In a Newtonian fluid:
Try it first: pick an option, then read the explanation.
Correct answer: A. The shear stress is directly proportional to the rate of fluid deformation
Asked in SSC JE 2011
Detailed Explanation
The defining rheological criterion of a Newtonian fluid is linear proportionality between the applied shear stress and the resulting shear strain rate.
Why “The shear stress is directly proportional to the rate of fluid deformation” Is Correct
By definition, a Newtonian fluid exhibits a constant dynamic viscosity, such that shear stress varies linearly with the rate of fluid deformation (\(\tau = \mu \frac{du}{dy}\)).
| Fluid type | Viscosity changes with rate of shear? | Examples |
|---|---|---|
| Ideal fluid | No (μ = 0) | Theoretical only |
| Newtonian fluid | No (μ = const) | Water, air, oil, mercury |
| Non-Newtonian | Yes | Blood, toothpaste, ketchup, paint |
| Ideal plastic (Bingham) | No, but needs yield stress τ₀ first | Fresh concrete, drilling mud |
Why the Other Options Are Wrong
- B. Dynamic viscosity is directly proportional to the rate of fluid deformation: Dynamic viscosity is a constant property of the fluid, not proportional to the rate of deformation.
- C. Kinematic viscosity is directly proportional to the rate of fluid deformation: Kinematic viscosity is also constant for a Newtonian fluid at a given temperature and pressure.
- D. Dynamic viscosity is zero: Zero dynamic viscosity characterizes an ideal fluid, not a Newtonian fluid.
Key Point
Newtonian fluid: shear stress is directly proportional to the rate of shear deformation; viscosity is constant.
Key Concepts for Students
- Constant viscosity implies a straight line through the origin on a τ vs du/dy plot.
- Water, motor oils, air, and gasoline behave as Newtonian fluids under normal conditions.
- Fluids whose viscosity changes with shear rate are non-Newtonian.
Practice more: this is question 55 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.