According to Newton's law of viscosity, the shear stress of a fluid element layer is directly proportional to the:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 07/06/2024 (09am-11am)
Detailed Explanation
Newton's law of viscosity describes how fluids deform continuously under shear. Unlike elastic solids where shear stress is proportional to shear strain, in fluids shear stress is proportional to the rate of shear strain.
\[ \tau \propto \frac{d\theta}{dt} = \frac{du}{dy} \;\implies\; \tau = \mu \frac{du}{dy} \]
Why “rate of shear strain” Is Correct
In a fluid layer, shear deformation occurs continuously over time. The shear stress \(\tau\) is directly proportional to the rate of angular deformation or velocity gradient \(\frac{du}{dy}\). The constant of proportionality is the dynamic viscosity \(\mu\).
Why the Other Options Are Wrong
- A. elastic modulus: Elastic modulus relates stress to strain in solid materials under Hooke's law, not fluids in shear.
- B. pressure: Static fluid pressure acts normal to surfaces and does not govern viscous shear stress in laminar flow.
- C. bulk modulus: Bulk modulus governs volumetric compressibility under hydrostatic pressure, not shear deformation.
Key Point
Newton's law: τ = μ(du/dy), where shear stress is proportional to rate of shear strain.
Key Concepts for Students
- Newtonian fluids exhibit constant dynamic viscosity μ independent of shear rate.
- Rate of shear strain dθ/dt is geometrically identical to velocity gradient du/dy for parallel laminar flow.
- Fluids cannot sustain static shear stress; they deform continuously as long as shear is applied.
Practice more: this is question 1 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.