What is Pressure?

Pressure is the force per unit of area, which is present in liquids, in air and on surfaces. We can calculate it using the formula:

  • P = Pressure in pascals (Pa)
  • F = Force in newtons (N)
  • A = Area in metres squared (m2)

Pressure is typically measured in pascals (Pa), which is equivalent to newtons per square metre (N/m²). So, 1 Pa = 1 N/m².

Pressure in Fluids

A fluid is a substance that can flow, such as a liquid or a gas. The liquid and gas particles constantly collide with their surroundings and generate pressure.

For example, if we had a container of gas, the gas particles will collide with the surface of the container and generate pressure. This is because each particle collision applies a force to the inside area of the container.

The same process happens with liquids, for example with a beaker of water. The water particles apply forces outwards in all directions. As the water particles collide with the walls of the beaker, this generates pressure.

We refer to both gas pressure and liquid pressure as fluid pressure. But regardless of the source, the pressure in a fluid always results in a force that is normal (at right angles) to the surface of the container.

When a particle collides with a surface at a perfect right angle, the entire force will be used to generate pressure. Whereas, if a particle collides with a surface at another angle, its full force will not be used to generate pressure.

Speed and pressure

The faster the speed of the particles when they collide with the surface of the container, the greater the force exerted by these collisions. So, particles travelling at a high speed will generate a greater force than particles travelling at a slower speed. This greater force will translate to greater pressure on the surface, as we know that P = F / A.

Application of Pressure and Surface Area

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

Since pressure is defined as force divided by area, when you apply a force to the broad side of a drawing pin, that same force is transmitted 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 won’t injure yourself, as the surface area is greater.

When you push the pin, the pressure exerted on the wall by the sharp point is greater than that exerted by the broad side. Therefore, the drawing pin can penetrate the wall or surface. This is due to the smaller surface area on the sharp point of the pin.

Example

Calculate the pressure on the thumb and the wall when pushing a drawing pin into a wall.

  • The force exerted (when you push 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

Which is equal to 40,000 N/m² or 40,000 Pa

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

Which is equal to 100,000 N/m² or 100,000 Pa

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

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