What is Bulk Modulus?
- The Bulk modulus of a substance is a measure of its resistance to compression. It is defined as the proportion of the infinitesimal pressure increase to the resulting relative volume decrease.
- Other moduli describe the material's response (strain) to different types of stress: shear modulus describes shear stress, and Young's modulus describes normal (lengthwise stretching) stress. Only the bulk modulus is relevant for a fluid. For a complex anisotropic solid, such as wood or paper, these three moduli are insufficient to describe its behavior, and the full generalized Hooke's law must be used. The isothermal compressibility is defined as the reciprocal of the bulk modulus at a fixed temperature.
Definition of Bulk Modulus:
Bulk modulus is the change in relative volume of an object caused by uniformly applying a unit compressive or tensile stress to its surface.
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Bulk Modulus: Types
There are three types of bulk modulus of elasticity based on the type of stress applied and the resulting strain:
|
Type of Bulk Modulus |
Description |
|
Bulk Modulus |
It is defined as the volumetric stress to strain ratio and is denoted by B. |
|
Young's Modulus |
It is denoted by Y as the ratio of longitudinal stress to longitudinal strain. |
|
Shear Modulus |
It is significant as the shear stress to shear strain ratio, as noted by G, S. |
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Bulk Moudulus formula
Given below formula is known as the Bulk Modulus formula
K = ΔP × V / ΔV
Where,
K = Bulk modulus (Pascal)
V = Actual volume of object (m3)
ΔP = Change in pressure (Pascal)
ΔV = Change in volume (m3)
Note: Dimension of Bulk modulus is, L-1M1T-2
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Derivation for Bulk Modulus Formula
According to Hooke's Law,
Strain is directly proportional to stress.
Volume strain Hydraulic stress
Hydraulic stress = B × Volume strain
The proportionality constant is B, and B is the bulk modulus of elasticity.
p = B × ΔV / V
∴ B = ΔP × V / ΔV
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Bulk Modulus Formula: Uses
Bulk modulus is a measurement of a material's incompressibility. For example, the value of K for steel is 1.61011 N/m2, while the value of K for glass is 41010 N/m2. In this case, k for steel is more than three times that of K for glass. As a result, glass is more compressible than steel.
If we try to calculate the value of a diamond and compare it to the values of glass and steel, we will find that
- Atmospheric Pressure = 1.01×105 N/m2
- Bulk Modulus of Bone = 1.5×1010 N/m2
- Pressure at deep point = 1.09×108 N/m2