Specific Gravity

The specific gravity of a substance is the ratio of its density to a specified reference substance. This ratio is a pure number, containing no units.

If the specific gravity ratio for a given substance is less than 1, that means the material will float in the reference substance. When the specific gravity ratio for a given material is greater than 1, that means the material will sink in the reference substance.

This is related to the concept of buoyancy. The iceberg floats in the ocean (as in the picture) because its specific gravity in reference to the water is less than 1.

This rising vs. sinking phenomenon is the reason that the term "specific gravity" is applied, although gravity itself plays no significant role in this process. Even in a substantially different gravitational field, the density relationships would be unchanged. For this reason, it would be far better to apply the term "relative density" between two substances, but for historical reasons, the term "specific gravity" has stuck around.

Specific Gravity for Fluids

For fluids, the reference substance is usually the water, with a density of 1.00 x 10³ kg/m³ at 4 degrees Celsius (water's densest temperature), used to determine whether or not the fluid will sink or float in water. In homework, this is usually assumed to be the reference substance when working with liquids.

Specific Gravity for Gases

For gases, the reference substance is usually normal air at room temperature, which has a density of approximately 1.20 kg/m³. In homework, if the reference substance is not specified for a specific gravity problem, it is usually safe to assume that you are using this as your reference substance.

Equations for Specific Gravity

The specific gravity (SG) is a ratio of the density of the substance of interest (ρ_i) to the density of the reference substance (ρ_r). (Note: The Greek symbol rho, ρ, is commonly used to represent density.) That can be determined using the following formula:

SG = ρ_i ÷ ρ_r = ρ_i / ρ_r

Now, considering that the density is calculated from mass and volume through the equation ρ = m/V, this means that if you took two substances of the same volume, the SG could be rewritten as a ratio of their individual masses:

SG = ρ_i / ρ_r

SG = m_i/V / m_r/V

SG = m_i / m_r

And, since the weight W = mg, that leads to a formula written as a ratio of weights:

SG = m_i / m_r

SG = m_ig / m_rg

SG = W_i / W_r

It is important to remember that this equation only works with our earlier assumption that the volume of the two substances is equal, so when we talk about the weights of the two substances in this last equation, it is the weight of equal volumes of the two substances.

So if we wanted to find out the specific gravity of ethanol to water, and we know the weight of one gallon of water, then we would need to know the weight of one gallon of ethanol to complete the calculation. Or, alternately, if we knew the specific gravity of ethanol to water, and knew the weight of one gallon of water, we could use this last formula to find the weight of one gallon of ethanol. (And, knowing that, we could use it to find the weight of another volume of ethanol by converting. These are the sorts of tricks that you may well find among homework problems that incorporate these concepts.)

Applications of Specific Gravity

Specific gravity is a concept that shows up in a variety of industrial applications, particularly as it relates to fluid dynamics. For example, if you've ever taken your car in for service and the mechanic showed you how small plastic balls floated in your transmission fluid, you've seen specific gravity in action.

Depending on the specific application in question, those industries may use the concept with a different reference substance than water or air. The earlier assumptions applied only to homework. When you are working on a real project, you should know for sure what your specific gravity is in reference to, and shouldn't have to make assumptions about it.