Bulk modulus of a fluid is the ratio of:
Try it first: pick an option, then read the explanation.
Correct answer: C. increase in pressure to the volumetric strain
Asked in SSC JE 2013
Detailed Explanation
The bulk modulus of elasticity quantifies the volumetric stiffness of a fluid under uniform hydrostatic pressure.
From the definition of bulk modulus \(K\):
\[ K = \frac{\text{Increase in pressure}}{\text{Volumetric strain}} = \frac{dp}{-dV / V} = -\frac{V\,dp}{dV} = \rho \frac{dp}{d\rho} \]
Why “increase in pressure to the volumetric strain” Is Correct
Bulk modulus is the ratio of increase in hydrostatic pressure (compressive stress) to the resulting volumetric strain (-dV/V).
| Property | Formula | SI unit | Standard value (water, 4°C) |
|---|---|---|---|
| Density ρ | m/V | kg/m³ | 1000 kg/m³ |
| Specific weight γ | ρg | N/m³ | 9810 N/m³ |
| Specific gravity S | ρ/ρ_water | — | 1.0 |
| Specific volume v | 1/ρ | m³/kg | 0.001 m³/kg |
| Bulk modulus K | −dp/(dV/V) | Pa | 2.06 GPa |
| Compressibility β | 1/K | Pa⁻¹ | 4.85 × 10⁻¹⁰ Pa⁻¹ |
Why the Other Options Are Wrong
- A. shear stress to shear strain: Shear stress to shear strain defines the modulus of rigidity (G).
- B. increase in volume to the viscosity of fluid: Volume change to viscosity is not a standard physical modulus.
- D. critical velocity to the velocity of fluid: Critical velocity ratio relates to Reynolds number, not bulk modulus.
Key Point
Bulk modulus K = increase in pressure / volumetric strain = −dp / (dV/V).
Key Concepts for Students
- Bulk modulus has units of pressure (Pa, N/m², GPa).
- Speed of sound in a fluid medium is c = √(K / ρ).
- Liquids have high bulk moduli (water K ≈ 2.06 GPa); gases have low bulk moduli (air K ≈ 101 kPa).
Practice more: this is question 74 in Properties of Fluid MCQs – Part 5. Try the whole set and check every answer instantly.