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# Bulk Modulus Formula

Today we will look at the interesting topics in physics which is the bulk modulus. Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain for any material. In much 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 a fluid when pressure is applied. In this article, we will discuss the bulk modulus formula with examples. Let us learn this interesting property of material!

## Bulk Modulus Formula

### Definition

The bulk modulus property of the material is related to its behavior of elasticity. It is one of the measures of mechanical properties of solids. Other such elastic modulii are Young’s modulus and Shear modulus. In all cases, the bulk elastic properties of a material are used to find out how much it will compress under a given amount of external pressure. It is very important to find the ratio of the change in pressure to the fractional volume compression.

Elastic Modulii – Young’s Modulus

The Bulk Modulus is defined as the relative change in the volume of a body produced by a unit compressive or tensile stress acting throughout the surface uniformly.

The bulk modulus describes how a substance reacts when it is compressed uniformly. It is a fact that when the external forces are perpendicular to the surface, it is distributed uniformly over the surface of the object. This may also occur when an object is immersed in a fluid and undergo a change in volume without a change in shape.

The δ P is volume stress and we define it as the ratio of the magnitude of the change in the amount of force δ F to the surface area. The bulk modulus of any liquid is a measure of its compressibility. We computed it as the pressure required to bring about a unit change in its volume.

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### Bulk modulus formula is –

K =$$\frac{ V × Δ P}{Δ V}$$

Where,

 K Bulk Modulus δ P Change in pressure δ V Change in volume V Original volume

The units for the bulk modulus is Pa or KPa and MPa as higher units.

We represent it with a symbol of K. Its dimension is force per unit area. We express it in the units of newton per square meter (N/m²) in the metric system.

## Solved Examples on Bulk Modulus Formula

Q.1: Find out the change in volume if the atmospheric pressure of 0.1 MPa of a metal block is decreased to zero when this unit is put in a vacuum. The bulk modulus of the material of the object is 120000 MPa.

Solution: As given values in the problem:

Bulk modulus, K = 120000 MPa

Change in pressure, δP = 0.0 – 0.1

\Delta P = -0.1 MPa

As we know the formula for Bulk Modulus,

K =$$\frac{ V \times \Delta P}{\Delta V}$$

$$\frac{ \Delta V}{ V } = −\frac { \Delta P}{ K }$$

$$\frac { \Delta V}{ V } = −\frac {-0.1 }{ 120000 }$$

$$\frac{ \Delta V }{ V } = 8.3 \times 10^{ -7 }$$

i.e. Fractional change in volume = $$8.3× 10^{ -7 }$$

Hence, the fractional change in volume is $$8.3 × 10^{-7}$$

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