Which of the following represents the unit of kinematic viscosity?
Try it first: pick an option, then read the explanation.
Correct answer: A. cm²/s
Asked in SSC JE 27-01-2018 (Evening Shift)
Detailed Explanation
Kinematic viscosity is defined as dynamic viscosity divided by mass density (ν = μ/ρ). Its dimensional formula is [L² T⁻¹], leading to area per unit time units.
In the CGS system:
\[ \nu = \frac{\mu}{\rho} = \frac{\text{g}/(\text{cm}\cdot\text{s})}{\text{g}/\text{cm}^3} = \frac{\text{cm}^3}{\text{cm}\cdot\text{s}} = \text{cm}^2/\text{s} = \text{stoke} \]
Why “cm²/s” Is Correct
cm²/s is the CGS unit of kinematic viscosity (1 stoke = 1 cm²/s = 10⁻⁴ m²/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. dyne-sec/cm²: dyne·s/cm² is the poise, the CGS unit of dynamic viscosity.
- C. gm/cm-sec: g/(cm·s) is the poise expressed in mass base units for dynamic viscosity.
- D. gm/cm²-sec: g/(cm²·s) does not represent a standard viscosity quantity.
Key Point
Kinematic viscosity unit = cm²/s (CGS stoke) or m²/s (SI).
Key Concepts for Students
- 1 stoke = 1 cm²/s = 10⁻⁴ m²/s.
- Kinematic viscosity describes diffusion of momentum.
- Dimensions: [L² T⁻¹].
Practice more: this is question 36 in Properties of Fluid MCQs – Part 3. Try the whole set and check every answer instantly.