7.1 Weight and upthrust - why do some objects float in a fluid and others sink?

Why do objects float or sink in fluids?

When an object is partially or wholly submerged in a fluid it experiences a force from all directions due to the pressure of the fluid (gas or liquid).

This force acts at right angles to the whole of the surface of an object.

Also, the pressure increases with depth.

But, because pressure increases with depth, an object immersed in a liquid experiences a greater force at its bottom compared to the top - this is illustrated in the diagram below of a solid block immersed in a liquid.

The net resulting force on the object, acting in an upward direction, is called the upthrust an is equal to the weight of fluid displaced.

Height (or depth) h2 corresponds to the higher pressure p2 at the greater depth at the bottom of the block.

Height (or depth) h1 corresponds to the lower pressure p1 at a shallower depth at the top of the block.

The difference in height (depth) = ∆h, which corresponds to the difference in pressure ∆p.

Because of the difference in pressures, the immersed object experiences a resultant force upwards is called the upthrust - due to the higher fluid pressure at the bottom of the object compared to the lower pressure at the top of the object.

The upthrust force is equal to the weight of the fluid displaced by the object

(see the diagram above).

The displaced fluid equals the volume of the object that is actually in the fluid - partially or completely immersed in the fluid.

If an object floats the weight of the fluid displaced equals the weight of the object floating, which equals the upthrust.

If an object sinks, its weight is greater than the weight of fluid displaced, its weight is greater than the upthrust.

This is why a helium balloon floats and rises in air. Helium is less dense than air (~0.18 kg/m³).

Our average density must be less than water, because we can 'float'.

Porous balsa wood (density 340 kg/m³) floats on water -

( see 'floating-sinking' experiments in section 7.2.)

 

SO, the deciding factor is the comparison of the densities of the object and the fluid.

(i) If the density of the object is greater than that of the fluid, it will sink to the bottom - complete immersion.

An object that is more dense that the fluid it is placed in, cannot displace enough fluid to equal its weight.

Brick, iron objects are more dense than water, so sink in it.

For objects more dense than the fluid, the weight of the object is always larger than the upthrust and so it cannot float and will sink.

But beware, the shape of the object can mean high density materials can float.

Iron is nearly eight times more dense than water, but shape it into a boat and it floats.

This is because the boat shape allows the displacement of water equal to the weight of the iron ship, so it floats!

 

(ii) If the density of the object is exactly the same as the liquid, the object neither moves up or down and will float with its upper surface coincident with the surface of the liquid - wholly immersed BUT floating.

I did find a block of wood with a density of 1000 kg/m³, and it did exactly as predicted - see 'kitchen' experiment D.

 

(iii) If the density of the object is less than the density of the fluid it is immersed in, then the object will float upwards to the surface and some of the object will be above the surface of the liquid - partial immersion.

An object that is less dense than the fluid it is put in, weighs less than the volume of fluid equal to its own volume.

Consequently, the object can only displace a volume of fluid equal to its own weight before it can be completely submerged - so it floats because the objects weight is equal to the upthrust.

Ice has density of 920 kg/m³ and floats on water (density 1000 kg/m³).

Ice sinks in petrol or diesel whose densities are only 775 and 830 kg/m³ respectively.

 

You are used to the idea of objects floating in water, but helium balloons float in air!

 The weight of the helium balloon is far less than the weight of the volume of air it displaces.

 Therefore the upthrust from the air is greater than the weight of the balloon which will rise - as you will have observed as you see a 'freed' helium balloon rise high into the atmosphere.

Helium balloons are used by weather scientists and weather forecasters to get information on the weather conditions at high altitudes.

Since atmospheric pressure decreases with height, the imbalance between the balloon's internal and external pressures results in the helium balloon expanding.

Density is very important property to know about a material, but shape of object is important too.

e.g. if the average density of an object is less than that of water (~1000 kg/m³) it floats

if the average density of an object is more than that of water it sinks!

In general: if the object has an average density < fluid it floats and if the average density of the object is > fluid it sinks.

Note the phrase 'average density' - this is one way of explaining e.g. why a steel boat floats!

Because of the shape of the boat, the average density of the boat (steel + contents + air) is less than water.

Therefore the ship can displace a volume of water equal to its weight, without sinking and can therefore float.

This must be appreciated using explanation is to do with upthrust and displaced of fluid as described above.

Of course, if the boat develops a leak, the less dense air is displaced by the more dense water and when the ship fills up, due to the steel, the average density is greater than water and the ship sinks!

See also FORCES 6. Pressure in liquid fluids and hydraulic systems