# 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 **mass per unit volume**. Mass is a property.

- What is weight and what is mass? - the difference between weight and mass

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 *slugs/ft ^{3}*.

Pounds per cubic foot - *lb/ft ^{3} - *is often used as a measure of density in the US, but 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

*(lb*.

_{m})*1 slug**= 32.174 lb*= 14.594 kg_{m}_{}*1 kg = 2.2046 lb*_{m}= 6.8521x10^{-2}slugs- Unit converter - mass
- Unit converter - density

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 helpful for identification of substances.

- 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 then be calculated as

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

* = 1184 kg/m ^{3}*

#### Example - Density to Identify a Material

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/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 find that ethyl alcohol - or ethanol - has a density of *789 kg/m ^{3}*. The liquid may be ethyl alcohol!

#### Example - Density to Calculate Volume Mass

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

*0.17 m*volume titanium can be calculated as

^{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**.

- What is weight and what is mass? - 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 (9.807 m/s^{2}, 32.174 ft/s^{2})

The SI units for specific weight are *N/m*^{3}. The imperial units are l*b/ft ^{3}*.

Local acceleration *g* is (under normal conditions) *9.807 m/s ^{2}* in SI units and

*32.174 ft/s*in imperial units.

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

The density of water is *1000 kg/m ^{3}* at

*4*. The specific weight in SI units is

^{o}C (*39*)^{o}F

γ = (1000 kg/m^{3}) (9.81 m/s^{2})

= 9810 (N/m^{3})

= 9.81 (kN/m^{3})

The density of water is *1.940 slugs/ft^{3}* at

*39*. The specific weight in Imperial units is

^{o}F (*4*)^{o}C

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

= 62.4 (lb/ft^{3})

#### Specific Weight for Some common Materials

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

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

Aluminum | 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 - *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 = ρ_{substance}/ ρ_{H2O}(3)

where

SG= Specific Gravity of the substance

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

ρ_{H2O}= density of water - normally at temperature 4^{o}C (kg/m^{3})

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

*1000 kg/m*

^{3 }or

*62.4 lb/ft*.

^{3}Specific Gravity - *SG* - is dimensionless and has the same value in the SI system and the imperial English system (BG). Water is normally also used as reference when calculating the specific gravity for solids.

- Thermal Properties of Water - Density, Freezing temperature, Boiling temperature, Latent heat of melting, Latent heat of evaporation, Critical temperature ...

#### Specific Gravities 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 (4^{o}C) | 1.00 |

Water, sea | 1.02 |

#### Example - Specific Gravity of Iron

The density of iron is *7850 kg/m ^{3}*. The specific gravity of iron related to water with density

*1000 kg/m*is

^{3}

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

= 7.85

**Specific Gravities of Gases**

The Specific Gravity of a gas 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 = ρ_{gas}/ ρ_{air}(3)

where

SG= specific gravity of gas

ρ_{gas}= density of gas (kg/m^{3})

ρ_{air}= density of air (normally at NTP- 1.205kg/m^{3})

- NTP - Normal Temperature and Pressure - defined as
*20*and 1^{o}C (293.15 K, 68^{o}F)*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.

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