Specific Weight

What is Specific Weight

Specific weight, also known as unit weight, is a physical quantity that represents the weight per unit volume of a substance or material. It is defined as the weight of a substance divided by its volume and is typically expressed in units of force per unit volume, such as Newtons per cubic meter (N/m³) or pounds-force per cubic foot (lbf/ft³).

Specific weight takes into account the effect of gravity on the substance and is different from density, which is the mass of a substance divided by its volume. While density is a measure of how tightly packed the molecules in a substance are, specific weight is a measure of the gravitational force acting on a unit volume of the substance.

The specific weight of a substance depends on its density; that is, the amount of mass per unit volume of a substance.

Formula & Units

Specific weight = weight / volume

𝛾 = 𝜌 g

Where:

$𝛾$ is the specifc weight of the material
$𝜌$ is the density of the material
$g$ is the standard acceleration due to gravity

The SI unit of specific weight is Newton per cubic meter (N/m³).

The US customary unit of specific weight is pounds-force per cubic foot (lbf/ft³).

Specific Weight Example

The density of water at 20 °C is 997.13 kg/m³. Knowing that the gravitational acceleration on earth is 9.81 m/s², find the specific weight of water at 20 °C.

Solution

Using the formula of specific weight:

𝛾 = 𝜌 g = 997.13 \times 9.81 = 9781.85 N / m^{3}

Factors Affecting Specific Weight

The specific weight of a material is influenced by several factors, including:

Gravity: The specific weight of a material is affected by the strength of the gravitational field in which it is located. This means that the specific weight of the same material will vary on different planets or at different elevations on Earth.
Density: The density of a material is related to its specific weight, but they are not the same thing. A material with a higher density will generally have a higher specific weight.
Temperature: Changes in temperature can cause changes in the specific weight of a material, especially if the material is a gas or liquid.
Pressure: Changes in pressure can also affect the specific weight of a material, particularly if the material is a gas.
Chemical composition: The arrangement of molecules and the chemical composition of a material can influence its specific weight.

Applications of Specific Weight

Specific weight has various applications in science and engineering, including:

Structural analysis: Engineers use specific weight to analyze the stability and load-bearing capacity of buildings, bridges, and other structures.
Fluid mechanics: Specific weight is used to calculate the pressure and forces exerted by fluids on submerged objects. This is important in the design of hydraulic systems, such as water turbines and pumps.
Soil mechanics: Specific weight is used to analyze the stability of soil and to determine the weight of soil that can be supported by a foundation.
Aerospace engineering: Specific weight is important in designing spacecraft and space missions, where weight is a critical factor in determining launch and fuel requirements.
Environmental engineering: Specific weight is used to calculate the weight of contaminants and pollutants in air, water, and soil. This is important in developing effective remediation strategies and managing environmental risks.

Specific Weight Summary
Definition	The weight of a material or substance per unit volume.
Symbol	$𝛾$
Formula	$𝛾 = 𝜌 g$
Units	SI Unit (N/m³)	US Unit (lbf/ft³)

What is the difference between specific weight and density?: Specific weight and density are related, but they represent different physical properties of a material. Density is the mass of a material per unit volume, while specific weight is the weight of a material per unit volume. Density is an intrinsic property of a material, while specific weight depends on the gravitational field in which the material is located.

What is the relationship between specific weight and density?: The relationship between specific weight and density is proportional. That is, as density increases, specific weight increases, and vice versa. For a given material, if the density is known, specific weight can be determined by multiplying the density by the gravitational constant, which on earth is (9.81 m/s²).

What factors can affect the specific weight of a material?: Several factors can affect the specific weight of a material, including its chemical composition, temperature, and pressure. The specific weight of a material can also vary based on the gravitational force to which it is located.

Are specific weight and specific gravity the same?: No, specific weight and specific gravity are not the same. Specific weight is a measure of a material’s weight per unit volume, whereas specific gravity is a measure of a material’s density relative to that of water.