Pressure

Pressure (usually denoted by $P$) is measured as the distributed force over an area/surface.

Definition §

While the idea of forces is a useful concept, a more realistic concept is pressure, which helps explain why bullets are so strong, while falling flat on a pool of water hurts so much, why drills are always cone shaped, etc.

Pressure applies to all states of matter: solids as well as fluids (gasses and liquids)

Pressure is defined by the surface, not the body as a whole

I think a lot of people (including me!), misunderstand pressure. A body can have non-zero pressure while still having a net force of zero. Take a plane for example, with equal force on both sides. On each side (surface), we have a positive pressure. However, the plane as a whole is composed of both surfaces, so we take the vector sum of the forces, which is 0.

Formula §

Pressure

$$P=\frac{\Vert \vec{F}\Vert }{\Vert \vec{A}\Vert }$$

Terms §

• $P$ = Pressure (in Pascals, $\text{Pa}$ )
• $\Vert \vec{F}\Vert$ = Magnitude of Force (in Newtons, $\text{N}$)
• $\Vert \vec{A}\Vert$ = Magnitude of Area (in metres squared, ${\text{m}}^2$)

#tosee pressure is a tensor

Atmospheric Pressure §

Through the use of a pressure sensor, we can compare how much force is applied by the atmosphere at sea level.

$$1\text{ atm}=1.01\times 10^5\text{ Pa}\approx 100\text{ kPa}$$

In some cases, this is notated with $P_0$ This is the force exerted on a region of vacuum by the atmosphere. It is very strong.

Force due to Change in Pressure §

Since Pressure is defined as the Force on a surface, if we take a two dimensional plane, then a pressure difference means there is a force acting on the plane:

Pressure .excalidraw