Fluid Pressure

Definition

A pressure is the force acting per unit area by a fluid. Let’s denote $F$ as the force, $A$ as the area upon which the force acts, and $P$ as the pressure. Then,

$$ P=\dfrac{F}{A} [\mathrm{N/m^{2}}] $$

Description

The unit of pressure is newtons per square meter $\mathrm{N/m^{2}}$, known as Pascal, and denoted by $\mathrm{Pa}$.

$$ 1 \mathrm{Pa} = 1 \mathrm{N/m^{2}} $$

A characteristic feature of pressure is that it acts perpendicularly to the surface of all objects in contact with the fluid.

Derivation

Suppose a fluid exerts force on area $A$. Then, as area $A$ expands, the total force exerted by the fluid also increases. It might help to think of this as more water (or oxygen) molecules touching the area. The larger the area in contact with the fluid, the greater the total force, implying a proportional relationship.

$$ F \propto A $$

Expressing this using a proportionality constant,

$$ F=CA $$

At this point, the proportionality constant $C$ is precisely what we call the pressure.

$$ P=\dfrac{F}{A} $$