Physics:Specific weight
The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as 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]
Definition
The specific weight, γ, of a material is defined as the product of its density, ρ, and the standard gravity, g: [math]\displaystyle{ \gamma = \rho \, g }[/math]
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
- The unit weight of a soil when void spaces of the soil contain both water and air.
[math]\displaystyle{ \gamma = \frac{(1+w)G_s\gamma_w}{1+e} }[/math]
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
- 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]\displaystyle{ \gamma_d = \frac{G_s\gamma_w}{1+e} = \frac{\gamma}{1+w} }[/math]
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
- 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]\displaystyle{ \gamma_s = \frac{(G_s+e)\gamma_w}{1+e} }[/math]
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
- 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:
[math]\displaystyle{ \gamma' = \gamma_s - \gamma_w }[/math]
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 |
| 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 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 |
| 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 |
References
- ↑ National Council of Examiners for Engineering and Surveying (2005). Fundamentals of Engineering Supplied-Reference Handbook (7th ed.). ISBN:1-932613-00-5.
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 Finnemore, J. E. (2002). Fluid Mechanics with Engineering Applications. New York: McGraw-Hill. ISBN:0-07-243202-0.
- ↑ Das, Braja M. (2007). Principles of Geotechnical Engineering. Canada: Chris Carson. ISBN:0-495-07316-4.
- ↑ The Transtec Group, Inc. (2012). Basic Definitions and Terminology of Soils. [1] (Page viewed December 7, 2012
External links
- Submerged weight calculator
- Specific weight calculator
- http://www.engineeringtoolbox.com/density-specific-weight-gravity-d_290.html
- http://www.themeter.net/pesi-spec_e.htm
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