The compressibility of the fluid is given as 5 × 10⁻¹¹ Pa⁻¹. What is the Bulk modulus (GPa) of fluid?
Try it first: pick an option, then read the explanation.
Correct answer: C. 20
Asked in SSC JE 23.01.2018 (Evening Shift)
Detailed Explanation
Bulk modulus of elasticity is the reciprocal of compressibility. Converting from Pa to GPa provides the answer in standard engineering units.
Given compressibility \(\beta = 5 \times 10^{-11}\text{ Pa}^{-1}\):
\[ K = \frac{1}{\beta} = \frac{1}{5 \times 10^{-11}\text{ Pa}^{-1}} = 0.2 \times 10^{11}\text{ Pa} = 20 \times 10^9\text{ Pa} = 20\text{ GPa} \]
Why “20” Is Correct
Inverting 5 × 10⁻¹¹ gives 2 × 10¹⁰ Pa, which equals 20 GPa (since 1 GPa = 10⁹ Pa).
| 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. 10: 10 GPa corresponds to compressibility of 10 × 10⁻¹¹ Pa⁻¹.
- B. 15: 15 GPa is an incorrect intermediate distractor.
- D. 25: 25 GPa corresponds to compressibility of 4 × 10⁻¹¹ Pa⁻¹.
Key Point
K = 1 / β; 1 / (5 × 10⁻¹¹) = 20 × 10⁹ Pa = 20 GPa.
Key Concepts for Students
- Bulk modulus represents volumetric stiffness.
- 1 GPa = 10⁹ Pa = 10³ MPa = 10⁶ kPa.
- Typical bulk modulus for water is ~2 GPa, so 20 GPa represents a very stiff fluid.
Practice more: this is question 46 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.