Bulk Modulus| Daily Life Examples

The bulk modulus measures a material’s resistance to compression; it quantifies how much a substance will decrease in volume under increased pressure. For instance, squeezing a sponge decreases its volume, and the bulk modulus characterises how much the sponge resists compression.

Daily Life Examples of Bulk Modulus

1. Car Tires: The bulk modulus of air in car tires (typically around 1.4 x 10⁵ Pa) affects how much the tire compresses under varying pressures.
2. Balloon Inflation: When inflating a balloon, the rubber’s bulk modulus (around 6 x 10⁸ Pa) determines how much the balloon’s volume changes with added air.
3. Hydraulic Systems: In hydraulic brakes, the bulk modulus of hydraulic fluid (about 2.2 x 10⁹ Pa) is crucial for transmitting pressure efficiently.
4. Deep-Sea Diving: The bulk modulus of water (2.2 x 10⁹ Pa) is significant for understanding pressure changes at different depths during deep-sea diving.
5. Ear Protection: The bulk modulus of ear protection materials (e.g., foam, rubber) influences their ability to absorb sound waves, providing a comfortable environment.

Mathematical Relation

The bulk modulus (K) is mathematically related to the pressure (P) and the fractional change in volume (ΔV/V) of a material under pressure. The formula for bulk modulus is given by:

K=−V(ΔP​/ΔV)

Where:

• K is the bulk modulus,
• ΔP is the change in pressure,
• ΔV is the change in volume,
• V is the original volume of the material.

In some cases, this formula is also expressed using the bulk modulus of elasticity (Y) and the material’s original volume (V):

K=Y(1​/3−2ν)

Where:

• Y is the Young’s modulus of the material,
• ν is Poisson’s ratio (a dimensionless ratio describing the lateral contraction to longitudinal extension)

This second formula is often used when the Young’s modulus and Poisson’s ratio are known.

Simple Case Study: Bulk modulus of the material used in the diving suit.

Given:

• Original volume of the diving suit material, V=0.05 m³
• Initial pressure at sea level, P1=1 atm≈101.325 kPa
• Final pressure at depth, P2=20 atm≈2026.5 kPa
• Change in volume, ΔV=−0.01 m³

Using the bulk modulus formula:

K=−V(ΔP/ΔV)

Bulk Modulus (K)=0.05 m³{(2026.5 kPa−101.325 kPa)/0.01 m³) = −96258.75 N/m²