Bulk Modulus of Elasticity

What Is Bulk modulus?

• Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain of specified material while the material deformation is within the&nbsp elastic limit.
• In simpler words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a solid or fluid when pressure is applied to all the surfaces.
• The bulk modulus of elasticity is one of the measures of the mechanical properties of solids. 
•  Other elastic modules include Young’s modulus and Shear modulus. 
• In any case, the bulk elastic properties of a material are used to determine how much it will compress under a given amount of external pressure. 
• Here, it is important to find and note the ratio of the change in pressure to the fractional volume compression.
• The value is denoted with a symbol of K, and it has the dimension of force per unit area. 
• It is expressed in the units per square inch (psi) in the English system and newtons per square meter (N/m²) in the metric system.

in the units per square inch (psi) in the English system and newtons per square meter (N/m²) in the metric system.

Following is the table explaining other related concepts:

Bulk Modulus of Elasticity Formula

It is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material.

Mathematically, it is represented as follows:

B = ΔP /(ΔV/V)

Where:

B: Bulk modulus

ΔP: change of the pressure or force applied per unit area on the material

ΔV: change of the volume of the material due to the compression

V: Initial volume of the material in the units of in the English system and N/m² in the metric system.

Solved Example

What is the bulk modulus of a body that experienced a change of pressure of 5*10⁴N/m² and its volume goes from 4 cm³ to 3.9 cm³?.
The bulk modulus is calculated using the formula,

B = ΔP /(ΔV/V)

B = (5*10⁴ N/m²)/((4 cm³ – 3.9 cm³)/4 cm³) = 0.125 *10⁴ N/m²

B = 1.25 *10⁴ N/m²

Uses

• Bulk modulus measures how incompressible a solid is. 
• Besides, the more the value of K for a material, the higher its nature is incompressible. 
• For example, the value of K for steel is 1.6×10¹¹N/m², and the value of K for glass is 4×10¹⁰N/m². 
• Here, K for steel is more than three times the value of K for glass. 

• This implies that glass is more compressible than steel.

• While in solids, Young’s modulus is commonly used, the value of K varies in gases, as they are extremely compressible. The concept of Bulk Modulus is also used in liquids. Temperatures of fluid and entrained air content are the two factors highly controlled by the bulk modulus.

Watch the video and understand solids’ elastic and plastic behaviour

Frequently Asked Questions – FAQs

Q1

What is elastic modulus?

The ratio of stress to strain is known as elastic modulus. Elastic modulus defines the amount of force required per unit of deformation.

Q2

What is permanent deformation?

Permanent deformation is also known as plastic deformation, it is irreversible. It is a type of deformation that stays even after the removal of applied forces.

Q3

What is temporary deformation?

Temporary deformation is also known as elastic deformation; it is reversible. It is a type of deformation that disappears after the removal of applied forces.

Q4

Define stress.

Stress is defined as force per unit area within materials that arise from externally applied forces, uneven heating, or permanent deformation and that permits an accurate description and prediction of elastic, plastic, and fluid behaviour.

Q5

What is strain?

Strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body.

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