# Bulk Modulus Formula

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

The bulk modulus describes how a substance reacts when squeezed uniformly. When the external forces are perpendicular to the surface, it is distributed uniformly over the surface of the object. This may occur when an object is immersed in a fluid and undergo a change in volume but no change in shape.

The ∆P is volume stress defined as the ratio of the magnitude of the change in the amount of force ∆F to the surface area.

The bulk modulus of any liquid is a measure of its compressibility and the pressure required to bring about a unit change in its volume.

Hence, Bulk modulus formula is given by

K = V(∆P) / ∆V

Where,

∆P denotes change in pressure

∆V denotes change in volume

The units for the bulk modulus K are psi or kPa.

Example 1

Determine the change in volume if the atmospheric pressure of 0.1 MPa of an aluminium block is reduced to zero when this unit is put in a vacuum. The bulk modulus of aluminium is 120000 MPa.

Solution

Bulk Modulus K = (−ΔP) / ΔV/V

∆V / V = −(∆P) / K

∆V / V = −(−0.1) / 120000

∆V / V = 8.3 x 10-3

Hence, the fractional change in volume is 8.3 x10-3

Example 2

In ammunition testing center the pressure is found to be 255 MPa. Calculate the change in volume of the piece of copper piece when subjected to this pressure in percentage. The bulk modulus of copper is 1.38 x 1011 Pa.

Solution

The pressure in the testing center is 255 MPa.

The bulk modulus is K = (−ΔP) / ΔV(V)

(−ΔP) because ∆ V is negative when the ∆ P is positive

The change in percentage = (ΔV / V) × 100

= (ΔP / K) × 100

= 255×106 / 1.38×1011

Therefore, the change in volume percentage is 0.184 %