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| Unit | Value | Common Use |
|---|
Theory & Formulas
Density (\(\rho\)) is a fundamental intensive property of matter — it depends only on the material and its state, not on the quantity. It is defined as mass per unit volume:
Specific gravity (SG) is the dimensionless ratio of a material's density to water's density at 4°C (\(\rho_{\text{water}} = 1000 \text{ kg/m}^3\)):
SG < 1 → floats in water (e.g. wood, ice, oil). SG > 1 → sinks. SG is numerically equal to density in g/cm³.
Any object submerged in a fluid experiences an upward buoyant force equal to the weight of displaced fluid: \(F_b = \rho_{\text{fluid}} \times V_{\text{sub}} \times g\). A hollow steel ship floats because its average density (accounting for air-filled volume) is less than water's density.
[Image of Archimedes principle buoyant force diagram]Density is used in: structural dead load calculation (weight = \(\rho \times V \times g\)), material selection, buoyancy analysis, concrete mix design, fluid flow analysis (mass flow = \(\rho \times Q\)), and quality control (measured vs theoretical density reveals voids).
| From | To kg/m³ | Multiply by | Notes |
|---|---|---|---|
| g/cm³ | kg/m³ | 1,000 | Water = 1 g/cm³ = 1000 kg/m³ |
| kg/L | kg/m³ | 1,000 | Same as g/cm³ numerically |
| lb/ft³ | kg/m³ | 16.0185 | Steel ≈ 490 lb/ft³ |
| lb/in³ | kg/m³ | 27,679.9 | Lead ≈ 0.41 lb/in³ |
| oz/in³ | kg/m³ | 1,729.99 | Used for small dense objects |
| t/m³ | kg/m³ | 1,000 | Same as g/cm³ numerically |
Frequently Asked Questions
1. What is density and why is it called an intensive property?
Density is mass per unit volume (ρ = m/V), typically expressed in kg/m³ or g/cm³. It is an intensive property because it does not change with the amount of material: a 1 kg block of steel has the same density as a 1000 kg block of the same alloy. Intensive properties depend only on the material's identity and state (temperature, pressure, phase), not on how much of it you have.
2. Why does ice float on water if they are the same substance?
Water is unique: it expands upon freezing (unlike most substances). At 0°C, liquid water has density ≈ 999.8 kg/m³, while ice at 0°C has density ≈ 917 kg/m³. Because ice is less dense, it floats. This anomaly arises from the hexagonal crystal lattice of ice, which holds molecules further apart than liquid water's more compact hydrogen-bonded network. This property is critical for aquatic ecosystems.
3. How is density used in concrete mix design?
In concrete, density helps calculate dead loads. Fresh concrete density ≈ 2400 kg/m³ (standard). The theoretical air-free density of a mix can be calculated from component masses and specific gravities (cement ≈ 3150 kg/m³, fine aggregate ≈ 2650, coarse aggregate ≈ 2700) to determine air content from measured fresh density.
4. What is the difference between density, unit weight, and specific weight?
Density (ρ) = mass/volume (kg/m³). Specific weight (γ) = weight/volume = ρ × g (N/m³ or kN/m³). For water: ρ = 1000 kg/m³, γ = 9.81 kN/m³. Specific gravity (SG) = ρ_material/ρ_water — dimensionless. Unit weight is used interchangeably with specific weight in geotechnical engineering.
5. Why do gases have much lower densities than liquids and solids?
In gases, molecules are highly separated — approximately 1000× lower density than liquids. Air at STP: ≈ 1.225 kg/m³ vs water at 1000 kg/m³. Gas density varies strongly with temperature and pressure (ideal gas law: ρ = PM/RT where M = molar mass, R = gas constant, T = temperature in Kelvin).
6. How does temperature affect the density of metals?
Metals expand linearly with temperature following the coefficient of thermal expansion (CTE). Volume = V₀(1 + 3α·ΔT). Density decreases as temperature rises. For steel (α ≈ 12×10⁻⁶/°C): a 500°C rise reduces density by about 1.8%. At temperatures near melting, density drops significantly.
7. What is the density of air and how does it affect structural design?
Dry air at sea level (15°C, 101.325 kPa): density ≈ 1.225 kg/m³. Wind pressure = 0.5 × ρ_air × v² (Pa). For a 50 m/s wind: pressure = 0.5 × 1.225 × 2500 = 1531 Pa ≈ 1.53 kPa. Air density decreases with altitude and increases slightly with humidity.
8. How is density measured experimentally?
Common methods: (1) Displacement — measure liquid displaced by solid in graduated cylinder. (2) Pycnometry — calibrated flask filled with liquid of known density. (3) Hydrostatic weighing — weigh in air and in liquid; ρ = m_air/(m_air−m_liquid) × ρ_liquid. (4) Oscillating U-tube densitometer for liquids.
9. What is bulk density and how does it differ from particle density?
Particle (true) density excludes voids: ρ_particle = m_solids/V_solids. Bulk density includes voids between particles: ρ_bulk = m_material/V_total. For a sand sample with void ratio e: ρ_bulk = ρ_particle/(1+e). Bulk density is critical in geotechnical engineering for soil settlement calculations.
10. How do you calculate the weight of a structural steel member?
Weight = ρ × V × g. For steel (ρ = 7850 kg/m³), a beam of length 6 m and cross-sectional area 0.0076 m²: Volume = 0.0456 m³, Mass = 357.9 kg, Weight = 357.9 × 9.81 ≈ 3.51 kN. This self-weight is included in dead load calculations.
11. Why do alloys have different densities than their constituent elements?
Alloy density ≈ weighted average: ρ_alloy = 1/Σ(w_i/ρ_i) where w_i are mass fractions. However, atom size differences and electronic interactions can cause slight volume changes on mixing. In practice, alloy densities are measured and tabulated in standards like ASTM.
12. What causes density stratification in water bodies?
Density stratification occurs when layers of different densities form due to temperature (thermocline) or salinity (halocline) gradients. Denser water sinks. Critical in dam design (thermal stratification affects outlet design), ocean engineering (buoyancy of submerged structures changes with depth), and pollutant dispersion modeling.