4.5.5.1Pressure in a fluid
Physics only — not assessed in Combined Science: Trilogy.
This part of the sub-topic comes in two halves, and it is worth knowing which is which before you start.
The first, for both tiers, is pressure at a surface — the force per unit area, wherever that force comes from. The second, Higher tier only, is pressure caused by the weight of a liquid above a point, which is what makes pressure increase with depth and what produces upthrust.
Both use the word pressure and both are measured in pascals, but they answer different questions: the first asks how a force is spread over an area, the second asks how deep you are.
4.5.5.1.1Pressure at a surface
Physics only — not assessed in Combined Science: Trilogy.
A fluid can be either a liquid or a gas. That definition is worth noting at the start — everything in this sub-topic applies to gases as well as liquids.
The pressure in fluids causes a force normal, meaning at right angles, to any surface.
The pressure at the surface of a fluid can be calculated using the equation:
pressure = force normal to a surface / area of that surface p = F / A
pressure, p, in pascals, Pa; force, F, in newtons, N; area, A, in metres squared, m².
You should be able to recall and apply this equation.
Worked example
A force of 60 N acts normal to a surface of area 0.015 m². Calculate the pressure.
- Write the equation: p = F ÷ A.
- Check the area is in metres squared — it is.
- Substitute: p = 60 ÷ 0.015.
- = 4000.
- Give the unit: pascals.
Answer: 4000 Pa
Common mistake
Area must be in m², not cm². There are 10 000 cm² in a m², so using cm² makes the pressure ten thousand times too small.
- Fluid
- a liquid or a gas
- Pressure
- the force normal to a surface divided by the area of that surface, measured in pascals
4.5.5.1.2Pressure due to a column of liquidHigher tier
Physics only, Higher tier — not assessed in Combined Science: Trilogy.
The pressure due to a column of liquid can be calculated using the equation:
pressure = height of the column × density of the liquid × gravitational field strength p = h ρ g
pressure, p, in pascals, Pa; height of the column, h, in metres, m; density, ρ, in kilograms per metre cubed, kg/m³; gravitational field strength, g, in newtons per kilogram, N/kg. In any calculation the value of g will be given.
This equation is given on the Physics equation sheet.
You should be able to explain why, in a liquid, pressure at a point increases with the height of the column of liquid above that point, and with the density of the liquid.
Both follow from the same idea. The pressure at a point is caused by the weight of the liquid above it pressing down. A greater height of liquid above the point means more liquid, so a greater weight, so a greater pressure. A denser liquid means more mass in the same volume, so again a greater weight above the point and a greater pressure.
You should also be able to calculate the differences in pressure at different depths in a liquid — subtract the pressures found at the two depths, or use the difference in height directly.
Worked example
Calculate the difference in pressure between a depth of 2.0 m and a depth of 5.0 m in water. Density of water = 1000 kg/m³, g = 9.8 N/kg.
- The pressure difference depends only on the difference in height.
- Difference in height: 5.0 − 2.0 = 3.0 m.
- Write the equation: p = h ρ g.
- Substitute: p = 3.0 × 1000 × 9.8.
- Give the unit: pascals.
Answer: 29 400 Pa
A partially or totally submerged object experiences a greater pressure on the bottom surface than on the top surface. This creates a resultant force upwards, and this force is called the upthrust.
The reason follows directly from p = h ρ g: the bottom surface is deeper, so the pressure on it is greater, so the upward force on it exceeds the downward force on the top.
You should be able to describe the factors which influence floating and sinking. An object floats if the upthrust equals its weight, and sinks if its weight is greater than the largest upthrust it can generate. Because the upthrust depends on the volume of fluid displaced and the density of the fluid, an object whose overall density is less than that of the fluid will float, and one that is denser will sink. That is why a steel ship floats: it is shaped to enclose a large volume of air, so its overall density is less than that of water.
Common mistake
Upthrust comes from the pressure difference between the top and bottom surfaces, not from the water "pushing up" in general. Say that the greater depth of the bottom surface gives it a greater pressure, so there is a resultant upward force.
4.5.5.2Atmospheric pressure
Physics only — not assessed in Combined Science: Trilogy.
The atmosphere is a thin layer, relative to the size of the Earth, of air round the Earth. The atmosphere gets less dense with increasing altitude.
Air molecules colliding with a surface create atmospheric pressure.
The number of air molecules — and so the weight of air — above a surface decreases as the height of the surface above ground level increases. So as height increases there is always less air above a surface than there is at a lower height. So atmospheric pressure decreases with an increase in height.
You should be able to describe a simple model of the Earth's atmosphere and of atmospheric pressure, and explain why atmospheric pressure varies with height above a surface.
The explanation has a fixed shape, and the specification writes it out almost as a chain of consequences:
1. Atmospheric pressure is caused by air molecules colliding with a surface. 2. As height increases, there is less air above the surface. 3. So there are fewer molecules above to collide with it, and the weight of air above is smaller. 4. So the atmospheric pressure decreases as height increases.
Giving all four steps is what separates a full answer from a partial one.
Worked example
Explain why a sealed empty plastic bottle, closed at the top of a mountain, is crushed when carried down to sea level.
- At the top of the mountain there is less air above, so the atmospheric pressure is low, and the air sealed inside the bottle is at that low pressure.
- Carrying the bottle down increases the height of atmosphere above it.
- There are now more air molecules above, so the atmospheric pressure outside is greater.
- The pressure inside is unchanged because the bottle is sealed.
- The pressure outside now exceeds the pressure inside, giving a resultant inward force that crushes the bottle.
Answer: Atmospheric pressure rises as the bottle is carried down, while the sealed air inside stays at the lower mountain-top pressure — so the greater outside pressure crushes it.
- Atmospheric pressure
- the pressure created by air molecules colliding with a surface; it decreases with altitude because there are fewer air molecules above the surface
Before you practise
- This sub-topic is physics only — it is not assessed in Combined Science: Trilogy.
- A fluid is a liquid or a gas, and fluid pressure causes a force normal to any surface.
- p = F / A must be recalled, with area in m².
- Higher tier: p = h ρ g is given on the equation sheet, for the pressure due to a column of liquid.
- Pressure in a liquid increases with the height of liquid above the point and with the density of the liquid, because both increase the weight above.
- Higher tier: the bottom of a submerged object is deeper, so the pressure there is greater — the resultant upward force is the upthrust.
- An object floats if the upthrust equals its weight; overall density less than the fluid's means it floats.
- Atmospheric pressure is caused by air molecules colliding with a surface, and it decreases with height because there is less air above.