What is the shear stress of fluid at rest?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 28-10-2020 (Evening)
Detailed Explanation
A fundamental defining characteristic of fluids is their inability to support static shear stress. In a static fluid, velocity gradients vanish, eliminating internal viscous forces.
From Newton's law of viscosity:
\[ \tau = \mu \frac{du}{dy} \]
For a fluid at rest, \(\frac{du}{dy} = 0\), which requires:
\[ \tau = 0 \]
Why “Zero” Is Correct
Because there is no relative motion between adjacent fluid layers, the velocity gradient is zero, which ensures that shear stress is identically zero throughout the fluid at rest.
Why the Other Options Are Wrong
- A. Unity: Shear stress in a static fluid is zero, never unity.
- C. Uniform: While pressure is uniform in horizontal planes, shear stress is not merely uniform—it is identically zero.
- D. Infinity: Infinity is physically impossible for a fluid in static equilibrium.
Key Point
For any fluid at rest, shear stress is strictly zero (τ = 0).
Key Concepts for Students
- Fluids deform continuously under any applied shear stress; hence static equilibrium requires τ = 0.
- All stresses on any plane in a static fluid are purely normal compressive pressures.
- Hydrostatic pressure acts perpendicular to boundary surfaces at all points.
Practice more: this is question 30 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.