#### Buoyancy-Archimedes Principle, Physics tutorial

Concepts of Buoyancy:

Buoyancy is the concept which explains floatation of the object in fluids usually. Buoyancy has thus got to do with density of the object. The ability of the object to float when it is placed in the fluid is known as buoyant force. For instance, the swimmer experiences this thought of buoyancy, floatation in water as he/she swims in it. Water supports body of swimmer that makes him appear to weigh less. This is case with any liquid. This is due to when you go in water, you displace some liquid and liquid applies upthrust on you. This is also true of gases but as body would displace the very smaller weight of air, upthrust is much less.

What happen to body in given three conditions:

If its weight (W) is greater than upthrust (U)

Body sinks. For instance the stone placed in water.

W > U⇒ Sinking of object

• Now, if upthrust (U) is greater than weight (W)

You are right if you say body rises. For instance, if the helium-filled balloon is left in air, balloon rises

U > W⇒ Rising of object

• If weight (W) of object balances if is equal to upthrust (U)

Objects float in fluid. For example, a boat or a ship floating on sea.

W = U⇒ floating of object

These three conditions describe,

• Archimedes' Principle and
• The law of floatation.

Archimedes' Principle:

Archimedes' Principle defines that when the body is either partly or completely immersed in the fluid, it will experience the upthrust equal to weight of fluid displaced. Assume weight of body in air is W, when body is now immersed in the fluid partly or completely, it experiences the upthrust (U). New weight registered by scale (A) is now less than that of air (W). A is known as apparent weight that is it seems to be weight of object. Relationship between apparent weight (A), upthrust (U) and actual weight in air (W) is given below.

Weight in air (W) = Apparent weight in fluid (A) + upthrust (U) experienced.

W = A + U

Thus The upthrust U = Weight in air (W) - Weight in fluid (A) U = W - A.............Eq.1

Theoretically, weight of the body in air is equivalent to apparent weight as displaced air will apply the upthrust but typically, this upthrust is very small compared with weight that it can be ignored. Upthrust on body is equivalent to weight of fluid displaced.

Relative Density:

When we compare density of the substance with density of water then we are talking about relative density of that substance. Or we can say, we are saying how many times this substance is as heavy as water.

By definition,

Relative Density of the substance = Density of substance/ Density of water

Consider ρr = Relative density of substance

ρ = Density of the substance

ρ = Density of water

Thus, expression for relative density is

ρr = ρ/ρw

ρ = ρrρw

The actual density of the substance is equivalent to relative density of substance times the density of water. It can be noted from the definition of relative density, that it has no unit as it is a ratio.

Application of Archimedes' Principle:

1) Ship:

i) Ship would sink to the certain level until weight is equal to buoyant force.

ii) To prevent this, a plimsoll line is marked on hull of all ships to demonstrate depths which are safe for them to navigate.

2) Submarine:

i) When afloat, water is driven out from ballast tanks by compressed the larger buoyant force.

ii) Submarine can submerge to the depth where buoyant to the depth where buoyant force is equal to weight.

3) Hot-air Balloons:

i) When envelope of the balloon is filled with the gas of lower density than air like hydrogen, helium or hot air, its weight decreases.

Total weight of balloon = weight of fabric + weight of the gas in envelope.

ii) Balloon experiences the buoyant force = (volume of balloon) X (density of surrounding air) X g

iii) If buoyant force is greater than total weight of balloon, it would be accelerated upwards by the net upwards force.

The Law of Floatation:

The law of floatation defines that floating body displaces the own weight of liquid in which it floats. This is actually the special case of Archimedes' Principle and it is condition in which weight of body is accurately balanced by upthrust from fluid. This thus implies that if the body is to float, it should displace its own weight of fluid in which it is floating. If the body is floating in the liquid, body is probable to float with certain amount of itself above fluid or it is completely immersed. The floating ice block in water and floating balloon in air are typical examples.

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