Newton's law of viscosity is a relationship between:
Try it first: pick an option, then read the explanation.
Correct answer: D. Shear stress and rate of shear strain
Asked in SSC JE 3 MARCH 2017 Morning Shift
Detailed Explanation
Isaac Newton postulated that internal friction in a flowing fluid is directly proportional to the relative sliding rate between adjoining layers.
Why “Shear stress and rate of shear strain” Is Correct
Newton's law of viscosity states that shear stress (\(\tau\)) is directly proportional to the rate of shear strain or velocity gradient (\(\frac{du}{dy}\)), with dynamic viscosity as the proportionality constant.
| 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. Pressure, velocity and temperature: The equation does not relate pressure, velocity, and temperature.
- B. Rate of shear strain and temperature: Newton's law does not directly couple shear strain rate with temperature.
- C. Shear stress and velocity: Shear stress depends on the velocity gradient (spatial change in velocity), not the absolute velocity itself.
Key Point
Newton's law of viscosity: τ = μ(du/dy); relates shear stress to rate of shear strain.
Key Concepts for Students
- Constitutive law for Newtonian fluids.
- Rate of shear strain dθ/dt is mathematically equivalent to velocity gradient du/dy.
- Fluids obeying this relation have constant viscosity at constant temperature and pressure.
Practice more: this is question 53 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.