Pressure explains a wide range of everyday effects โ why a sharp knife cuts, why dams are thicker at the bottom, how hydraulic brakes work, and why we are not crushed by the atmosphere. In CSEC Physics you study pressure in solids, in liquids and in gases, together with floating and sinking.
What pressure is
Pressure is the force acting per unit area:
pressure = force รท area P = F / A (units: pascal, Pa, where 1 Pa = 1 N/mยฒ)
For the same force, a smaller area gives a larger pressure. This is why a sharp knife (small area) cuts easily, why nails are pointed, and why skis (large area) stop you sinking into snow by spreading your weight.
Density
Closely linked is density, the mass per unit volume:
density = mass รท volume (units: kg/mยณ or g/cmยณ)
Density decides whether something floats: an object floats in a fluid that is denser than itself.
Pressure in liquids
Pressure in a liquid:
- increases with depth (the deeper you go, the more liquid is pressing down โ which is why a dam is built thicker at its base);
- acts equally in all directions at a given depth;
- depends on the density of the liquid;
- does not depend on the shape or width of the container.
The pressure due to a column of liquid is given by P = ฯ g h (density ร gravity ร height).
Transmitting pressure โ hydraulics
In a confined liquid, pressure applied at one point is transmitted equally throughout the liquid (because liquids are virtually incompressible). This is the basis of hydraulic machines such as car brakes and jacks. A small force on a small piston creates a pressure that, acting on a larger piston, produces a much larger force โ a force multiplier. (Because pressure is the same, the larger area gives the larger force.)
Atmospheric pressure
The air around us has weight and so exerts atmospheric pressure (about 100,000 Pa at sea level). It acts in all directions, which is why:
- a drinking straw works (you reduce the pressure inside; atmospheric pressure pushes the liquid up);
- a suction cup sticks (air is excluded, atmospheric pressure holds it on);
- atmospheric pressure decreases with altitude (less air above you).
It is measured with a barometer, and gas pressure with a manometer.
Floating, sinking and upthrust
When an object is placed in a fluid it experiences an upward force called upthrust (buoyancy).
- Archimedes' principle: the upthrust equals the weight of fluid displaced by the object.
- The law of flotation: a floating object displaces its own weight of fluid.
So an object floats if it can displace a weight of fluid equal to its own weight before it is fully submerged โ this happens when the object's average density is less than the fluid's. A steel ship floats, despite steel being dense, because its hull shape displaces a large volume (and weight) of water. An object sinks if its weight is greater than the maximum upthrust available (its density is greater than the fluid's).
Worked examples
Pressure of a solid. A box weighs 600 N and its base measures 2 m ร 1.5 m, so the base area is 3 mยฒ. The pressure it exerts on the floor is P = F รท A = 600 รท 3 = 200 Pa. If the same box stood on a smaller end of area 0.5 mยฒ, the pressure would rise to 600 รท 0.5 = 1200 Pa โ six times greater for the same weight, simply because the area is smaller.
Pressure in a liquid. Using P = ฯ g h, the pressure due to 5 m of water (density 1000 kg/mยณ, g = 10 N/kg) is 1000 ร 10 ร 5 = 50,000 Pa. Doubling the depth to 10 m doubles the pressure โ which is exactly why a dam must be built much thicker near its base than at the top.
Hydraulic force multiplier. If a force of 20 N is applied to a small piston of area 0.001 mยฒ, the pressure created is 20 รท 0.001 = 20,000 Pa. Since this pressure is transmitted equally through the liquid to a larger piston of area 0.02 mยฒ, the output force is P ร A = 20,000 ร 0.02 = 400 N โ twenty times the input. The trade-off is that the large piston moves a much smaller distance, so energy is conserved.
How a manometer measures pressure
A manometer is a U-shaped tube partly filled with liquid. When one side is connected to a gas supply, the gas pressure pushes the liquid down on that side and up on the other. The difference in the two liquid levels (h) measures how much the gas pressure exceeds atmospheric pressure, since the extra pressure supports that column of liquid (the height difference relates to pressure through P = ฯgh). A large height difference means a large pressure. This simple device shows pressure ideas in action and is a common practical question.
Common exam mistakes
- Mixing up the effect of area โ smaller area gives larger pressure for the same force.
- Saying liquid pressure depends on container shape or width โ it depends on depth and density only.
- Forgetting that pressure in a liquid acts in all directions, not just downwards.
- Confusing upthrust (weight of fluid displaced) with the object's own weight.
Key terms to remember
- Pressure โ force per unit area; P = F/A, measured in pascals (Pa).
- Pascal (Pa) โ one newton per square metre (1 N/mยฒ).
- Density โ mass per unit volume; density = mass/volume.
- P = ฯgh โ the pressure due to a column of liquid (density ร gravity ร height).
- Hydraulics โ using a confined liquid to transmit pressure and multiply force.
- Atmospheric pressure โ the pressure of the air, about 100,000 Pa at sea level.
- Upthrust (buoyancy) โ the upward force on an object in a fluid.
- Archimedes' principle โ upthrust = weight of fluid displaced.
- Law of flotation โ a floating object displaces its own weight of fluid.
Quick recap
- P = F/A (Pa); small area โ high pressure.
- Density = mass/volume; an object floats if less dense than the fluid.
- Liquid pressure increases with depth and density, acts in all directions, and is independent of container shape.
- Confined liquids transmit pressure equally โ hydraulics multiply force.
- Upthrust = weight of fluid displaced (Archimedes); a floating object displaces its own weight (flotation).