Density and Pressure
Learn how to calculate density and pressure, and understand how pressure varies in fluids
Under Pressure
From atmospheric to deep-sea
Density (ρ) measures how much mass is packed into a given volume. It's calculated using the formula:
ρ = m ÷ V
density = mass ÷ volume
The SI unit for density is kilograms per cubic metre (kg/m³), though g/cm³ is also commonly used. Different substances have different densities—gold (19,300 kg/m³) is much denser than water (1,000 kg/m³).
Unusually, ice is less dense than liquid water (917 kg/m³ vs 1,000 kg/m³), which is why ice floats. This property is crucial for aquatic life in frozen lakes.
Pressure (P) is the force acting perpendicular to a surface divided by the area of that surface:
P = F ÷ A
pressure = force ÷ area
Pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m². Pressure increases when force increases or area decreases. This explains why a sharp knife cuts better—the same force over a smaller area creates higher pressure.
In fluids (liquids and gases), pressure acts equally in all directions and increases with depth. The pressure at a given depth is calculated using:
P = ρgh
pressure = density × gravity × height
Atmospheric pressure at sea level is approximately 101,000 Pa, caused by the weight of air above us. Divers experience increased pressure underwater—at 10m depth, the total pressure is roughly double atmospheric pressure.
ρ = m ÷ V
density = mass ÷ volume
Common Densities (kg/m³)
Gold
19,300
Lead
11,340
Iron
7,870
Water
1,000
Ice
917
Air
1.2
Density
Question:
A diver swims to a depth of 15 m in seawater (density = 1025 kg/m³). Calculate the pressure due to the water at this depth. (g = 9.8 m/s²)
Answer:
Using P = ρgh:
P = 1025 × 9.8 × 15 = 150,675 Pa
Total pressure = water pressure + atmospheric pressure
= 150,675 + 101,000 = 251,675 Pa (about 2.5 atmospheres)
What is the formula for density?