## Bulk Modulus Calculator :

Enter the calculator its Additional pressure on object (ΔP) in pascals(pa), Change in volume (ΔV) in m³, Original volume (V₀) in m³, Bulk modulus (B) in pascals(pa), and you get the calculation below the calculator check it.

## Bulk Modulus Formula :

Bulk modulus K_{(pa) }in pascal is equal to the product of the actual volume of the object V_{(m}^{3}_{) }in meter cube multiply by the change in pressure _{ }(∆P_{(pa)}) in pascal is divided by the change in volume ∆V_{(m}^{3}_{)}In meter cube. Hence the bulk modulus formula has been written as,

**K _{(pa)} = V_{(m}^{3}_{) }(∆P_{(pa)}) / ∆V_{(m}^{3}_{)}**

Where,

K→ bulk modulus in (pascal)

∆P denotes the change in pressure →(pascal)

∆V denotes the change in volume → (m^{3})

V denotes the actual volume of the object→ (m^{3})

## Sample Problems :

### Example 1:

In ammunition testing center the pressure is found to be 355 MPa. Calculate the change in volume of the piece of the copper piece when subjected to this pressure in percentage. The bulk modulus of copper is 1.38 x Pa.

### Solution :

The pressure in the testing center is 255 MPa.

Bulk modulus, K = V(∆P) / ∆V

Substituting the values,

k= (ΔV / V)

k = 355×10^{6}/ 1.38×10^{11}× 100

Therefore, the change in volume percentage is 2.5724 %.

### Example 2:

If the pressure of the liquid is increased from 80 N/cm^{2} to 150 N/cm^{2}, calculate the bulk modulus of elasticity. The amount of liquid in the container shrinks by 0.16 %.

### Solution :

ΔV = V × 0.16 /100

= 16V × 10^{-4} m^{3},

Volume of liquid = V m3,

ΔP = 150 – 80

= 70 N/cm^{2}

Volumetric Strain = 16 × 10^{-4 }

K = ΔP × V / ΔV

K = 70 / 16 × 10^{-4}

K = 4 3× 10^{4} N/cm^{2}.