Bulk Modulus Calculator
Calculate bulk modulus, bulk stress, and volumetric strain for materials under pressure
Calculation Mode
Original volume before pressure is applied
Additional pressure applied to the material
Change in volume due to applied pressure (negative for compression)
Results
Formula used: B = -ΔP/(ΔV/V₀)
Example Calculation
Hydraulic Press Example
System: Hydraulic press with oil
Operating pressure (ΔP): 21 × 10⁶ Pa (21 MPa)
Oil volume (V₀): 0.001155 m³
Oil bulk modulus (B): 5 × 10⁹ Pa (5 GPa)
Solution
Using formula: ΔV = -(ΔP × V₀) / B
ΔV = -(21 × 10⁶ Pa × 0.001155 m³) / (5 × 10⁹ Pa)
ΔV = -24,255 / (5 × 10⁹)
ΔV = -0.000004851 m³ = -4.851 mL
The oil volume decreases by 4.851 mL under pressure.
Common Material Properties
Key Concepts
Bulk Modulus (B)
Resistance to uniform compression
Bulk Stress (ΔP)
Pressure applied uniformly
Bulk Strain (ΔV/V₀)
Fractional volume change
Incompressibility
Higher B = harder to compress
Understanding Bulk Modulus
What is Bulk Modulus?
Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies how much pressure is needed to cause a specific fractional change in volume. Materials with high bulk modulus are difficult to compress, while those with low bulk modulus compress easily.
Physical Significance
- •Related to the speed of sound in the material
- •Important in fluid mechanics and hydraulics
- •Critical for pressure vessel design
- •Used in seismic wave analysis
Formulas and Relationships
Primary Formula
B = -ΔP / (ΔV/V₀)
Negative sign accounts for volume decrease under compression
From Elastic Constants
B = E / [3(1 - 2ν)]
For isotropic materials only
Bulk Strain
εᵥ = ΔV/V₀
Volumetric strain (dimensionless)
B: Bulk modulus (Pa, GPa)
ΔP: Pressure change (Pa)
ΔV: Volume change (m³)
V₀: Initial volume (m³)
E: Young's modulus (Pa)
ν: Poisson's ratio