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# Specific weight

The specific weight, also known as the unit weight, is the weight per unit volume of a material.

A commonly used value is the specific weight of water on Earth at 4 °C (39 °F), which is 9.807 kilonewtons per cubic metre or 62.43 pounds-force per cubic foot.[1]

The terms specific gravity, and less often specific weight, are also used for relative density. A common symbol for specific weight is γ, the Greek letter Gamma.

## Definition

The specific weight, γ, of a material is defined as the product of its density, ρ, and the standard gravity, g:

${\displaystyle \gamma =\rho \,g}$

The density of the material is defined as mass per unit volume, typically measured in kg/m3. The standard gravity is acceleration due to gravity, usually given in m/s2, and on Earth usually taken as 9.81 m/s2.

Unlike density, specific weight is not a fixed property of a material. It depends on the value of the gravitational acceleration, which varies with location. 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.[2]

## 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.[2]

### Soil mechanics

Specific weight is often used as a property of soil to solve earthwork problems.

In soil mechanics, specific weight may refer to:

• Moist unit weight, which is the unit weight of a soil when void spaces of the soil contain both water and air.
${\displaystyle \gamma ={\frac {(1+w)G_{s}\gamma _{w}}{1+e}}}$
where
γ is the moist unit weight of the material
γw is the unit weight of water
w is the moisture content of the material
Gs is the specific gravity of the solid
e is the void ratio
• Dry unit weight, which is 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:
${\displaystyle \gamma _{d}={\frac {G_{s}\gamma _{w}}{1+e}}={\frac {\gamma }{1+w}}}$
where
γ is the moist unit weight of the material
γd is the dry unit weight of the material
γw is the unit weight of water
w is the moisture content of the material
Gs is the specific gravity of the solid
e is the void ratio
• Saturated unit weight, which is 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:
${\displaystyle \gamma _{s}={\frac {(G_{s}+e)\gamma _{w}}{1+e}}}$
where
γs is the saturated unit weight of the material
γw is the unit weight of water
Gs is the specific gravity of the solid
e is the void ratio[3]
• Submerged unit weight, which is defined as the difference between the saturated unit weight and the unit weight of water.[4] It is often used in the calculation of the effective stress in a soil. The formula for submerged unit weight is:
${\displaystyle \gamma ^{'}=\gamma _{s}-\gamma _{w}}$
where
γ is the submerged unit weight of the material
γs is the saturated unit weight of the material
γw is the unit weight of water

### 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

Temperature(°C) 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
Specific weight of water at standard sea-level atmospheric pressure (Metric units) [2]
Temperature(°F) 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 water at standard sea-level atmospheric pressure (English units) [2]

## Specific weight of air

Temperature(°C) 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
Specific weight of air at standard sea-level atmospheric pressure (Metric units) [2]
Temperature(°F) 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
Specific weight of air at standard sea-level atmospheric pressure (English units) [2]

## References

1. ^ National Council of Examiners for Engineering and Surveying (2005). Fundamentals of Engineering Supplied-Reference Handbook (7th ed.). ISBN 1-932613-00-5.
2. Finnemore, J. E. (2002). Fluid Mechanics with Engineering Applications. New York: McGraw-Hill. ISBN 0-07-243202-0.
3. ^ Das, Braja M. (2007). Principles of Geotechnical Engineering. Canada: Chris Carson. ISBN 0-495-07316-4.
4. ^ 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
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