The unit of dynamic viscosity of a fluid is:
Try it first: pick an option, then read the explanation.
Correct answer: D. N.s/m²
Asked in SSC JE 23-09-2019 (Morning)
Detailed Explanation
Dynamic viscosity characterizes the tangential shear force required to sustain a unit velocity gradient between parallel fluid layers. It is expressed in force-time per area units.
\[ \mu = \frac{\tau}{du/dy} = \frac{\text{N/m}^2}{(\text{m/s})/\text{m}} = \frac{\text{N/m}^2}{1/\text{s}} = \text{N}\cdot\text{s/m}^2 \]
Why “N·s/m²” Is Correct
Shear stress has units of N/m² and velocity gradient has units of s⁻¹. Dividing stress by velocity gradient yields N·s/m².
| 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.m²/s: N·m²/s has incorrect dimensional exponents.
- B. N/s²/m: N/s²/m does not represent dynamic viscosity.
- C. N.m/s: N·m/s represents power (Watt or Joules per second).
Key Point
Dynamic viscosity unit: N·s/m² = Pa·s = kg/(m·s).
Key Concepts for Students
- 1 N·s/m² = 10 poise.
- Dynamic viscosity represents absolute resistance to shear.
- Dimensions: [M L⁻¹ T⁻¹].
Practice more: this is question 32 in Properties of Fluid MCQs – Part 3. Try the whole set and check every answer instantly.