Pressure in Liquids, Fluids and Gases

Pressure tells us how spread out a force is. A fluid is a liquid or a gas. Fluids press on surfaces because their particles move and push on whatever they touch.

Pressure, Force and Area

Pressure increases with bigger force and decreases with bigger area: $p = \frac{F}{A}$. Unit: pascal (Pa) where 1 Pa = 1 N/m².

• Standing on snow: narrow boots sink (small area → high pressure); skis spread your weight (large area → low pressure).
• Drawing pin: a small sharp tip gives high pressure, so it enters the board easily.

Pressure in Liquids (with Depth)

In a liquid, pressure increases with depth because more liquid is above you, adding weight. It depends on the liquid’s density $\rho$, gravity $g$, and the change in depth $\Delta h$:

$$\Delta p = \rho g \Delta h$$

• At the same depth, pressure is the same in all directions and does not depend on the shape of the container.
• Real-world: ears “pop” when diving; dams are thicker at the bottom.

Gas Pressure (particle model)

Gas particles move quickly and collide with surfaces, creating pressure. Heating makes particles move faster, increasing pressure if volume is fixed. If temperature is constant, making the gas occupy more volume spreads the particles out, lowering pressure.

For a fixed mass of gas at constant temperature: $$p_1 V_1 = p_2 V_2$$

• Syringe: pushing in halves the volume and roughly doubles the pressure (if temperature stays the same).
• Tyres feel harder when pumped because the gas pressure increases.