What is (Mechanical) Pressure?

The pressure \( \mathit{\Pi} \) is defined as the force \(F\) acting perpendicularly on a surface area \(A\):

The pressure is abbreviated here with the Greek capital letter \( \mathit{\Pi} \) (pronounced: Pi). Sometimes the pressure is also abbreviated with the letter \(p\), but that is avoided here because \(p\) is already used for the momentum.

Pressure unit:
The force \(F\) has the unit \( \mathrm{N} \) (newtons) and stands for the unit \( \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{s}^2} \) (kilograms per second squared). The area \(A\) has the unit \( \mathrm{m}^2\) (square meter). Because of equation 1 the pressure \( \mathit{\Pi} \) must have the unit \( \frac{\mathrm{N}}{\mathrm{m}^2} \). Newton per square meter is usually abbreviated with the unit \( \mathrm{Pa} \) (Pascal) for pressure.

From the definition 1 of pressure, we can read the following information:

• The larger the force \(F\), the larger the pressure \(\mathit{\Pi}\).

• The smaller the surface \(A\) on which the force is applied, the greater the pressure \(\mathit{\Pi}\).

There are several special names of pressure, but they can all be traced back to the definition 1. Here are some examples:

• Air pressure - is caused by the gravitational force exerted by the air. The air pressure at sea level is \( 10^5 \, \mathrm{Pa} \). Therefore, the unit "bar" is usually used for air pressure: \( 1\, \mathrm{bar} = 10^5 \, \mathrm{Pa} \).

• Gravity pressure - is also caused by the gravitational force exerted by a liquid or gas.