Today we will look at of of the interesting topics in physics that is bulk modulus. To begin with, bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain of a specified material, while the material deformation is within elastic limit. To put in more simple words, 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 on all the surfaces.

Bulk modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic modules include Young’s modulus and Shear modulus. In any case, the bulk elastic properties of a material is 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 of per square inch (psi) in the English system and newtons per square meter (N/m^{2}) in the metric system.

## Bulk Modulus Of Elasticity Formula

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

**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/m^{2} in the metric system.

### Uses

Bulk modulus is used to measure how incompressible a solid is. Besides, the more the value of K for a material, higher is its nature to be incompressible. For example, the value of K for steel is 1.6×1011N/m^{2} and the value of K for glass is 4×1010N/m^{2}. Here, K for steel is more than three times the value of K for glass. This implies that glass is more compressible than steel.

Now, a quick exercise for you. Try finding the value for diamond and comparing it with the value of steel and glass.

Consider this situation. You go deep sea diving into the Mariana Trenches. This is the following information you have in hand.

Bulk Modulus of Bone = 1.5×1010N/m^{2}

Atmospheric Pressure = 1.01×105N/m^{2}

Pressure at deep point = 1.09×108N/m^{2}

You have two tasks;

- Find out what the value of dVV will be for your bones
- Appreciate atmospheric pressure because you don’t die here

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.

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**Some questions:**

**What is the bulk modulus of a body that experienced a change of pressure of 5*104N/m**^{2}and a its volume goes from 4 cm^{3}to 3.9 cm^{3}?.

** –** The bulk modulus is calculated using the formula,

B = ΔP /(ΔV/V)

B = (5*104 N/m^{2})/((4 cm^{3} – 3.9 cm^{3})/4 cm^{3}) = 0.125 *104 N/m^{2}

B = 1.25 *104 N/m^{2}