Density
Density is defined as an objects mass per unit volume. Mass is a property.
The density can be expressed as
ρ = m / V = 1 / vg (1)
where
ρ = density (kg/m3)
m = mass (kg)
V = volume (m3)
vg = specific volume (m3/kg)
The SI units for density are kg/m3. The imperial (BG) units are lb/ft3 (slugs/ft3). While people often use pounds per cubic foot as a measure of density in the U.S., pounds are really a measure of force, not mass. Slugs are the correct measure of mass. You can multiply slugs by 32.2 for a rough value in pounds.
The higher the density, the tighter the particles are packed inside the substance. Density is a physical
property constant at a given temperature and density can help to identify a substance.
Example - Use the Density to Identify the Material:
An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).
The density 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 densities of some common substances, we can find that ethyl alcohol, or ethanol, has a density of 790 kg/m3. Our unknown liquid may likely be ethyl alcohol!
Example - Use Density to Calculate the Mass of a Volume
The density of titanium is 4507 kg/m3 . Calculate the mass of 0.17 m3 titanium!
m = 0.17 (m3) 4507 (kg/m3)
= 766.2 kg
Specific Weight
Specific Weight is defined as weight per unit volume. Weight is a force.
Specific Weight can be expressed as
γ = ρ g (2)
where
γ = specific weight (kN/m3)
The SI-units of specific weight are kN/m3. The imperial units are lb/ft3. The local acceleration g is under normal conditions 9.807 m/s2 in SI-units and 32.174 ft/s2 in imperial units.
Example - Specific Weight Water
Specific weight for water at 60 oF is 62.4 lb/ft3 in imperial units and 9.80 kN/m3 in SI-units.
Example - Specific Weight Some other Materials
|
Product |
Specific Weight - γ |
|
Imperial Units
(lb/ft3) |
SI Units
(kN/m3) |
| Ethyl Alcohol |
49.3 |
7.74 |
| Gasoline |
42.5 |
6.67 |
| Glycerin |
78.6 |
12.4 |
| Mercury |
847 |
133 |
| SAE 20 Oil |
57 |
8.95 |
| Seawater |
64 |
10.1 |
| Water |
62.4 |
9.80 |
Specific Gravity
The Specific Gravity - SG - is a dimensionless unit defined as the ratio of density of the material to the density of water at a specified temperature. Specific Gravity can be expressed as
SG = = ρ / ρH2O (3)
where
SG = specific gravity
ρ = density of fluid or substance (kg/m3)
ρH2O = density of water (kg/m3)
It is common to use the density of water at 4 oC (39oF) as reference - at this point the density of water is at the highest.
- Thermal Properties of Water Density, Freezing temperature, Boiling temperature, Latent heat of melting, Latent heat of evaporation, Critical temperature ...
Since Specific Weight is dimensionless it has the same value in the metric SI system as in the imperial English system (BG). At the reference point the Specific Gravity has same numerically value as density.
Example - Specific Gravity
If the density of iron is 7850 kg/m3, 7.85 grams per cubic centimeter (cm3), 7.85 kilograms per liter, or 7.85 metric tons per cubic meter - the specific gravity of iron is:
SG = 7850 kg/m3/ 1000 kg/m3
= 7.85
(the density of water is 1000 kg/m3)
