Pressure in a fluid 1 — AQA GCSE Physics
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Pressure in a fluid 1 explained
A fluid is anything that flows, which covers both liquids and gases and excludes solids.
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In a solid the particles are held in fixed positions and can only vibrate, so a solid keeps its shape. In a liquid the particles touch but slide past one another, so a liquid takes the shape of its container while keeping its volume. In a gas the particles are far apart and move randomly at speed, so a gas fills whatever space it is given. Because their particles can move, both liquids and gases press outwards on every surface they touch, and both can be pumped along a pipe. The differences matter too: a gas can be compressed because of the space between its particles, and its density is far lower, which is why pressure changes with depth much faster in water than in air.
The pressure in fluids causes a force normal (at right angles) to any surface.
Pressure is not a force with a direction of its own. The particles of a fluid move randomly and strike whatever surface they meet, and averaged over many collisions the push is always at right angles to that surface, whichever way the surface faces. So the water in a tank pushes outwards on the sides as well as down on the base, and the air pushes up on the underside of a table as hard as it pushes down on the top. The size of the force follows from the area, so the same pressure produces a much larger force on a large window than on a small one. Where the pressures on the two faces of a surface differ, the resultant force is normal too, and it points from the high pressure side towards the low pressure side.
The pressure at the surface of a fluid can be calculated using the equation:
Pressure at a surface is the force acting normally per unit area. For a fluid, the pressure at the surface is calculated using p = F ÷ A, where p is pressure in pascals (Pa), F is the normal force in newtons (N) and A is the area in square metres (m²). A pascal is one newton per square metre. To use the equation, identify the force acting perpendicular to the surface and the area of that surface. For example, a force of 20 N acting normally on an area of 0.5 m² gives p = 20 N ÷ 0.5 m² = 40 Pa. If the area is given in cm², convert to m² by dividing by 10 000 before substituting. The equation shows that pressure increases if the force increases or if the area decreases. This applies to any fluid at a surface, including liquids and gases.
pressure = force normal to a surface / area of that surface
A fluid, which can be either a liquid or a gas, exerts pressure on any surface it is in contact with. The particles in the fluid collide with the surface, creating a force that acts at right angles (normal) to it. The concentration of this force over a given area determines the pressure. For example, if the water pressure on a submarine window of area 0.20 m² is 500,000 Pa, the normal force exerted by the water is 100,000 N. Understanding this allows engineers to design containers, pipes, and submersible vehicles that can withstand the forces exerted by the fluids they hold or move through. Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m².
p = F / A
This equation defines pressure as the normal force divided by the area over which it acts. In symbols, p is pressure in pascals, F is the normal force in newtons and A is the area in square metres. A force of 50 N spread over 0.25 m² gives p = 50 ÷ 0.25 = 200 Pa. The equation can be rearranged to F = p × A or A = F ÷ p. Because area appears on the bottom, a smaller area gives a larger pressure for the same force, which is why a drawing pin has a sharp point. When using the equation, convert areas such as 20 cm² to 0.0020 m² before substituting, and make sure the force is perpendicular to the surface.
pressure, p, in pascals, Pa
Pressure, p, measures how concentrated a force is over an area and is measured in pascals, Pa. One pascal is equal to one newton per square metre (1 Pa = 1 N/m²). In a fluid (a liquid or a gas), this pressure causes a force that acts at right angles (normal) to any surface it contacts, such as the walls of a container. To use the quantity, select the equation p = F ÷ A, ensure the area is in square metres (for example, converting 250 cm² to 0.0250 m²), substitute the values, and state the final answer with the unit Pa or N/m². Always state pressure with a valid unit, and ensure the force used is perpendicular to the surface.
force, F, in newtons, N
Force, F, is a push or pull measured in newtons, N, and in pressure calculations it is the force acting perpendicular to a surface. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s². In p = F ÷ A, F is the total force normal to the area, so a 600 N person standing on both feet exerts 600 N on the floor whatever the area. If the area changes, the force stays the same but the pressure changes. To find force from pressure, rearrange to F = p × A, keeping area in m² so the answer is in N. Weight is a force and is calculated using W = m × g, where g is about 9.8 N/kg on Earth. Always identify which force acts perpendicular to the surface before substituting into the pressure equation.
area, A, in metres squared
Area, A, is the size of a surface measured in square metres (m²). In pressure calculations, A is the area of the surface that the force acts on at right angles. For a rectangular surface, multiply length by width, both in metres, so a 2 m by 3 m face has A = 6 m². For a circular piston, use A = πr², converting the radius to metres first. If a measurement is in cm, convert by dividing by 100 before squaring; for example, 50 cm = 0.50 m, so 0.50² = 0.25 m². Area is not the same as volume: volume uses m³. Always match the area to the surface actually in contact with the fluid or force.
Students should be able to recall and apply this equation.
This statement requires you to remember the pressure equation and use it in calculations. The equation is p = F ÷ A, where p is pressure in pascals (Pa), F is the normal force in newtons (N) and A is the area in square metres (m²). Recall means writing it from memory; apply means substituting values, rearranging and calculating. For example, a force of 200 N acting on 0.50 m² gives p = 200 ÷ 0.50 = 400 Pa. Rearranged forms are F = p × A and A = F ÷ p. One pascal is one newton per square metre (1 Pa = 1 N/m²). Keep units consistent and convert cm² to m² before substituting.
Your focus
- Classify given substances as fluids or not, and justify each choice.
- Describe the particle arrangement in a liquid and in a gas that allows both to flow.
- Explain why a gas can be compressed but a liquid can barely be.
Show all 27 objectives
- Draw the direction of the force a fluid exerts on a vertical, a horizontal and a sloping surface.
- Calculate the force on a surface from the fluid pressure and the area.
- Explain why an aircraft window experiences a net outward force at cruising altitude.
- Recall and apply the equation p = F ÷ A to calculate pressure at a surface.
- Convert between square centimetres and square metres correctly when using the pressure equation.
- Explain how changing the force or the area affects the pressure at a surface.
- State that fluids exert a force normal to any surface they contact.
- Calculate pressure, force, or area using the equation p = F / A in fluid contexts.
- Convert areas into square metres to correctly determine pressure in pascals.
- Use the equation p = F / A to calculate pressure.
- Rearrange the equation to find force or area.
- Apply correct SI units and conversions when solving pressure problems.
- State that pressure is measured in pascals (Pa) or newtons per square metre (N/m²).
- Calculate pressure using p = F ÷ A with area converted to square metres.
- Describe fluid pressure as causing a force normal to a surface.
- State that force is measured in newtons and describe it as a push or pull.
- Calculate an unknown force using F = p × A with consistent SI units.
- Use W = m × g to find the force exerted by a weight on a surface.
- State that area is measured in metres squared (m²).
- Calculate the area of a rectangle or circle in m² from measurements given in metres or centimetres.
- Use the correct area in a pressure or force calculation and give the answer with the unit m².
- Recall the equation p = F ÷ A and the units of pressure, force and area.
- Apply the equation to calculate pressure, force or area when the other two quantities are known.
- Convert area to m² and present the final answer with the correct unit.
Pressure in a fluid 1 exam tips
Marking Points
- one mark for a fluid identified as a substance that can flow
- one mark for both liquids and gases counted as fluids
- one mark for a particle arrangement that allows the particles to move past one another
- one mark for stating that a fluid exerts pressure on every surface it touches
- one mark for the force acting at right angles, or normal, to the surface
- one mark for the force arising from fluid particles colliding with the surface
- one mark for stating that this holds whatever the orientation of the surface
- one mark for a resultant force found from the difference in pressure multiplied by the area
- State the pressure equation as p = F ÷ A, where p is pressure, F is normal force and A is area.
- Identify the force acting perpendicular to the surface and the area of that surface from the information given.
- Convert area to square metres when it is given in other units, for example 1 cm² = 1 × 10⁻⁴ m².
- Substitute values into the equation with correct units and calculate the pressure in pascals.
- Rearrange the equation to calculate force or area when required, for example F = p × A or A = F ÷ p.
- Explain that pressure increases when the force increases or when the area decreases, for a constant value of the other variable.
- Identify that a fluid (liquid or gas) exerts a force at right angles (normal) to any surface it contacts.
- Use the equation p = F / A to calculate pressure, force, or area in fluid contexts.
- Convert units correctly, ensuring force is in newtons (N), area in square metres (m²), and pressure in pascals (Pa).
- Rearrange the pressure equation to find the normal force exerted by a fluid on a given area.
- Identify p as pressure in pascals, F as normal force in newtons and A as area in square metres.
- Substitute values into p = F / A and evaluate correctly.
- Rearrange the equation to calculate force as F = p × A or area as A = F / p.
- Convert areas from cm² or mm² to m² before substitution.
- Interpret a large pressure as a large force acting on a small area.
- State that the unit of pressure is the pascal (Pa) and that 1 Pa = 1 N/m².
- Identify that fluids (liquids and gases) exert pressure that causes a normal force on surfaces.
- Use p = F ÷ A correctly, including rearranging to F = p × A or A = F ÷ p.
- Convert areas into square metres before substituting, for example 250 cm² = 0.0250 m².
- Give answers with the correct unit, Pa or N/m², and recognise that the force acts at right angles to the surface.
- State that force is measured in newtons, N, and is a push or pull acting on an object.
- Identify the force perpendicular to the surface when using p = F ÷ A.
- Rearrange p = F ÷ A to F = p × A and substitute pressure in Pa and area in m².
- Calculate weight as a force using W = m × g and use it as F in pressure problems.
- Recognise that changing the contact area changes pressure but not the applied force.
- State that area is measured in square metres (m²), not metres or cubic metres.
- Calculate the area of a rectangle by multiplying its length in metres by its width in metres.
- Calculate the area of a circle using A = πr², with the radius converted to metres before squaring.
- Convert centimetres to metres by dividing by 100, and convert cm² to m² by dividing by 10 000.
- Select the area of the surface in contact with the force or fluid, not the total surface area of the object.
- Substitute the area into pressure or force equations with consistent SI units.
- Recall the equation p = F ÷ A and state the meaning of each symbol.
- State the units: pressure in pascals (Pa), force in newtons (N) and area in square metres (m²).
- Substitute known values into p = F ÷ A and calculate the pressure.
- Rearrange the equation to F = p × A or A = F ÷ p when the question asks for force or area.
- Convert area from cm² to m² by dividing by 10 000 before substitution.
- Recognise that 1 Pa = 1 N/m² and use this to check unit consistency.
Examiner Tips
- 💡If a question says fluid, check whether the substance in the figure is a gas; the same equations still apply.
- 💡Use the word flow in any definition, because that is what is being tested.
- 💡Draw the arrow perpendicular to the surface, not vertically down the page.
- 💡For a resultant force, subtract the two pressures first and then multiply by the area once.
- 💡Write the equation p = F ÷ A before substituting values, so the examiner can see your method.
- 💡Check that the area is in square metres and the force is in newtons before calculating.
- 💡Give the unit pascal (Pa) with your answer, and remember that 1 Pa = 1 N m⁻².
- 💡If the question asks for pressure at the surface of a fluid, use the normal force acting on that surface, not the weight of the fluid unless it is the relevant force.
- 💡When calculating the force on a container wall, ensure you use the area of that specific wall and the pressure acting on it.
- 💡Always check if the area needs calculating first from given dimensions (e.g., a rectangular window) before substituting into the pressure equation.
- 💡Quote the equation, show the substitution, then state the answer with the unit Pa.
- 💡If the answer looks very large or very small, check the area conversion before moving on.
- 💡Use standard symbols p, F and A in working so the examiner can follow your method.
- 💡Write the equation p = F ÷ A, substitute values with units, then give the answer in Pa to an appropriate number of significant figures.
- 💡When a question gives an area in cm² or mm², convert to m² first and show the conversion clearly to secure method marks.
- 💡Underline the force and the area in the question, then check that the force is perpendicular to the area before calculating.
- 💡Show the rearrangement F = p × A explicitly when force is the unknown, and keep units with substituted values.
- 💡If mass is given, calculate weight first using g = 9.8 N/kg and state that this weight is the force acting on the surface.
- 💡Write the unit m² every time you state an area, and check that the unit matches the calculation.
- 💡Convert all lengths to metres before calculating area, then square the conversion factor if the original unit was cm².
- 💡In pressure questions, underline the word area and identify which surface the force acts on before substituting values.
- 💡Write the equation from memory before substituting numbers, then rearrange only after writing the base equation.
- 💡Check that the area is in m² and the force is in N before calculating pressure in Pa.
- 💡Give the unit with every numerical answer and use standard form for very large or very small pressures.
Common Mistakes
- restricting the word fluid to liquids only
- saying a gas has no mass or exerts no pressure
- describing the particles in a liquid as far apart, which is the arrangement in a gas
- claiming a liquid can be compressed as easily as a gas
- drawing the force from a fluid as acting downwards only
- assuming a fluid presses on the base of a container but not on its sides
- using an area in square centimetres without converting it to square metres
- calculating a resultant from the larger pressure alone rather than from the difference
- Using the area in square centimetres without converting to square metres; correct this by converting cm² to m² by dividing by 10 000 before calculating.
- Using a force that is not perpendicular to the surface; correct this by using the component of force acting normally to the surface.
- Confusing pressure with force; correct this by stating that pressure is force per unit area and is measured in pascals, while force is measured in newtons.
- Forgetting to square the conversion factor when converting areas; correct this by remembering that 1 m = 100 cm, so 1 m² = 10 000 cm².
- Forgetting to convert area from cm² to m²; the correction is to divide the area in cm² by 10,000 (or multiply by 10⁻⁴) before calculating pressure.
- Assuming the force from fluid pressure acts downwards only; the correction is to recognise that fluid pressure acts normally (at right angles) to all surfaces of an object or container, regardless of orientation.
- Confusing the units of pressure; the correction is to remember that 1 Pa is exactly equivalent to 1 N/m², not N/m.
- Substituting an area in cm² directly into the equation; the correction is to convert to m² first, for example 20 cm² = 0.0020 m².
- Dividing area by force instead of force by area; the correction is to keep F on top and A on the bottom.
- Using a slanted force as F without resolving it; the correction is to use only the component normal to the surface.
- Using the area in cm² without converting to m², which makes the calculated pressure too small; correct by dividing the cm² value by 10,000.
- Quoting the answer for pressure in newtons (N); correct by checking that the calculation divides force by area and the unit is Pa or N/m².
- Forgetting that fluids include both liquids and gases; correct by applying the pressure equation to both gas containers and liquid vessels.
- Treating mass in kilograms as the force in newtons; correct by calculating weight with W = m × g before substituting into p = F ÷ A.
- Using a slanted or total surface area instead of the area perpendicular to the force; correct by identifying the contact area normal to the push or pull.
- Quoting force in pascals or pressure in newtons; correct by matching each quantity to its unit, N for force and Pa for pressure.
- Using the diameter instead of the radius in A = πr²; correct this by halving the diameter before squaring.
- Forgetting to square the unit conversion, so 50 cm² is treated as 0.50 m²; correct this by dividing by 10 000 to obtain 0.0050 m².
- Using the total surface area of a block when only one face is in contact with the fluid; correct this by identifying the contact face and using its area only.
- Multiplying force by area instead of dividing; correct this by using p = F ÷ A.
- Substituting area in cm² without converting; correct this by converting to m² first.
- Rearranging incorrectly when finding force; correct this by multiplying pressure by area to give F = p × A.