⚖️ Material Density

Density (ρ): 0 kg/m³

🌊 Hydrostatic Pressure

Pressure (p): 0 Pa
Atmospheres: 0 atm

Fluids and Density

Materials show a vast range of densities, from the low-density gases to the high-density metals like Lead or Gold. In AS Level Physics, we focus on how the density of fluids leads to hydrostatic pressure and upthrust.

ρ = Mass (m) / Volume (V)

1. Pressure in a Liquid

Pressure in a fluid acts equally in all directions. The pressure due to a column of liquid is proportional to the density of the liquid, the depth, and the gravitational field strength (g ≈ 9.81 m/s²).

Δp = ρgΔh

2. Archimedes’ Principle

When an object is fully or partially submerged in a fluid, it experiences an upward force called upthrust. This force is equal to the weight of the fluid that the object has displaced.

Upthrust = ρ_fluid × V_submerged × g
Exam Tip: Be careful with volume units. Calculations must be in m³. To convert cm³ to m³, you must multiply by 10⁻⁶, and for liters to m³, multiply by 10⁻³.

Deep Dive: Worked Examples

✅ Example 1: Pressure on a Submarine

A submarine is at a depth of 500m in sea water (ρ = 1030 kg/m³). Calculate the hydrostatic pressure.

Step 1: Formula p = ρgh
Step 2: Calculate p = 1030 × 9.81 × 500
Step 3: Solve p = 5.05 × 10⁶ Pa (or 5.05 MPa)

✅ Example 2: Upthrust on a Buoy

A spherical buoy of volume 0.8 m³ is completely submerged in fresh water. Calculate the upthrust.

Step 1: Archimedes Principle Upthrust = Weight of displaced water = ρVg
Step 2: Calculate U = 1000 × 0.8 × 9.81
Step 3: Solve U ≈ 7848 N

✅ Example 3: Finding Unknown Volume

An irregular gold crown has a mass of 2.5 kg. If the density of gold is 19,300 kg/m³, find its volume.

Step 1: Rearrange ρ = m/V V = m / ρ
Step 2: Calculate V = 2.5 / 19300
Step 3: Solve V ≈ 1.30 × 10⁻⁴ m³ (or 130 cm³)

✅ Example 4: Density of a Mixture

1 kg of water (ρ=1000) is mixed with 1 kg of alcohol (ρ=800). What is the density of the mixture?

Step 1: Find total volume V_tot = (1/1000) + (1/800) = 0.001 + 0.00125 = 0.00225 m³
Step 2: Total Mass m_tot = 2 kg
Step 3: ρ_mix = m_tot / V_tot ρ_mix = 2 / 0.00225 ≈ 889 kg/m³

✅ Example 5: Height of Atmosphere?

If air had a constant density of 1.2 kg/m³ and atmospheric pressure is 101 kPa, what would be the height of the atmosphere?

Step 1: Use p = ρgh h = p / (ρg)
Step 2: Calculate h = 101000 / (1.2 × 9.81)
Step 3: Solve h ≈ 8580 m (8.6 km)