Viscous force is the ............. of shear stress due to viscosity and cross sectional area of flow:
Try it first: pick an option, then read the explanation.
Correct answer: B. Product
Asked in SSC JE 3 MARCH 2017 Morning Shift
Detailed Explanation
Shear stress is defined as force per unit surface area. To find the total tangential resistance exerted on a boundary, stress must be integrated over the contact area.
By definition of shear stress \(\tau\):
\[ \tau = \frac{F_{\text{viscous}}}{A} \;\implies\; F_{\text{viscous}} = \tau \times A = \mu A \frac{du}{dy} \]
Why “Product” Is Correct
Viscous force equals the product of the viscous shear stress \(\tau\) and the shearing contact area \(A\).
Why the Other Options Are Wrong
- A. Sum: Sum has incompatible units of stress plus area.
- C. Difference: Difference is dimensionally meaningless between stress and area.
- D. Ratio: Ratio of shear stress to area would have units of N/m⁴, not force.
Key Point
Viscous force F = τ × A (product of shear stress and contact area).
Key Concepts for Students
- Shear stress has units of N/m²; multiplying by area in m² yields force in N.
- Newton's formula for laminar flow: F = μ A (du/dy).
- Total drag on a flat plate is obtained by integrating τ_w dA over the wetted surface.
Practice more: this is question 64 in Properties of Fluid MCQs – Part 5. Try the whole set and check every answer instantly.