The SI unit of kinematic viscosity is:
Try it first: pick an option, then read the explanation.
Correct answer: B. m²/s
Asked in SSC JE 30-10-2020 (Morning)
Detailed Explanation
Kinematic viscosity represents the ratio of dynamic viscosity to mass density, describing the rate of momentum diffusion in a fluid. Its dimensional formula involves only length and time.
\[ \nu = \frac{\mu}{\rho} = \frac{\text{kg}/(\text{m}\cdot\text{s})}{\text{kg}/\text{m}^3} = \frac{\text{m}^3}{\text{m}\cdot\text{s}} = \text{m}^2/\text{s} \]
Why “m²/s” Is Correct
Kinematic viscosity has dimensions of area divided by time, making m²/s its standard SI unit.
| Quantity | SI unit | CGS unit | Conversion |
|---|---|---|---|
| Dynamic viscosity μ | Pa·s (N·s/m²) | Poise (P) = dyne·s/cm² | 1 P = 0.1 Pa·s |
| Kinematic viscosity ν = μ/ρ | m²/s | Stoke (St) = cm²/s | 1 St = 10⁻⁴ m²/s |
| Surface tension T | N/m | dyne/cm | 1 dyne/cm = 10⁻³ N/m |
Why the Other Options Are Wrong
- A. N-s/m²: N·s/m² (or Pa·s) is the SI unit of dynamic viscosity.
- C. cm²/s: cm²/s (stoke) is the CGS unit of kinematic viscosity, not the SI unit.
- D. dyne-s/m²: dyne·s/m² is not a recognized coherent unit.
Key Point
SI unit of kinematic viscosity ν = m²/s; CGS unit = cm²/s (stoke).
Key Concepts for Students
- 1 stoke = 1 cm²/s = 10⁻⁴ m²/s.
- 1 centistoke (cSt) = 10⁻² stoke = 10⁻⁶ m²/s = 1 mm²/s.
- Kinematic viscosity of water at 20°C is approximately 1.0 cSt = 10⁻⁶ m²/s.
Practice more: this is question 31 in Properties of Fluid MCQs – Part 3. Try the whole set and check every answer instantly.