Pressure in Fluids

When calculating pressure, it’s important to know two things:

  • The weight or force applied – measured in newtons (N)
  • The surface area on which the weight or force is applied – measured in square metres (m²)

Pressure is present in liquids, in air and on surfaces. To calculate pressure, we use this formula:

Pressure is measured in pascals (Pa), which is equivalent to newtons per square metre (N/m²).

  • 1 Pa = 1 N/m²

So remember:

Physical QuantitySymbolUnitUnit Symbol
PressurePPascals or newtons metre squared or Newtons per centimetre squaredPa or N/m² or N/cm²
Weight or ForceFNewtonsN
AreaAMetres squared or centimetres squaredm² or cm²

Application of Pressure and Surface Area

In this example, we will look at drawing pins. These are flat-headed pins used for attaching paper to a wall or another surface.

As pressure is equal to force over area, when you apply force to the broad side of a drawing pin, that same amount of force is applied to the wall through the sharp point of the pin. However, the pressure exerted on your finger (when you push the pin) from the broad side is less than the sharp point. This means you are less likely to injure yourself, as the surface area is greater.

The pressure exerted on the wall (when you push the pin) from the sharp point is greater than the broad side, which means the drawing pin can penetrate the wall or surface. This occurs due to the smaller surface area.


Calculate the pressure on the thumb and the wall when pushing a drawing pin into a wall. Taking into account the following information:

  • The force exerted when pushing the drawing pin is 10 N
  • The surface area of the broad side of the pin is 2.5 cm²
  • The surface area of the sharp point of the pin is 1 cm²

Remember the equation: Pressure = Force ÷ Area

To work out the pressure applied to the thumb, the equation is 10 N ÷ 2.5 cm² = 4 N/cm²

To work out the pressure applied to the wall, the equation is 10 N ÷ 1 cm² = 10 N/cm²

The pressure exerted on the wall is greater than the pressure exerted on the thumb.

Atmospheric Pressure

The atmosphere exerts pressure on you and everything around you. You may have seen a demonstration of the effects of this atmospheric pressure.

Atmospheric pressure refers to the pressure exerted by the atmosphere.

The less density the air has, the less air pressure there will be and the more density the air has, the more pressure there will be. This pressure can change with altitude. It is important to remember:

  • At higher altitudes, the air pressure is lower
  • At lower altitudes, the air pressure is higher

An example of this is how at the top of a mountain, the amount of gas molecules is lower, which means there is less air pressure. However, at sea level, the molecules are more densely packed, which means there is more air pressure.

Pressure in liquids

Liquids also apply pressure on objects. Depth is what changes the pressure in liquids. Therefore, the deeper you go, the greater the liquid pressure.

The pressure in a liquid increases with depth due to the weight of the liquid above it. This increased pressure at greater depths can force water to spurt out more quickly when given an outlet (e.g. a hole). In contrast, at shallower depths where the pressure is lower, water spurts out less forcefully.

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