Density & Pressure

You’ll be able to

Compute density as ρ = m/V
Define pressure as force per unit area, P = F/A
Find how pressure increases with depth, P = ρgh

Density: how much mass per volume

Density is the amount of mass packed into a given volume, ρ = m/V, measured in kg/m³. It is an intrinsic property of a material — a small lead ball and a huge lead statue have the same density. Water’s density is about 1000 kg/m³, a convenient benchmark: materials denser than water sink in it, and less dense ones float.

Pressure spreads force over area

Pressure is force distributed over an area, P = F/A, measured in pascals (Pa) = N/m². The same force applied over a smaller area produces greater pressure — which is why a sharp knife cuts and snowshoes keep you from sinking. In a fluid, pressure pushes equally in all directions on any surface it touches.

Density, pressure, and pressure with depth

ρ = m/V · P = F/A · P = P₀ + ρgh

ρgh is the gauge pressure — the extra pressure from a depth h of fluid. P₀ is the pressure at the surface (often atmospheric).

Worked example

Find the gauge pressure at a depth of 5 m in water (ρ = 1000 kg/m³, g = 10 m/s²).

1.Gauge pressure is the pressure from the fluid column: P = ρgh.
2.Substitute: P = 1000 × 10 × 5.
3.Multiply step by step: 1000 × 10 = 10000, then × 5.
4.Result: P = 50000 Pa (50 kPa).

Answer: P = 50000 Pa of gauge pressure

Tip

Pressure in a fluid depends on depth, not on the shape or width of the container. A narrow tube and a wide lake have the same pressure at the same depth — only h matters in ρgh.

Checkpoint

A block has a mass of 600 kg and a volume of 0.2 m³. What is its density?

Checkpoint

What is the gauge pressure at a depth of 3 m in water? (ρ = 1000 kg/m³, g = 10 m/s²)

On the exam

Distinguish gauge pressure (ρgh, the pressure from the fluid alone) from absolute pressure (P₀ + ρgh, which adds the atmosphere on top). Read the question carefully to see which is asked.

Answer the 2 checkpoints as you read.