# Specific weight

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Specific_weight
> Markdown URL: https://mediated.wiki/source/Specific_weight.md
> Source: https://en.wikipedia.org/wiki/Specific_weight
> Source revision: 1323102216
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Weight per unit volume of a material}}
{{Distinguish|Specific gravity|Specific density|Specific force}}

The '''specific weight''', also known as the '''unit weight''' (symbol {{mvar|γ}}, the Greek letter [gamma](/source/gamma)), is a [volume-specific quantity](/source/Specific_quantity) defined as the [weight](/source/weight) {{mvar|W}} divided by the [volume](/source/volume) {{mvar|V}} of a material:
<math display=block>\gamma = \frac{W}{V} \ .</math>
Equivalently, it may also be formulated as the product of [density](/source/density), {{mvar|&rho;}}, and [gravity acceleration](/source/Standard_gravity), {{mvar|g}}: 
<math display=block>\gamma = \rho \, g .</math>
Its [unit of measurement](/source/unit_of_measurement) in the [International System of Units](/source/International_System_of_Units) (SI) is the [newton](/source/Newton_(unit)) per [cubic metre](/source/cubic_metre) (N/m<sup>3</sup>), expressed in terms of [base units](/source/base_units) as kg⋅m<sup>−2</sup>⋅s<sup>−2</sup>.
A commonly used value is the specific weight of [water](/source/water) on [Earth](/source/Earth) at {{convert|4|C|abbr=on}}, which is {{convert|9.807|kN/m3|disp=or|lk=on}}.<ref name="FE">National Council of Examiners for Engineering and Surveying (2005). ''Fundamentals of Engineering Supplied-Reference Handbook'' (7th ed.). {{ISBN|1-932613-00-5}}.
</ref>

== Discussion ==
The [density](/source/density) of a material is defined as [mass](/source/mass) divided by volume, typically expressed with the unit kg/m<sup>3</sup>. 
Unlike density, specific weight is not a fixed property of a material, as it depends on the value of the [gravitational acceleration](/source/gravitational_acceleration), which varies with location (e.g., [Earth's gravity](/source/Earth's_gravity)). 
In practice, the [standard gravity](/source/standard_gravity) (a constant) is often assumed, usually taken as {{val|9.80665|u=m|up=s2}}.

[Pressure](/source/Pressure) may also affect values, depending upon the [bulk modulus](/source/bulk_modulus) of the material, but generally, at moderate pressures, has a less significant effect than the other factors.<ref name="fluids" />

== Applications ==
=== Fluid mechanics ===
In [fluid mechanics](/source/fluid_mechanics), specific weight represents the [force](/source/force) exerted by [gravity](/source/gravity) on a unit volume of a fluid.  For this reason, units are expressed as force per unit volume (e.g., N/m<sup>3</sup> or lbf/ft<sup>3</sup>).  Specific weight can be used as a characteristic [property](/source/List_of_materials_properties) of a fluid.<ref name="fluids" />

=== Soil mechanics ===
Specific weight is often used as a property of soil to solve [earthwork](/source/Earthworks_(engineering)) problems.

In soil mechanics, specific weight may refer to:

{{glossary}}
{{term|Moist unit weight}}
{{defn|The unit weight of a soil when void spaces of the soil contain both water and air.
<math display=block>\gamma = \frac{(1+w)G_\text{s}\gamma_\text{w}}{1+e}</math>
where
* {{mvar|γ}} is the moist unit weight of the material 
* {{math|''γ''<sub>w</sub>}} is the unit weight of water
* {{mvar|w}} is the [moisture content](/source/moisture_content) of the material 
* {{math|''G''<sub>s</sub>}} is the [specific gravity](/source/specific_gravity) of the solid
* {{mvar|e}} is the [void ratio](/source/void_ratio)
}}

{{term|Dry unit weight}}
{{defn|The unit weight of a soil when all void spaces of the soil are completely filled with air, with no water.

The formula for dry unit weight is:
<math display=block>\gamma_\text{d} = \frac{G_\text{s}\gamma_\text{w}}{1+e} = \frac{\gamma}{1+w}</math>
where
* {{mvar|γ}} is the moist unit weight of the material 
* {{math|''γ''<sub>d</sub>}} is the dry unit weight of the material 
* {{math|''γ''<sub>w</sub>}} is the unit weight of water
* {{mvar|w}} is the [moisture content](/source/moisture_content) of the material 
* {{math|''G''<sub>s</sub>}} is the [specific gravity](/source/specific_gravity) of the solid
* {{mvar|e}} is the [void ratio](/source/void_ratio)
}}

{{term|Saturated unit weight}}
{{defn|The unit weight of a soil when all void spaces of the soil are completely filled with water, with no air.

The formula for saturated unit weight is:
<math display=block>\gamma_\text{s} = \frac{(G_\text{s}+e)\gamma_\text{w}}{1+e}</math>
where
* {{math|''γ''<sub>s</sub>}} is the saturated unit weight of the material 
* {{math|''γ''<sub>w</sub>}} is the unit weight of water
* {{math|''G''<sub>s</sub>}} is the [specific gravity](/source/specific_gravity) of the solid
* {{mvar|e}} is the [void ratio](/source/void_ratio)<ref name="soils">Das, Braja M. (2007). ''Principles of Geotechnical Engineering''. Canada: Chris Carson.  {{ISBN|0-495-07316-4}}.</ref>
}}

{{term|Submerged unit weight}}
{{defn|The difference between the saturated unit weight and the unit weight of water.<ref name="Intelligent Compaction">The Transtec Group, Inc. (2012). ''Basic Definitions and Terminology of Soils''. [http://www.intelligentcompaction.com/downloads/IC_RelatedDocs/SoilCmpct_Basic%20definitions%20of%20Soils.pdf] (Page viewed December 7, 2012</ref> It is often used in the calculation of the [effective stress](/source/effective_stress) in a soil.

The formula for submerged unit weight is:
<math display=block>\gamma' = \gamma_\text{s} - \gamma_\text{w}</math>
where
* {{math|''γ''&prime;}} is the submerged unit weight of the material
* {{math|''γ''<sub>s</sub>}} is the saturated unit weight of the material 
* {{math|''γ''<sub>w</sub>}} is the unit weight of water
}}
{{glossary end}}

=== Civil and mechanical engineering ===
Specific weight can be used in [civil engineering](/source/civil_engineering) and [mechanical engineering](/source/mechanical_engineering) to determine the weight of a structure designed to carry certain loads while remaining intact and remaining within limits regarding [deformation](/source/deformation_(engineering)).

== Specific weight of water ==
{{See also|Water (molecule)#Density of water and ice|l1=Water density}}
{| class="wikitable" style="text-align:center" 
|+ Specific weight of water at standard sea-level atmospheric pressure (metric units)<ref name="fluids" />
|-
! scope="col" | Temperature (°C)
! scope="col" | Specific weight (kN/m<sup>3</sup>)
|-
| 0 || 9.805
|-
| 5 || 9.807
|-
| 10 || 9.804
|-
| 15 || 9.798
|-
| 20 || 9.789
|-
| 25 || 9.777
|-
| 30 || 9.765
|-
| 40 || 9.731
|-
| 50 || 9.690
|-
| 60 || 9.642
|-
| 70 || 9.589
|-
| 80 || 9.530
|-
| 90 || 9.467
|-
| 100 || 9.399
|}

{| class="wikitable" style="text-align:center"
|+ Specific weight of water at standard sea-level atmospheric pressure (imperial units)<ref name="fluids">Finnemore, J. E. (2002). ''Fluid Mechanics with Engineering Applications''. New York: McGraw-Hill. {{ISBN|0-07-243202-0}}.</ref>
|-
! scope="col" | Temperature (°F)
! scope="col" | Specific weight (lbf/ft<sup>3</sup>)
|-
| 32 || 62.42
|-
| 40 || 62.43
|-
| 50 || 62.41
|-
| 60 || 62.37
|-
| 70 || 62.30
|-
| 80 || 62.22
|-
| 90 || 62.11
|-
| 100 || 62.00
|-
| 110 || 61.86
|-
| 120 || 61.71
|-
| 130 || 61.55
|-
| 140 || 61.38
|-
| 150 || 61.20
|-
| 160 || 61.00
|-
| 170 || 60.80
|-
| 180 || 60.58
|-
| 190 || 60.36
|-
| 200 || 60.12
|-
| 212 || 59.83
|}

== Specific weight of air ==
{{Main|Density of air}}
{| class="wikitable" style="text-align:center"
|+ Specific weight of air at standard sea-level atmospheric pressure (metric units) <ref name="fluids" />
|-
! scope="col" | Temperature (°C)
! scope="col" | Specific weight (N/m<sup>3</sup>)
|-
| −40 || 14.86
|-
| −20 || 13.86
|-
| 0 || 12.68
|-
| 10 || 12.24
|-
| 20 || 11.82
|-
| 30 || 11.43
|-
| 40 || 11.06
|-
| 60 || 10.4
|-
| 80 || 9.81
|-
| 100 || 9.28
|-
| 200 || 7.33
|-100 ii 89
|}

{| class="wikitable" style="text-align:center"
|+ Specific weight of air at standard sea-level atmospheric pressure (imperial units) <ref name="fluids" />
|-
! scope="col" | Temperature (°F)
! scope="col" | Specific weight (lbf/ft<sup>3</sup>)
|-
| −40 || 
|-
| −20 || 0.0903
|-
| 0 || 0.08637
|-
| 10 || 0.08453
|-
| 20 || 0.08277
|-
| 30 || 0.08108
|-
| 40 || 0.07945
|-
| 50 || 0.0779
|-
| 60 || 0.0764
|-
| 70 || 0.07495
|-
| 80 || 0.07357
|-
| 90 || 0.07223
|-
| 100 || 0.07094
|-
| 120 || 0.06849
|-
| 140 || 0.0662
|-
| 160 || 0.06407
|-
| 180 || 0.06206
|-
| 200 || 0.06018
|-
| 250 || 0.05594
|}

== References ==
{{reflist}}

== External links ==
* [https://www.ajdesigner.com/phpspecificgravity/specific_gravity_equation_submerged_water_weight_loss.php Submerged weight calculator]
* [http://www.fxsolver.com/solve/share/qtmx1x0eEynB9VGZDGMBLA==/ Specific weight calculator]
* http://www.engineeringtoolbox.com/density-specific-weight-gravity-d_290.html
* http://www.themeter.net/pesi-spec_e.htm

{{Authority control}}

Category:Soil mechanics
Category:Fluid mechanics
Category:Physical chemistry
Category:Physical quantities
Category:Density
Category:Volume-specific quantities

---
Adapted from the Wikipedia article [Specific weight](https://en.wikipedia.org/wiki/Specific_weight) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Specific_weight?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.