Bulk Modulus of Elasticity definition Formula

Bulk Modulus of Elasticity definition Formula

The elasticity of materials or the elasticity property plays an important role in engineering design. For instance, while constructing a structure, it is vital to understand the elastic characteristics of materials such as concrete, steel, etc. 

An experiment may demonstrate the connection between stress and strain for a specific material under tensile tension. In a conventional test of tensile characteristics, an external force is applied to a test cylinder or wire. The fractional change in length or strain, as well as the external force required to generate the strain, are measured and recorded. The external force is steadily raised in increments, while the length change is also recorded.

Elastic Moduli

For both structural and industrial engineering designs, the proportionate area inside the elastic limit of the stress-strain curve is of the highest significance. The stress to strain ratio, which is called the modulus of elasticity, is a key attribute or feature of the material.

Bulk Modulus

It is one of the mechanical characteristics of solids that is measured. Young’s modulus and Shear’s modulus are also elastic moduli. In any event, the bulk elastic characteristics of a material are used to determine how much it will compress when subjected to a particular quantity of external pressure. Here, it is essential to determine and record the ratio of the pressure change to the fractional volume compression.

The value is represented by the letter K and its measurement is force per unit area. It is represented in the English system as pounds per square inch (psi) and in the metric system as newtons per square metre (N/m2).

The formula of Bulk Modulus of elasticity is-

B=ΔP/(ΔV/V)

Here,

B: Bulk modulus

ΔP: Pressure change

ΔV: change in volume

V: Initial volume

Solved Examples

Example 1:What is the bulk modulus of a body whose pressure changed by 5x104N/m2 and whose volume decreased from 4 cm3 to 3.9 cm3? 

Answer. 

Here the bulk modulus of the body is-

B = ΔP /(ΔV/V)

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

B= 0.125 x104 N/m2

B = 1.25 x104 N/m2