Density is defined as mass per unit volume. Mass is a property and the SI unit for density is [kg/m3].
Density can be expressed as
ρ = m / V = 1 / ν [1]where
ρ = density [kg/m3], [slugs/ft3]
m = mass [kg], [slugs]
V = volume [m3], [ft3]
ν = specific volume [m3/kg], [ft3/slug]
- What is weight and what is mass? - the difference between weight and mass
The Imperial (U.S.) units for density are slugs/ft3 but pound-mass per cubic foot - lbm/ft3 - is often used. Note that there is a difference between pound-force (lbf) and pound-mass (lbm). Slugs can be multiplied with 32.2 for a rough value in pound-mass (lbm).
- 1 slug = 32.174 lbm = 14.594 kg
- 1 kg = 2.2046 lbm = 6.8521x10-2 slugs
- density of water: 1000 kg/m3, 1.938 slugs/ft3
On atomic level - particles are packed tighter inside a substance with higher density. Density is a physical property - constant at a given temperature and pressure - and may be helpful for identification of substances.
Below on this page: Specific gravity (relative density), Specific gravity for gases, Specific weight, Calculation examples
Coefficient - variation with temperature and pressure, SI and Imperial units
Example 1: Density of a Golf ball
Example 1: Density of a Golf ball
Example 2: Using Density to Identify a Material
Example 3: Density to Calculate Volume Mass
Example 3: Density to Calculate Volume Mass
Specific Gravity (Relative Density) - SG - is a dimensionless unit defined as the ratio of the density of a substance to the density of water - at a specified temperature and can be expressed as
SG = ρsubstance / ρH2O [2]where
SG = Specific Gravity of the substance
ρsubstance = density of the fluid or substance [kg/m3]
ρH2O = density of water - normally at temperature 4 oC [kg/m3]
It is common to use the density of water at 4 oC (39oF) as a reference since water at this point has its highest density of 1000 kg/m3 or 1.940 slugs/ft3.
Since Specific Gravity - SG - is dimensionless, it has the same value in the SI system and the imperial English system (BG). SG of a fluid has the same numerical value as its density expressed in g/mL or Mg/m3. Water is normally also used as reference when calculating the specific gravity for solids.
Example 4: Specific Gravity of Iron
Specific Gravity for some common Materials
| Substance | Specific Gravity - SG - |
|---|---|
| Acetylene | 0.0017 |
| Air, dry | 0.0013 |
| Alcohol | 0.82 |
| Aluminum | 2.72 |
| Brass | 8.48 |
| Cadmium | 8.57 |
| Chromium | 7.03 |
| Copper | 8.79 |
| Carbon dioxide | 0.00198 |
| Carbon monoxide | 0.00126 |
| Cast iron | 7.20 |
| Hydrogen | 0.00009 |
| Lead | 11.35 |
| Mercury | 13.59 |
| Nickel | 8.73 |
| Nitrogen | 0.00125 |
| Nylon | 1.12 |
| Oxygen | 0.00143 |
| Paraffin | 0.80 |
| Petrol | 0.72 |
| PVC | 1.36 |
| Rubber | 0.96 |
| Steel | 7.82 |
| Tin | 7.28 |
| Zinc | 7.12 |
| Water (4oC) | 1.00 |
| Water, sea | 1.027 |
Specific Gravity of gases is normally calculated with reference to air - and defined as the ratio of the density of the gas to the density of the air - at a specified temperature and pressure.
The Specific Gravity can be calculated as
SG = ρgas / ρair [3]where
SG = specific gravity of gas
ρgas = density of gas [kg/m3]
ρair = density of air (normally at NTP - 1.204 [kg/m3])
- NTP - Normal Temperature and Pressure - defined as 20oC (293.15 K, 68oF) and 1 atm ( 101.325 kN/m2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr)
Molecular weights can be used to calculate Specific Gravity if the densities of the gas and the air are evaluated at the same pressure and temperature.
Specific Weight is defined as weight per unit volume. Weight is a force. The SI unit for specific weight is [N/m3]. The imperial unit is [lb/ft3].
Specific Weight (or force per unit volume) can be expressed as
γ = ρ ag [4]where
γ = specific weight (N/m3], [lb/ft3]
ρ = density [kg/m3], [slugs/ft3]
ag = acceleration of gravity (9.807 [m/s2], 32.174 [ft/s2] under normal conditions)
- What is weight and what is mass? - the difference between weight and mass
Example 5: Specific Weight of Water
Specific Weight for Some common Materials
| Product | Specific Weight - γ - | |
|---|---|---|
| Imperial Units (lb/ft3) | SI Units (kN/m3) | |
| Aluminum | 172 | 27 |
| Brass | 540 | 84.5 |
| Carbon tetrachloride | 99.4 | 15.6 |
| Copper | 570 | 89 |
| Ethyl Alcohol | 49.3 | 7.74 |
| Gasoline | 42.5 | 6.67 |
| Glycerin | 78.6 | 12.4 |
| Kerosene | 50 | 7.9 |
| Mercury | 847 | 133.7 |
| SAE 20 Motor Oil | 57 | 8.95 |
| Seawater | 63.9 | 10.03 |
| Stainless Steel | 499 - 512 | 78 - 80 |
| Water | 62.4 | 9.81 |
| Wrought Iron | 474 - 499 | 74 - 78 |
Examples
A golf ball has a diameter of 42 mm and a mass of 45 g. The volume of the golf ball can be calculated as
V = (4/3) π (42 [mm] * 0.001 [m/mm]/2)3 = 3.8 10-5 [m3]
The density of the golf ball can then be calculated as
ρ = 45 [g] * 0.001 [kg/g] / 3.8 10-5 [m3] = 1184 [kg/m3]
An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml (milliliter).
The density of the substance can be calculated as
ρ = (18.5 [g] /1000 [g/kg]) / (23.4 [ml] /(1000 [ml/l] * 1000[l/m3]))= 18.5 10-3 [kg] /23.4 10-6 [m3] = 790 [kg/m3]
If we look up the densities of some common liquids we find that ethyl alcohol - or ethanol - has a density of 789 kg/m3. The liquid may be ethyl alcohol!
The density of titanium is 4507 kg/m3. The mass of 0.17 m3 volume titanium can be calculated as
m = 0.17 [m3] * 4507 [kg/m3] = 766.2 [kg]
Note! - be aware that there is a difference between "bulk density" and actual "solid or material density". This may not be clear in the description of products. Always double check values with other sources before important calculations.
Example 4: Specific Gravity of Iron
The density of iron is 7850 kg/m3. The specific gravity of iron related to water with density 1000 kg/m3 is
SG(iron) = 7850 [kg/m3] / 1000 [kg/m3] = 7.85
The density of water is 1000 kg/m3 at 4 °C (39 °F).
The specific weight in SI units is
γ = 1000 [kg/m3] * 9.81 [m/s2] = 9810 [N/m3] = 9.81 [kN/m3]
The density of water is 1.940 slugs/ft3 at 39 °F (4 °C).
The specific weight in Imperial units is
γ = 1.940 [slugs/ft3] * 32.174 [ft/s2] = 62.4 [lb/ft3]
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