# Density, Specific Weight and Specific Gravity

## An introduction and definition of density, specific weight and specific gravity - formulas with examples

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**Density**

Density is defined as an objects mass per unit volume. Mass is a property.

- Mass and Weight - the Difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

The density can be expressed as

ρ = m / V= 1 / v_{g }(1)

where

ρ= density (kg/m^{3}, slugs/ft^{3})

m= mass (kg, slugs)

V= volume (m^{3}, ft^{3})

v_{g}= specific volume (m^{3}/kg, ft^{3}/slug)

The SI units for density are *kg/m*^{3}. The imperial (U.S.) units are *lb/ft ^{3} (slugs/ft^{3})*. 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.

*1 gram/cm*^{3}= 1000 kg/m^{3}= 62.4 lb/ft^{3}- Unit converter

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.

#### Relative Density (Specific Gravity)

Relative density of a substance is the ratio of the substance to the density of water at 4^{o}C, i.e.

Substance | Relative density |
---|---|

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 (4^{o}C) | 1.00 |

Water, sea | 1.02 |

- density of water at different temperatures - SI and Imperial units

#### Example - Density of a Golf ball

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} m^{3}*

The density of the golf ball can be calculated as

*ρ = (45 g) (0.001 kg/g) / (3.8 10 ^{-5} m^{3})*

* = 1184 kg/m ^{3}*

#### 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/m^{3})]

= (18.5 10^{-3}kg) / (23.4 10^{-6}m^{3})

= 790 (kg/m^{3})

If we look up densities of some common liquids, we can find that ethyl alcohol, or ethanol, has a density of *789 kg/m ^{3}*. The liquid may be ethyl alcohol!

#### Example - Use Density to Calculate the Mass of a Volume

The density of titanium is *4507 kg/m ^{3}*. Calculate the mass of

*0.17 m*titanium!

^{3}

m= (0.17 m^{3}) (4507 kg/m^{3})

= 766.2 (kg)

### Specific Weight

**Specific Weight** is defined as weight per unit volume. Weight is a **force**.

- Mass and Weight - the difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

Specific Weight can be expressed as

γ = ρ g(2)

where

γ= specific weight (N/m^{3}, lb/ft^{3})

ρ= density (kg/m^{3}, slugs/ft^{3})

g= acceleration of gravity (9.81 m/s^{2}, 32.174 ft/s^{2})

The SI-units of specific weight are *N/m*^{3}. The imperial units are l*b/ft ^{3}*. The local acceleration

*g*is under normal conditions

*9.807 m/s*in SI-units and

^{2}*32.174 ft/s*in imperial units.

^{2}#### Example - Specific Weight Water

Specific weight for water at *39 ^{o}F (4 ^{o}C)* is

*62.4 lb/ft*in imperial units.

^{3}(9.81 kN/m^{3})With a density of water *1000 kg/m ^{3}* - specific weight in SI units can be calculated as

γ = (1000 kg/m^{3}) (9.81 m/s^{2})

= 9810 (N/m^{3})

= 9.81 (kN/m^{3})

With a density of water *1.940 slugs/ft^{3}* - specific weight in SI units can be calculated as

γ = (1.940 slugs/ft^{3}) (32.174 ft/s^{2})

= 62.4 (lb/ft^{3})

#### Example - Specific Weight Some other Materials

Product | Specific Weight - γ | |
---|---|---|

Imperial Units(lb/ft^{3}) | SI Units(kN/m^{3}) | |

Aluminium | 172 | 27 |

Brass | 540 | 84.5 |

Copper | 570 | 89 |

Ethyl Alcohol | 49.3 | 7.74 |

Gasoline | 42.5 | 6.67 |

Glycerin | 78.6 | 12.4 |

Mercury | 847 | 133.7 |

SAE 20 Oil | 57 | 8.95 |

Seawater | 64 | 10.1 |

Stainless Steel | 499 - 512 | 78 - 80 |

Water | 62.4 | 9.81 |

Wrought Iron | 474 - 499 | 74 - 78 |

**Specific Gravity (Relative Density)**

**Specific Gravity Liquids**

The Specific Gravity - *SG* - of a liquid is a dimensionless unit defined as the ratio of density of the liquid to the density of water at a specified temperature. Specific Gravity of a liquid can be expressed

SG = ρ / ρ_{H2O}(3)

where

SG= specific gravity

ρ= density of fluid or substance (kg/m^{3})

ρ_{H2O}= density of water (kg/m^{3})

It is common to use the density of water at *4 ^{o}C (39^{o}F)* as reference - at this point the density of water is at the highest -

*1000 kg/m*

^{3 }or

*62.4 lb/ft*.

^{3}- 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/m ^{3}, 7.85 grams per cubic centimeter (cm^{3})*,

*7.85 kilograms per liter*, or

*7.85 metric tons per cubic meter*- the specific gravity of iron is:

SG= (7850 kg/m^{3}) / (1000 kg/m^{3})

= 7.85

- water density is
*1000 kg/m*^{3}

**Specific Gravity Gases**

The Specific Gravity - *SG* - of a gas is a dimensionless unit defined as the ratio of density of the gas to the density of air at a specified temperature and pressure. In general conditions according NTP - Normal Temperature and Pressure - defined as air at *20 ^{o}C (293.15 K, 68^{o}F)* and 1

*atm ( 101.325 kN/m2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr)*, where density of air is

*1.205 kg/m*, is used.

^{3}Note that the density of both gases should be evaluated at the same pressure and temperature - and when this happens the *SG* can be calculated utilizing only the molecular weights.

SG = ρ / ρ_{air}(3)

where

SG= specific gravity

ρ= density of gas or substance (kg/m^{3})

ρ_{air}= density of air (kg/m^{3})

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