What is (Mechanical) Pressure?

by Alexander FufaeV

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

Definition: Pressure

$$ \begin{align} \mathit{\Pi} ~=~ \frac{F}{A} \end{align} $$

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 $\mathit{\Pi}$.

Example: Pressure on a board

A force $F = 2 \, \mathrm{N}$ is applied to a board with area $A = 1 \, \mathrm{m}^2$. The board experiences the following pressure according to Eq. 1:

$$ \begin{align} \mathit{\Pi} ~=~ \frac{2 \, \mathrm{N}}{1 \, \mathrm{m}^2} ~=~ 2 \, \mathrm{Pa} \end{align} $$

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.

Example: Air pressure

Consider a ball. The air around the ball consists of many small particles moving around in any direction. As they move, they bump into the ball from all sides and bounce off. Since there are a lot of particles and therefore a lot of bounces, the ball experiences uniform pressure from all sides. The air pressure exerted on a ball is nothing more than the air particles colliding with the ball.