Specific Weight

The specific weight of an object is based on its material makeup. However, many times the specific weight is misunderstood in both its definition and application. Additionally, specific weight and specific gravity are two properties that may seem similar, but are not. Density plays a key role in both the specific weight and the specific gravity of a material or object.

The Difference Between Specific Weight and Density

The specific weight of a material is oftentimes confused with the density of that material. And while both are related, the difference between them is very important.

You may be more familiar with what density is. Generally speaking, it is the mass per unit volume of a material. For example, the density of lead is 11.29 g/cm3, indicating that a cubic-centimeter of lead has a mass of 11.29 grams.

Specific weight is not as well understood, which may be the biggest reason for confusing it with density. The specific weight of a material is a measure of weight per unit volume. It is important to remember that mass and weight are not the same thing.

The concept of weight is often confusing to someone without a science or engineering background. In fact, the weight of an object is a measure of the force of gravity pulling on that object. According to Newton’s Second Law, the force is mass times acceleration.

Are Specific Weight and Specific Gravity the Same?

Another term that specific weight is often confused with is specific gravity. However, unlike the relationship between specific weight and density, specific gravity is not related to specific weight in any way. In fact, specific gravity is related to density based on the following:

where ρ indicates the density of the substance or water. As seen from the equation, the specific gravity is the ratio between the density of a material and the density of water. The standard properties of water are often used in science and engineering as baselines to compare other materials against.

The specific gravity is a characteristic of a material. Often, it is used to determine if an object will float or sink in water. If the specific gravity is more than 1, the object will sink because it is denser than water. A value less than 1 indicates that the object is less dense than water, and will float.

Calculating Specific Weight from Density

The specific weight of a material is calculated from the density of the material using the following equation:

where γ is the specific weight, ρ is the density of the material, and g is gravitational acceleration.

Therefore, it can be seen that the specific weight is the density of a material times gravity. Looking at the individual units of each, density has units of kg/m3 and gravity has units of m/s2. When the two are multiplied together, the resulting unit is N/m3. This means that the specific weight is defined as the weight per unit volume.

Specific weight can be thought of as how much force gravity exerts on a certain volume of material. Objects with higher density will have a higher specific weight, but just because an object has a large volume does not mean it will have a large specific weight since its density could be lower.

How to Calculate the Specific Weight of Water

If one wants to calculate the specific weight of water, the above equation is all they will need. Taking the standard density of water at 4°C to be 997 kg/m3 and multiplying by the standard gravitational acceleration of 9.807 m/s2, the specific weight of water comes out to be 9777.579 N/m3. Oftentimes, this value is simply rounded to 1×103 N/m3.

Similarly, the density of water used in the calculation of specific gravity is oftentimes simplified to 1000 kg/m3. Both of these simplifications can be useful for basic initial calculations, but more specific measurements and calculations should use the correct values to ensure accuracy.

Specific Weight: Extensive or Intensive Property?

Specific weight, like Young’s Modulus is an intensive property.

An extensive property is one that depends on how much matter is present, while an intensive property is one that does not depend on how much matter there is. Examples of extensive and intensive properties are mass and color, respectively.

However, these definitions of properties can cause some difficulty with specifying what kind of property the specific weight is. Density is an intensive property because the density of an object does not depend on how much material there is.

Both the weight and volume of an object are extensive properties because they depend on how much material is present. The ratio between the two will be an intensive property. In this case, it is necessary to look at the units of the resulting property, rather than the units of properties used in the calculation.

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By Charlie Young, P.E.

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