Specific weight

{{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), is a volume-specific quantity defined as the weight {{mvar|W}} divided by the 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, {{mvar|ρ}}, and gravity acceleration, {{mvar|g}}: <math display=block>\gamma = \rho \, g .</math> Its unit of measurement in the International System of Units (SI) is the newton per cubic metre (N/m3), expressed in terms of base units as kg⋅m−2⋅s−2. A commonly used value is the specific weight of water on 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 of a material is defined as mass divided by volume, typically expressed with the unit kg/m3. Unlike density, specific weight is not a fixed property of a material, as it depends on the value of the gravitational acceleration, which varies with location (e.g., Earth's gravity). In practice, the standard gravity (a constant) is often assumed, usually taken as {{val|9.80665|u=m|up=s2}}.

Pressure may also affect values, depending upon the 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, specific weight represents the force exerted by gravity on a unit volume of a fluid. For this reason, units are expressed as force per unit volume (e.g., N/m3 or lbf/ft3). Specific weight can be used as a characteristic property of a fluid.<ref name="fluids" />

=== Soil mechanics === Specific weight is often used as a property of soil to solve earthwork 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''w}} is the unit weight of water * {{mvar|w}} is the moisture content of the material * {{math|''G''s}} is the specific gravity of the solid * {{mvar|e}} is the 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''d}} is the dry unit weight of the material * {{math|''γ''w}} is the unit weight of water * {{mvar|w}} is the moisture content of the material * {{math|''G''s}} is the specific gravity of the solid * {{mvar|e}} is the 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''s}} is the saturated unit weight of the material * {{math|''γ''w}} is the unit weight of water * {{math|''G''s}} is the specific gravity of the solid * {{mvar|e}} is the 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 in a soil.

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

=== Civil and mechanical engineering === Specific weight can be used in civil engineering and mechanical engineering to determine the weight of a structure designed to carry certain loads while remaining intact and remaining within limits regarding deformation.

== 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/m3) |- | 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/ft3) |- | 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/m3) |- | −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/ft3) |- | −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

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