What is the SI unit for dynamic viscosity?
Try it first: pick an option, then read the explanation.
Correct answer: A. Pascal second
Asked in SSC JE 23.03.2021 (Morning Shift)
Detailed Explanation
Dynamic viscosity connects shear stress (force per unit area) to velocity gradient (velocity per unit distance). Expressing this in SI units leads directly to Pascal second.
\[ \mu = \frac{\tau}{du/dy} = \frac{\text{N/m}^2}{(\text{m/s})/\text{m}} = \frac{\text{N/m}^2}{1/\text{s}} = \text{N}\cdot\text{s/m}^2 = \text{Pa}\cdot\text{s} \]
Why “Pascal second” Is Correct
Because shear stress has unit Pa (N/m²) and velocity gradient has unit s⁻¹, the SI unit of dynamic viscosity is Pascal second (Pa·s).
| 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
- B. Pascal: Pascal (Pa = N/m²) is the unit of pressure and normal stress, not viscosity.
- C. Stoke: Stoke (cm²/s) is the CGS unit of kinematic viscosity.
- D. Newton: Newton (N) is the SI unit of force.
Key Point
SI unit of dynamic viscosity: Pa·s = N·s/m² = kg/(m·s).
Key Concepts for Students
- 1 Pa·s = 10 poise = 1000 centipoise (cP).
- Kinematic viscosity has unit m²/s in SI.
- Dynamic viscosity dimension: [M L⁻¹ T⁻¹].
Practice more: this is question 27 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.