Key Stage 3 science · Physics – Motion and forces

KS3 pressure in fluids: air pressure, upthrust and floating

In Key Stage 3, children learn that pressure measures how concentrated a force is: the force divided by the area it acts on. They apply this to solids, then to fluids (liquids and gases). Air pressure falls as you go higher, pressure in a liquid increases with depth, and the difference in pressure on the top and bottom of an object creates upthrust, which decides whether it floats or sinks.

Pressure in fluids, floating and sinking, explained

Pressure is how much force acts on each unit of area, so pressure = force ÷ area. It is measured in newtons per square metre (N/m²), which is called the pascal (Pa), or sometimes newtons per square centimetre (N/cm²). Spreading a force over a larger area gives a smaller pressure, which is why snowshoes stop you sinking in and why a knife is sharpened to a thin edge. Pressure from a fluid always acts at right angles, which scientists call normal, to any surface it touches.

Air is a fluid, and the atmosphere has weight. Standing at sea level, you have the whole column of air above you pressing down, and the pressure is about 100,000 Pa, roughly 10 N on every square centimetre. It acts in every direction, not just downward, so it presses on the sides and underneath as well as the top. As you climb a mountain or fly in an aeroplane there is less air above you, so its weight is smaller and the atmospheric pressure decreases. That is why ears can pop in a plane and why the air is thin on high mountains.

In a liquid the pressure increases with depth, because there is a greater weight of liquid above. Water at the bottom of a deep pool pushes harder on your body than water near the surface, which is why divers feel pressure in their ears. That is why dams are built thicker at the bottom. The pressure at a given depth acts in all directions and depends on the depth, not on the width or shape of the container.

Pressure also explains floating and sinking. A submerged object has liquid pressing on its bottom surface at a greater depth than on its top, so the push up is bigger than the push down. The resultant is an upward force called upthrust. If the weight is greater than the biggest upthrust the liquid can give, the object sinks. If not, it floats, settling at the level where the upthrust exactly equals its weight. Many schools also compare the density of the object with the density of the liquid to predict which will happen: a ship floats because it pushes aside a lot of water for its weight.

Words your child will hear

Pressure: The force acting on each unit of area, found by force ÷ area.
Pascal (Pa): The unit of pressure: 1 newton on each square metre. 10,000 Pa equals 1 N/cm².
Fluid: A liquid or a gas, something that can flow.
Atmospheric pressure: The pressure caused by the weight of the air above, which gets less as you go higher.
Upthrust: The upward force from a fluid on an object placed in it.
Normal: At right angles to a surface. Fluid pressure acts normal to the surfaces it touches.
Density: How much mass there is in a given volume of a material.

What the National Curriculum says

The programme of study for Key Stage 3 says:

Pupils should be taught that atmospheric pressure decreases with increase of height as the weight of air above decreases with height
Pupils should be taught about pressure in liquids, increasing with depth; upthrust effects, floating and sinking
Pupils should be taught about pressure measured by the ratio of force over area – acting normal to any surface

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A person weighing 600 N stands on two feet, each with a sole area of 200 cm². Find the pressure on the ground in N/cm² and in pascals. Then compare it with the pressure under a stiletto heel of area 1 cm² carrying the full weight on one heel.

Find the total area touching the ground. Two feet of 200 cm² each make 400 cm².
```
area = 2 × 200 = 400 cm²
```
Use pressure = force ÷ area. The force on the ground is the person’s weight, 600 N.
```
pressure = 600 N ÷ 400 cm²
         = 1.5 N/cm²
```
To change to pascals, remember that 1 N/cm² = 10,000 Pa, because there are 10,000 cm² in 1 m².
```
1.5 × 10,000 = 15,000 Pa
```
For the heel, the same 600 N acts on only 1 cm².
```
600 N ÷ 1 cm² = 600 N/cm²
= 6,000,000 Pa
```
Compare: the heel pressure is 600 ÷ 1.5 = 400 times bigger, simply because the area is 400 times smaller. The weight has not changed.

Standing on two feet the pressure is 1.5 N/cm², or 15,000 Pa. Under a single 1 cm² heel it is 600 N/cm², or 6,000,000 Pa, which is 400 times greater, because the same force acts on a much smaller area.

Common mistakes and how to help

Thinking heavy objects sink and light ones float

Everyday examples are like a pebble sinking and a feather floating, so weight seems the only thing that matters.

What helps: Show a steel pin sinking and a huge steel ship floating. What decides it is whether the upthrust can balance the weight, which depends on how much liquid the object pushes aside, and on how spread out the material is.

Believing air pressure only pushes downward, or that suction pulls

Children feel the weight of things pressing down and imagine a straw or a sucker pulling things up.

What helps: Atmospheric pressure acts in all directions. When you drink through a straw you lower the pressure inside it, and the air pressure on the drink pushes the liquid up. Nothing is really pulling.

Thinking pressure and force are the same thing

In everyday speech, “pressure” and “force” both just mean pushing hard, so the two words get swapped.

What helps: Pressure depends on area as well as force. A drawing pin pressed with a thumb has the same force at its head and at its point, but the pressure under the tiny point is vastly greater.

Thinking pressure in water depends on how much water there is

More water sounds like more weight and so more pressure, so a lake seems as if it should push harder than a bath.

What helps: At the same depth, the pressure from the liquid is the same in a bath and in a lake. A narrow tall tube and a wide tank filled to the same depth give the same pressure at the bottom.

How to help at home

Footprint pressure. Draw round your child’s bare foot on squared paper and count the squares to estimate the area in cm². Use roughly 10 N for every kilogram to find the weight, and work out the pressure on one foot and on two feet. Then work out the pressure when they stand on tiptoe on one foot, using a smaller area.
Float or sink predictions. Collect a dozen safe objects such as a cork, a coin, a plastic spoon, an orange and a grape. Predict first, then test in a bowl or sink of water. Try a lump of modelling clay as a ball, then shaped into a boat, and ask why the shape matters.
The egg in salt water. Put an egg in a tall glass of tap water, where it sinks. Stir in salt, a spoonful at a time, until the egg floats. Ask why salty water pushes up harder. Do this over the sink and wipe up spills.
Feel the depth. At a swimming pool, with an adult close by, notice the pressure on your ears at the bottom of the shallow end compared with the surface. Stay within your depth, and never leave a child alone near water.
Straw investigations. Drink through a straw, then put a finger over the top end of a straw in a glass and lift. Ask why the water stays in the straw. Talk about the air pushing up on the open bottom end of the straw.

Leads on to

Key Stage 4: Forces, fields, work done and pressure
Key Stage 4: Motion, acceleration and road safety