Describe, qualitatively, how the pressure beneath the surface of a liquid changes with depth and density of the liquid

1.8 Pressure

What is Pressure?

Pressure is the force applied per unit area. In a fluid, it is the same in all directions at a given depth. Think of it like the gentle push you feel when you sit on a chair – the chair pushes back with a force that spreads over the area of your seat.

How Pressure Changes with Depth

When you go deeper into a liquid, you are surrounded by more liquid above you. Each layer of liquid pushes down on the layers below. The deeper you go, the more layers there are, so the pressure increases.

Mathematically, the pressure at depth \(h\) is given by

\( P = P_0 + \rho g h \)

• \(P_0\) – pressure at the surface (usually atmospheric pressure).
• \(\rho\) – density of the liquid.
• \(g\) – acceleration due to gravity (≈9.81 m s⁻²).
• \(h\) – depth below the surface.

🔵 Analogy: Imagine you’re a swimmer in a pool. The deeper you dive, the more water “presses” on you from all sides, just like a gentle hug that gets stronger as you go deeper.

Effect of Density

Density is how much mass is packed into a given volume. A liquid with higher density exerts more pressure at the same depth.

• Water: \(\rho \approx 1000 \text{ kg m}^{-3}\)
• Saltwater: \(\rho \approx 1025 \text{ kg m}^{-3}\)
• Oil: \(\rho \approx 800 \text{ kg m}^{-3}\)

So, at 10 m depth:

Exam Tips

1. Remember the formula \(P = P_0 + \rho g h\). Write it clearly and label each variable.
2. When asked “how does pressure change with depth?”, answer: “It increases linearly with depth.”
3. For “how does density affect pressure?”, answer: “Higher density → greater pressure at the same depth.”
4. Use the word “qualitatively” – focus on the direction of change, not exact numbers.
5. Draw a simple diagram: a vertical column of liquid with arrows showing pressure increasing downward.
6. Check units: pressure in pascals (Pa) or megapascals (MPa); depth in metres; density in kg m⁻³.