8.1 Fluids, Density, and Pressure

What is a fluid?

A fluid is any substance (liquid or gas) that flows and takes the shape of its container because it cannot maintain a fixed structure under shear stress. Fluids consist of many particles in constant motion, and we describe their behavior using bulk properties like density and pressure rather than tracking individual particles.

Density

Density (ρ) is mass per unit volume: ρ = m/V, measured in kg/m³. Density tells you how tightly packed matter is in a substance. Objects less dense than a fluid float; denser objects sink. Density is an intensive property — it doesn't depend on the amount of substance present, only its composition and state.

Pressure in fluids

Pressure (P) is force per unit area exerted perpendicular to a surface: P = F/A, measured in pascals (Pa = N/m²). In a fluid at rest, pressure acts equally in all directions at a given point and increases with depth due to the weight of fluid above: P = P₀ + ρgh, where h is depth below the surface.

Key terms

Density

ρ = m/V; mass per unit volume, measured in kg/m³.

Pressure

P = F/A; force per unit area, measured in pascals (Pa = N/m²).

Fluid

A substance (liquid or gas) that flows and takes the shape of its container.

Pressure vs. depth formula

P = P₀ + ρgh — pressure increases with depth due to the weight of fluid above.

Why objects float or sink

An object floats if its density is less than the fluid's density; it sinks if greater.

Try an AP-style question

An object has mass 500 kg and volume 0.5 m³. What is its density?

1. 250 kg/m³
2. 0.001 kg/m³
3. 1,000 kg/m³
4. 500 kg/m³