What is a fluid?
A fluid is anything that can flow. Liquids flow. Gases flow too. So both are fluids.
Why do they flow? Look inside. In a solid, particles (atoms or molecules) are held in fixed places. They can only shake. In a liquid, particles are close together but they can slide past each other. In a gas, particles are far apart and move fast in all directions.
Because the particles can move around, a fluid has no fixed shape. It takes the shape of its container. A liquid keeps its volume. A gas spreads out to fill the whole container.
Density: mass packed into a space
Density is the mass in each unit of volume:
ρ = m ÷ V
ρ is the Greek letter rho. The SI unit is kg/m³. You will also see g/cm³; 1 g/cm³ = 1000 kg/m³.
Useful values: air about 1.2 kg/m³, petrol about 740, cooking oil about 920, water 1000, sea water about 1025, honey about 1420, mercury 13 600 kg/m³.
Density is a property of the material, not of the amount. A cup of water and a bucket of water have the same density. If the fluid is the same everywhere (uniform), you can find the mass of any part: m = ρV.
Relative density and layering
Relative density (also called specific gravity) compares a substance with water:
relative density = ρ ÷ ρwater
It has no unit. Mercury has relative density 13.6, so it is 13.6 times as dense as water.
When liquids that do not mix are poured together, they stack in layers: the densest at the bottom, the least dense on top. Anything with relative density less than 1 floats on water; more than 1 sinks.
The ideal fluid model
Real fluids are complicated, so physicists use a simpler model called an ideal fluid. An ideal fluid:
- is incompressible: you cannot squash it, so its density stays constant;
- has no viscosity (no internal friction), so it flows without losing energy;
- flows steadily: at any one point, the speed does not change with time.
Liquids like water are close to incompressible. Gases are easy to squash, so their density changes with pressure and temperature. When we study a fluid, we often treat a chosen part of it as a system with its own mass, volume and density.
Try it: a density tower
Pour syrup, water and oil into one glass, one at a time, slowly. Guess the order first. Then test small objects: a grape, a plastic bead, a cork. Each one stops at the layer whose density matches its own. This is how we compare densities without a balance.
Key formulas and definitions
- ρ = m ÷ V (density)
- m = ρ × V, V = m ÷ ρ
- Relative density = ρsubstance ÷ ρwater (no unit)
- 1 g/cm³ = 1000 kg/m³; 1 L = 0.001 m³
- ρwater ≈ 1000 kg/m³; 1 L of water ≈ 1 kg
Worked examples
1. A tank holds 2 m³ of water. What is the mass of the water?
m = ρV = 1000 × 2 = 2000 kg.
2. A 0.5 L bottle of oil has mass 0.46 kg. Find the density of the oil.
V = 0.5 L = 0.0005 m³. ρ = m ÷ V = 0.46 ÷ 0.0005 = 920 kg/m³.
3. Mercury has density 13 600 kg/m³. Find its relative density.
Relative density = 13 600 ÷ 1000 = 13.6 (no unit).
4. What volume does 1 kg of petrol (ρ = 740 kg/m³) take up, in litres?
V = m ÷ ρ = 1 ÷ 740 = 0.00135 m³ = 1.35 L.
5. A room is 5 m × 4 m × 3 m. Air has density 1.2 kg/m³. Find the mass of air in the room.
V = 5 × 4 × 3 = 60 m³. m = ρV = 1.2 × 60 = 72 kg. Air is light, but a room full of it is heavier than many people expect.
6. Equal volumes of water (1000 kg/m³) and honey (1420 kg/m³) are mixed well. Find the density of the mixture.
Take 1 m³ of each. Mass = 1000 + 1420 = 2420 kg. Volume = 2 m³. ρ = 2420 ÷ 2 = 1210 kg/m³ (the average, because the volumes are equal).
Common mistakes
- Thinking only liquids are fluids. Gases flow too, so they are fluids.
- Forgetting to change litres to m³: 1 L = 0.001 m³, not 1 m³.
- Giving relative density a unit. It is a ratio, so it has none.
- Thinking a bigger amount has a bigger density. A bucket and a cup of water have the same density; only the mass changes.