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When external forces are applied to a rigid solid material to impose pressure, the objects remain at the same size. It may break into pieces, but the gross volume that all the object particles occupy does not change. However, when such external pressure is exerted on an elastic object or material, the material decreases in the total volume that it occupies in the space. The bulk modulus deals with such elastic properties of materials. Other moduli like Young’s modulus also give the elasticity of the materials. The article detailly describes what is bulk modulus and expresses the bulk modulus SI unit.

Elastic materials 

Some materials can resist destruction when they are subjected to external pressure. Those materials or objects are called elastic materials. After the halt of the external pressure, an elastic material comes to its original shape and size. This property of resisting destruction even when it is compressed is called elasticity.

Numerous laws deal with the elastic materials to calculate and quantitate their elastic ability. These laws are also used to define their elasticity. Such laws or formulae include bulk modulus, shear modulus, Young’s modulus, Hooke’s law, etc.

Bulk modulus 

Bulk modulus correlates with the elastic property of a material. The bulk modulus employs the stress and strain exerted on an object to determine the incompressibility of the material. It means how much the object takes in a compression pressure before coming into its original shape and dimensions. 

  • The alphabet K or B represents the bulk modulus of a material. 
  • It is the estimate of how idle the material is on compression. 
  • Bulk modulus is the ratio of the pressure exerted on the material to how far the material has decreased in its size and volume on experiencing the pressure.
  • It can also be defined as the amount of the normal stress on the material divided by the volumetric strain of the material. 

K = Stress / Strain

  • The bulk modulus is calculated in isothermal conditions, mostly.

Compressibility

The bulk modulus calculation provides the numerical value of how incompressible the corresponding material or substance is. Thus, the material’s compressibility is calculated by taking the inverse of the value of the material’s bulk modulus. 

Compressibility is inversely related to Bulk modulus. Therefore, the compressibility of a material can be termed as = 1 / K

Bulk modulus formula

As per the definition of bulk modulus, the following expression shows the formula of the bulk modulus. 

K = Pressure on the material / Change in its volume

Where,

K → Bulk modulus, B also represents the Bulk modulus

P → External Pressure applied on the elastic material 

V0 → original volume of the material

Vn → New volume of the material

Since the volume decreases when external pressure is applied, the formula can be expressed as 

K = dP / -(dV / V)

K = -V(dP/dV) 

Bulk modulus formula in terms of density

When in terms of density, the bulk modulus is quantitated by the formula

K = ⍴ (dP/d⍴)

Where, 

K → Bulk modulus, B also represents the Bulk modulus

⍴ → the density of the material

dP → change or increase in pressure

d⍴ → change in the density of the material 

Here, the volume is written in terms of density as V = m/⍴.

SI unit of Bulk Modulus

According to the International System of Units, the SI unit of Bulk modulus is Pascal. It is expanded as N/m2. The bulk modulus has a dimensional formula of [M L-¹ T-²].

Applications of bulk modulus

The applications of bulk modulus in the real world are noticeable in the following cases.

  • Since the bulk modulus deals with the pressure and density of the material, the bulk modulus helps us determine or find the pressure that we will experience inside a waterbody and its compressibility. It is easy to calculate when the depth of the waterbody is provided on hand. 
  • The pressure is first calculated by multiplying the depth, acceleration due to gravity, and density of the waterbody. The pressure value is used to find the bulk modulus, or how compressed the waterbody is. The pressure of the water can be found when the bulk modulus is provided.
  • Unlike any other moduli, the bulk modulus also applies to liquids. Liquids are highly incompressible. We need enormous pressure to compress even a small quantity of liquids. However, solids are not so. Elastic solids compress easily to their maximum limit and reshape themselves. 
  • It helps characterise materials based on their elasticity and details how stiff a material is on applying how much pressure. It demonstrates how much a material shortens on compression.
  • It is employed in manufacturing commercial elastic products—for example, skyscrapers, crane ropes, tires of vehicles, etc.

Conclusion

The elastic materials reshape and resize themselves even after experiencing an external compression force and measuring the elasticity of the materials required in many real-life scenarios like designing weight lifting ropes, tires, etc. Determining the elasticity of a material employs the concept and calculation of bulk modulus. Bulk modulus is the numerical value of how incompressible an elastic material can be. It is used in the cases of liquids, too. It aids in obtaining the value of the pressure of a waterbody based on its compressibility property. The article describes the bulk modulus and explains the bulk modulus SI unit.