Specific weight

The specific weight (also known as the unit weight) is the weight per unit volume of a material. The symbol of specific weight is γ (the Greek letter Gamma).

A commonly used value is the specific weight of water on Earth at 5°C which is 9.807 kN/m³ or 62.43 lbf/ft³. ^[1]

The terms specific gravity, and less often specific weight, are also used for relative density.

General formula

$\gamma =\rho \,g$

where

$\gamma$ is the specific weight of the material (weight per unit volume, typically N/m³ units)

$\rho$ is the density of the material (mass per unit volume, typically kg/m³)

$g$ is acceleration due to gravity (rate of change of velocity, given in m/s², and on Earth usually given as 9.81 m/s²)

Changes of specific weight

Unlike density, specific weight is not absolute. It depends upon the value of the gravitational acceleration, which varies with location. A significant influence upon the value of specific gravity is the temperature of the material. 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]

Uses

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 lb/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.

$\gamma ={\frac {(1+w)G_{s}\gamma _{w}}{1+e}}$

where

$\gamma$ is the moist unit weight of the material

$\gamma _{w}$ 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:

$\gamma _{d}={\frac {G_{s}\gamma _{w}}{1+e}}={\frac {\gamma }{1+w}}$

where

$\gamma$ is the moist unit weight of the material

$\gamma _{d}$ is the dry unit weight of the material

$\gamma _{w}$ 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:

$\gamma _{s}={\frac {(G_{s}+e)\gamma _{w}}{1+e}}$

where

$\gamma_s$ is the saturated unit weight of the material

$\gamma _{w}$ 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^[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:

$\gamma ^{{'}}=\gamma _{s}-\gamma _{w}$

where

$\gamma ^{{'}}$ is the submerged unit weight of the material

$\gamma_s$ is the saturated unit weight of the material

$\gamma _{w}$ is the unit weight of water

Mechanical engineering

Specific weight can be used in 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/m^3)
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 (lb/ft^3)
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/m^3)
−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 (lb/ft^3)
−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]

See also

• Density
• Relative density
• Specific gravity

References

1. National Council of Examiners for Engineering and Surveying (2005). Fundamentals of Engineering Supplied-Reference Handbook (7th ed.). Clemson: National Council of Examiners for Engineering and Surveying. 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

External links

• Water Weights & Weight Belts (Arrow Weights Manufacturing)
• Specific weight calculator
• http://www.engineeringtoolbox.com/density-specific-weight-gravity-d_290.html
• http://www.themeter.net/pesi-spec_e.htm