The coefficient of viscosity (μ) is the resisting property of a fluid to shearing force. The units of dynamic viscosity are Pa-s and poise. What is the relation between poise and Pa-s?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 16.11.2022
Detailed Explanation
Dynamic viscosity can be expressed in SI units (Pa·s or N·s/m²) or CGS units (poise = dyne·s/cm²). Converting force and length units between CGS and SI yields the fundamental conversion factor.
Derivation of conversion from CGS to SI:
\[ 1\text{ poise} = 1\frac{\text{dyne}\cdot\text{s}}{\text{cm}^2} \]
Since \(1\text{ dyne} = 10^{-5}\text{ N}\) and \(1\text{ cm}^2 = 10^{-4}\text{ m}^2\):
\[ 1\text{ poise} = \frac{10^{-5}\text{ N}\cdot\text{s}}{10^{-4}\text{ m}^2} = 10^{-1}\text{ N}\cdot\text{s/m}^2 = \frac{1}{10}\text{ Pa}\cdot\text{s} = 0.1\text{ Pa}\cdot\text{s} \]
Why “1 poise = 1/10 Pa-s” Is Correct
1 poise = 0.1 Pa·s = 1/10 Pa·s, making option (d) correct.
| 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. poise = 0.5 Pa-s: poise = 0.5 Pa·s is an arbitrary incorrect factor.
- B. 1 poise = 1/100 Pa-s: 1/100 Pa·s corresponds to 1 centipoise (cP), not 1 poise.
- C. 1 poise = 1 Pa-s: 1 poise is not equal to 1 Pa·s; it is one-tenth of a Pa·s.
Key Point
1 poise = 0.1 Pa·s = 1/10 Pa·s; 1 Pa·s = 10 poise; 1 cP = 10⁻³ Pa·s.
Key Concepts for Students
- Poise is named after Jean Léonard Marie Poiseuille.
- Water at 20°C has dynamic viscosity μ ≈ 1.002 cP = 1.002 × 10⁻³ Pa·s.
- 1 Pa·s = 1 N·s/m² = 1 kg/(m·s).
Practice more: this is question 17 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.