**Bulk modulus** is one of the key properties of materials and fluids to detect how it may behave when under pressure from all directions. Let us learn more about what is the **bulk modulus**, What is the bulk modulus formula, and usage.

Article Synopsis

## What is Bulk Modulus?

When a material or fluid is under pressure from all directions, it changes its volume. When the pressure is withdrawn, the object goes back to its original shape.

Bulk modulus is the ability of a material or fluid to resist the volumetric deformation due to applied pressure. It is equal to the quotient of applied pressure divided by the amount of deformation.

## Bulk modulus formula

Bulk modulus is the ratio of applied pressure to the volumetric strain.

Let us consider the initial volume of an object is **V1**. Pressure **P **is applied to all surfaces of the object. Due to this pressure, the volume got decreased, and the new volume is **V2**.

So the deformation is ( V1-V2). The strain, in this case, is the amount of deformation divided by the original volume which is equal to **(V1-V2)/V1.**

The bulk modulus in this case would be as shown below.

**Bulk Modulus= [P/ {(V1-V2)/V1}]**

In an ideal case scenario, we need to adjust the pressure to see variable deformation. Right? Let’s assume that the initial pressure is **P1**. And you need to put **P2** pressure to get the new volume **V2**. In this case, the bulk modulus will be what is shown below.

**Bulk Modulus= Volumetric stress / Volumetric strain= [(P1-P2)/ {(V1-V2)/V1}]**

## The relation between bulk modulus and Young’s modulus

Bulk modulus deals in resistance to volumetric deformation whereas Young’s modulus deals in longitudinal deformation. However, the logic is almost the same. Bulk modulus is more suitable for fluids whereas Young’s modulus is for metals.

Both modules work in the elastic zone region. More pressure or force will take the object into the plastic zone and then into failure.

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## Unit of Bulk Modulus

In the English system, the unit of Bulk modulus is pound per square inch (PSI). In the metric system, the unit is Newton per meter square(N/M^{2})

## Bulk modulus usage

Bulk modulus is used for predicting the resistance to deformation of an object under variable pressure conditions. The more the value of bulk modulus, the more pressure is required to get the same amount of deformation.

Bulk modulus along with Young’s modulus and Hooke’s law describe a material response to streets and strain

## Bulk modulus of common materials

Material | Bulk Modulus (Gpa) |
---|---|

Steel | 160 |

Diamond | 443 |

Limestone | 65 |

Sandstone | .7 |

Glass | 30-55 |

Rubber | 1.5-2 |

Granite | 50 |

Chalk | 9 |

Shale | 10 |

## Bulk modulus of fluids and other substances

Fluids | Bulk Modulus (Gpa) |
---|---|

Water | 2.15 |

Petrol | 1.07 |

Gasoline | 1.3 |

Kerosine | 1.3 |

Seawater | 2.3 |

Mercury | 28.5 |

Glycerin | 4.35 |

SAE 30 oil | 1.5 |

Ethyl Alcohol | 1.06 |

## Conclusion

As I said before, the bulk modulus is a key property of materials and especially for fluids. It shows how the object may behave when pressure is applied. Along with Young’s modulus and Hooke’s law, bulk modulus helps us to find how the object may behave in different loading condition

That’s all I have in this article. In this article, I tried to cover the basics of Bulk Modulus. So it is expected that you may have questions. If you have a question or query, do write in the comment section and I will be happy to reply.

## Frequently Asked Questions (FAQ)

### What is Bulk Modulus?

The bulk modulus is a mechanical property of materials and fluid to predict how the object will behave in different pressure conditions from all sides. Mathematically it is the ratio of volumetric stress to the volumetric strain

### What is the value of bulk modulus for an incompressible liquid?

The bulk modulus of in-compressible fluid is infinite. The reason is that the incompressible fluid does not change volume due to pressure. Due to that, the Bulk modulus will be equal to (Pressure / 0) which is equal to ∞ .

### How to calculate bulk modulus of elasticity?

Bulk modulus of elasticity can calculated as the ratio of volumetric stress to volumetric strain