# The Law Of Floatation

## Floatation

Ships, canoes and ferry boats move on the upper part of the water bodies, we say they float. It may happen that due to accident or overloading they sink. Example Titanic went to the bottom of North Atlantic Ocean after hitting the larger iceberg.

A balloon filled with a lighter gas such as hydrogen will keep rising up when released from the hand and a hot air balloon will keep rising as well with the people in carriage once the air in the balloon has been heated and expanded.

Therefore 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 opposite of floatation is sinking and can be defined as the tendency of an object to go to the lower levels of the fluid.

## The law of floatation

The law of floatation states that a floating body displaces its own weight of the fluid in which it floats.

This means if a log of 200kg (2000N) floats in water displaces 200kg (2000N) of water, if the same log is placed in other liquid and be able to float it will displace the same 200kg of fluid in which it floats.

## Conditions for objects to float

1. The average density of the object should be less than the density of the fluid in which the object has to float.

Example, a ship is very heavy but it floats because it is hollow inside it contains air, this causes its average density to be lower than that of water.

2. The upthrust force of the fluid on the object must be equal to the total weight of the object (law of floatation).
Example, a coin will sink to the bottom when placed on the surface of the water, this is because the up thrust of water on the coin is less than its weight.
3. The volume of an object submerged must be large so as to displace a large amount of fluid.

## Application of law of floatation in everyday life:

In transportation by waterways

The law of floatation is applied in all vessels which travel by waterways that include ships, submarines and ferry boats.

In transportation by airways

It is also applied in some vessels which travel by airways such as hot air balloon and airship.

In decoration

Balloons of different colors and shapes are filled with lighter gas so that will float in the air.

In measurement of specific gravity of liquids

Hydrometer is an instrument which is used to measure the specific gravity of liquids, and in its operation, it employs the law of floatation.

Other uses include making of bulges and transportation of logs down the river.

## Ships

A ship is like an iron bowl floating in water, although iron is denser than water the bowl does not sink. Being hollow it contains air causing its average density to be lower than that of water.

Sand can be poured into the bowl but it will keep floating, in the excess mass of sand the bowl will sink, in the ship we call it overloading.

Ships are made of metals such as steel or aluminium alloy which is denser than water, so to make it be able to float it is hollow and filled with air making the average density lower than the density of water even when it is loaded with her cargo.

Ship travels in different densities of water, sea water or fresh water, (hot or cold)

So by changing waterways ship can displace more or less water in which it floats that means it may gain or lose up thrust. If the upthrust becomes lower than its own weight the ship sinks.

So for safe loading of the ship under different sea conditions, plimsol lines are provided.

Plimsol lines are lines which show a maximum height of the ship that should be under water.

Plimsol lines are also referred as plimsol marks.

## Submarine

The submarine is a ship which can travel deep underwater and also at the surface of the water, it owes its ability to dive and come up to the law of floatation.it contains ballast tanks at either side which are filled with water when it has to dive and are empty when it has to come up. The tanks are filled and emptied by special pumps.

## Hot air balloon

To watch the animals at Serengeti helicopters is noisy and it would scare the animals. A plane is faster and it would pass without clear vision but hot air balloon will do.

Hot air balloon consists of three parts, the balloon, the burner and the basket.

The burner uses the propane gas to heat up the air in the balloon as the air in the balloon gets hot it expands, its density becomes lower than the surrounding air so it raises.

To get the balloon down the pilot can open a parachute valve at the top of the balloon causing cold air to enter in the balloon and decrease the temperature inside the balloon so the density; also the pilot can let the air inside the balloon to cool itself by burning less fuel.

## Air ship

Airship uses a lighter gas such as helium, hydrogen or hot air to rise up, and manoeuvring is done by means of a propeller attached to it, for example, a cabin.

The lighter gas gives it lifting and the engine is used to propel it.

## Density and relative density

The concept of density.

The figure below shows two identical flasks one filled with water to 250cm3 mark and the other filled with kerosene to the same 250cm3 mark, when measured in electronic balance the flask filled with water is found to be heavier than that filled with kerosene why? The answer is in finding the mass per unit volume of kerosene and water in respective flasks.

The mass of the flask filled with water is 330g, and the mass of flask filled with kerosene 280g, the empty flasks were measured and found to be 80g, therefore, the mass of water only is 250g and kerosene only is 200g.

Mass per unit volume of water is 250g/  250cm3 this is 1g/cm3.

Mass per unit volume of kerosene is 200g/ 250cm3this is 0.8g/cm3.

The results 1g/cm3 and 0.8g/cm3 are the densities of water and kerosene respectively.

Therefore the density of a substance is the mass per unit volume of a given substance.

The SI unit of density is kilogram per meter cubic (kg/m3) also gram per centimeter cubic (g/cm3). The symbol for density is rho (ρ) ρ=mass/volume.

## Density bottle

The density bottle (pycnometer) consists of ground glass stopper with a fine hole through it.

The function of the fine hole in a stopper is that, when the bottle is filled and the stopper is inserted, the excess liquid rises through the hole and runs down outside the bottle, by this way the bottle will always contain the same volume of whatever the liquid is filled in provided the temperature remains constant.

Density bottle is used to measure density and relative density, relative density is comparison of one density to another, thus a density of a given volume of a substance to a density of equal volume of referenced substance, for example a ratio of a density of a given volume of substance to a density of an equal volume of water, this is referred to a relative density of a given substance or Specific gravity of a given substance. The term specific gravity is used when the reference substance is water.

Measurement of density of the liquid by relative density bottle

• The mass of bottle is found when dry and empty
• The bottle is then filled with the liquid density is to be determined
• The stopper is then inserted causing the liquid to overflow
• The bottle is dried up by using blotting paper
• The mass of the liquid and the bottle is found
• Density is found from the collected data

Mass of empty bottle=m1g

Volume of liquid in the bottle=V

mass of bottle and the liquid=m2g

mass of liquid only=(m2-m1)g

density= mass /volume

density= .(m2-m1)g/V

The volume of the bottle is known, usually 25ml, 30ml or 50ml

## RELATIVE DENSITY

The relative density of a substance is the ratio of the density of the substance to the density of water.

Or

The relative density of a substance is the ratio of the mass of any volume of the substance to the mass of an equal volume of water.