 kg (about 3000 N) of water.

EXAMPLE 7.8

A cube of wood floating in water supports a 300 g mass at the centre of its top face. When the mass is removed, the cube rises by 3 cm. Determine the volume of the cube.

Solution

Let each side of the cube be l. The volume occupied by 3 cm depth of cube,

V=(3cm) × l² = 3l²cm

According to the principle of floatation, we have

Vρg = mg ⇒ Vρ = m

ρ is density of water = 1000 kg m^-3

(3l² × 10^-2m) × (1000 kgm^-3)=300 × 10^-3 kg

l = 10 × 10^-2m = 10 cm

Therefore, volume of cube V = l³ = 1000 cm³

Examples of floating bodies:

i) A person can swim in sea water more easily than in river water.

ii) Ice floats on water.

iii) The ship is made of steel but its interior is made hollow by giving it a concave shape.