Specific weight, also called unit weight or sometimes weight density, describes the weight of a substance relative to its volume. It is often used as a characteristic property of fluids and soils in the fields of fluid mechanics and soil mechanics, respectively. The specific weight of any given substance is not constant — it can change based on temperature and pressure.
The lower-case Greek letter gamma, which looks something like a “y,” usually represents specific weight in equations. Typically, the equation “gamma = rho*g” is used to calculate specific weights. Rho, a Greek letter which looks like a rounded “p,” represents the density of the substance — the mass of the substance relative to its volume. Sometimes called the local constant, “g” represents the acceleration due to gravity, which is 32.2 feet per square second (about 9.81 meters per square second) at the Earth’s surface.
Standard units of density are slugs per cubic foot (slugs/ft^3) or pounds-mass per cubic foot (lbm/ft^3) in imperial units and kilograms per cubic meter (kg/m^3) in metric units. The constant “g” is measured in feet per square second (ft/s^2) or meters per square second (m/s^2). Multiplying density by “g” results in units of pounds-force per cubic foot (lbf/ft^3) or Newtons per cubic meter (N/m^3).
As an example, water has a density of 1,000 kg/m^3 in metric units. Multiplying by 9.81 m/s^2 results in a specific weight of 9,810 N/m^3. In imperial units, the density of water is 1.94 slugs/ft^3, and multiplying by 32.2 ft/s^2 results in 62.4 lb/ft^3. This calculation is not used, however, when density is measured in lbm. One pound-mass is equivalent to one pound-force, so if a substance has a density of 10 lbm/ft^3, it will have a specific weight of 10 lbf/ft^3.
When used in reference to soils, specific weight is generally referred to as unit weight and is calculated somewhat differently. Two types of unit weight are typically calculated for soil samples: the bulk unit weight and the dry unit weight. Bulk unit weight is the unit weight of the sample when the pores in the soil contain both air and water. To determine dry unit weight, laboratory equipment is used to completely dry out a soil sample so it contains no water. Bulk unit weight is defined as the total weight divided by the total volume, while dry unit weight is the dry weight divided by the total volume.
Density changes based on pressure and temperature, and since specific weight is based on density, it can change as well. The density decreases as the temperature increases because the molecules in the substance move farther apart. Density increases as pressure increases because pressure forces the molecules closer together.