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Pressure, pressure in liquids, upthrust and floating, and atmospheric pressure, built up from everyday examples.
Picture two people walking across soft sand. One wears trainers and the other wears high heels. The person in heels sinks in with every step, even though they might weigh less. The difference is not how heavy they are. It is how that weight is spread out.
That spreading is called pressure. Pressure tells you how concentrated a force is. A big force on a tiny area gives a big pressure. The same force spread over a large area gives a small pressure.
Here is a picture to hold on to. Press your thumb into a bag of flour, then press your whole flat hand with the same push. The thumb makes a deep dent. The flat hand hardly marks it. Same push, different area, different pressure.
Pressure also explains why your ears hurt when you dive to the bottom of a pool, why a ship made of steel can float, and why a crisp packet puffs up on a plane. Water and air are both fluids, which means they can flow, and they press on everything in them.
By the end of this lesson you will be able to do three things. First, calculate pressure from a force and an area. Second, explain why pressure in water grows with depth, and at Higher tier calculate it. Third, explain floating, sinking and the fall in air pressure as you go up.
Pressure is the force acting on each unit of area. In words: pressure = force ÷ area. In symbols: p = F ÷ A. You use it whenever a force is pressing on a surface.
The units are important. Force is in newtons, N, and area is in square metres, m². Pressure is then in pascals, written Pa. One pascal is one newton on every square metre, so 1 Pa = 1 N/m².
The same force on a smaller area gives a bigger pressure, because you are dividing by a smaller number. That is why a sharp knife cuts and a blunt one does not. The sharp edge has a tiny area, so the same push makes a huge pressure.
The opposite is also true. A bigger area gives a smaller pressure. Snowshoes spread your weight over a wide area, so you do not sink. A tractor has wide tyres for the same reason, so it does not sink into a muddy field.
Now try the numbers. A force of 600 N pushes on an area of 0.05 m². Pressure = 600 ÷ 0.05 = 12 000 Pa. Make the area smaller and the pressure rises, and that is the main idea in this part of the topic.
Most pressure questions give you two of the three quantities and ask for the third. Write the equation, put the numbers in, work it out and add the unit. Stay calm and take it one step at a time.
To find the pressure, divide: p = F ÷ A. A force of 200 N on an area of 0.5 m² gives 200 ÷ 0.5 = 400 Pa. Dividing by 0.5 is the same as doubling, so the answer is bigger than the force.
To find the force, multiply: F = p × A. A pressure of 3000 Pa on an area of 0.4 m² gives a force of 3000 × 0.4 = 1200 N. To find the area, divide: A = F ÷ p.
Watch the units of area. Pressure in pascals needs the area in square metres. If an area is given in cm², divide by 10 000 to change it to m². For example, 500 cm² is 0.05 m².
Check your answer makes sense. A narrow area should give a large pressure and a wide area a small one. If you end up with a tiny pressure for a tiny area, you probably multiplied when you should have divided. A good habit is to estimate first, because a big force on a tiny area should give a very large number.
A liquid presses on everything in it. A fluid is anything that can flow, which means liquids and gases. If you dive down in a pool, you can feel the water pressing on your ears.
Pressure in a liquid acts in all directions. It pushes on the sides, the top and the bottom of a diver. It always acts at right angles to any surface it touches, so water pushes outwards on the walls of a bucket.
Pressure in a liquid increases with depth. The reason is the weight of the liquid above. At the surface there is almost no water above you. At the bottom of a deep pool there is a whole column of water pressing down on you.
This is why a dam wall is much thicker at the bottom than at the top. It is also why a hole low down in a plastic bottle of water squirts further than a hole near the top. The lower hole has more water above it. Submarines and deep-sea divers need strong walls and suits for the same reason.
Pressure also depends on the density of the liquid. Density is how much mass there is in each cubic metre. A denser liquid, such as sea water, gives a bigger pressure at the same depth than a less dense liquid, such as oil.
At Higher tier you work out the pressure caused by a column of liquid. In words: pressure = height × density × gravitational field strength. In symbols: p = h × ρ × g. The Greek letter ρ, called rho, is the symbol for density.
The height h is the depth of the liquid above the point, in metres, m. The density ρ is in kilograms per cubic metre, kg/m³. Take g = 10 N/kg. The pressure comes out in pascals, Pa.
For water, the density is 1000 kg/m³. At a depth of 4 m the pressure from the water is 4 × 1000 × 10 = 40 000 Pa. At 10 m it is 100 000 Pa, and the straight line on the graph shows that.
You can rearrange the equation. To find the depth, h = p ÷ (ρ × g). A pressure of 30 000 Pa in water gives h = 30 000 ÷ (1000 × 10) = 3 m. Divide by both the density and g, not just one of them.
Notice that every extra metre of depth adds the same amount of pressure. In water that is 10 000 Pa for each metre. If the liquid is less dense, such as oil at 800 kg/m³, each metre adds less pressure.
Why does a beach ball pop back up when you push it under water? The water pushes up on it. The upward force a fluid exerts on an object in it is called upthrust.
Upthrust comes from the difference in pressure. The bottom of a submerged object is deeper than the top, so the pressure on the bottom is greater. The upward push on the bottom is bigger than the downward push on the top, so there is an upward force left over.
The size of the upthrust equals the weight of the fluid that the object pushes out of the way. When you get into a bath, the water level rises because your body moves water aside. The weight of that moved water is the upthrust on you.
An object floats when its weight equals the upthrust. Then the forces are balanced and it stays still. An object sinks if its weight is bigger than the biggest upthrust the water can give it.
That is how a steel ship floats even though a steel nail sinks. The ship has a wide hull that pushes aside a huge amount of water. The weight of that water is big enough to equal the ship's weight. A floating duck is simpler, because its weight pulls down and the water pushes up with a force of the same size.
The atmosphere is a layer of gas that surrounds the Earth. Gas particles are always moving, and they collide with every surface. All those collisions push on the surface, and that push is atmospheric pressure.
You can also say the pressure comes from the weight of the air above you. At sea level that pressure is about 100 000 Pa, so every square metre has the weight of a column of air pressing on it. You do not feel it because the air inside your body presses back equally.
As you go higher there is less air above you, so the pressure drops. The air also becomes thinner, which means there are fewer particles in each cubic metre. Fewer particles means fewer collisions, so the pressure falls.
You can notice this. Your ears pop when you drive up a mountain or take off in a plane. A sealed crisp packet puffs up as you climb, because the air pressure outside falls while the air inside pushes outwards.
A suction cup is another example. When you press it onto a smooth surface, you push the air out from under it. The air outside then presses the cup onto the surface, and that is what holds it on. The same idea explains why climbers find it harder to breathe near the top of a very high mountain, where the air is thin.
Pressure is the force acting on each unit of area. p = F ÷ A, in pascals, Pa. The same force on a smaller area makes a bigger pressure, which is why knives are sharp and snowshoes are wide. Always check the units before you start, and change cm² to m² if you need to.
Pressure in a liquid acts in all directions and increases with depth, because there is more liquid above. At Higher tier, p = h × ρ × g, and for water ρ = 1000 kg/m³.
Upthrust is the upward force from a fluid, caused by greater pressure at the bottom of an object. It equals the weight of fluid pushed out of the way, and an object floats when its weight equals the upthrust.
Atmospheric pressure comes from air particles colliding with surfaces, or the weight of the air above. It falls as you go higher because there is less air above.
How this is asked in an exam: a calculation wants the equation, the numbers and the unit. An explain question wants a clear link, such as smaller area, so greater pressure, or more water above, so greater pressure. A float question wants upthrust equals weight.
A force of 200 N acts on an area of 0.5 m². Work out the pressure.
Answer: 400 Pa
Work out the pressure caused by water at a depth of 4 m. Water has a density of 1000 kg/m³. Take g = 10 N/kg.
Answer: 40 000 Pa
A pressure of 50 000 Pa acts on an area of 0.02 m². Work out the force.
Answer: 1000 N
Pressure in fluids practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
A force of 50 N acts on an area of 0.25 m². Work out the pressure.
Answer: 200 Pa
A force of 60 N acts on an area of 0.5 m². Work out the pressure.
Answer: 120 Pa
Name the unit of pressure.
Answer: pascal
Name the upward force a fluid exerts on an object in it.
Answer: upthrust
Work out the pressure caused by water at a depth of 2 m. Water has a density of 1000 kg/m³ and g = 10 N/kg.
Answer: 20 000 Pa
Work out the pressure caused by oil at a depth of 5 m. The oil has a density of 800 kg/m³ and g = 10 N/kg.
Answer: 40 000 Pa
A pressure of 3000 Pa acts on an area of 0.4 m². Work out the force.
Answer: 1200 N
Explain why a diver feels more pressure at a greater depth.
Answer: There is more water above, so the pressure is greater.
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
A woman weighs 600 N. She stands on two shoes with a total area of 0.05 m². (a) Work out the pressure under her shoes. [2 marks] (b) She stands on one narrow heel with an area of 0.01 m². Work out the pressure now. [1 mark] (c) Explain why the pressure is larger. [1 mark]
Answer: (a) 12 000 Pa (b) 60 000 Pa (c) The same force acts on a smaller area.
A diver is 5 m below the surface of the sea. The density of seawater is 1000 kg/m³ and g = 10 N/kg. (a) Work out the pressure caused by the water. [2 marks] (b) The diver goes deeper. Explain what happens to the pressure. [2 marks]
Answer: (a) 50 000 Pa (b) It increases, because there is more water above the diver.
Mixing up pressure and force
Pressure is force per unit area, in pascals. Force is in newtons.
Using an area in cm² in the pressure equation
Change cm² to m² first by dividing by 10 000.
Forgetting g in p = h × ρ × g
Multiply height, density and gravitational field strength. Take g = 10 N/kg.
Saying pressure in a liquid acts only downwards
Pressure in a liquid acts in all directions, at right angles to the surface.
Saying a floating object has more upthrust than weight
For a floating object that is still, the upthrust equals the weight.
Pressure in fluids is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 6.
Mixing up pressure and force. Pressure is force per unit area, in pascals. Force is in newtons.
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.
See how the papers are set: AQA Combined Science papers and Edexcel Combined Science papers.
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