Viscous Force Definition – Relation to Shear Stress and Area In viscous flow, the resultant viscous force acting on a surface equals the shear stress due to viscosity multiplied by the area over which that stress acts.

Introduction:
The item probes the basic relationship F = tau * A for shear forces in viscous flow, where tau is the shear stress and A is the area. This is foundational for wall shear calculations and drag estimation.

Given Data / Assumptions:

• Continuum mechanics applies; Newtonian fluid.
• Shear stress tau is known or determined from velocity gradients and viscosity.
• Uniform average shear over area A for the purpose of this relation.

Concept / Approach:

Stress is force per unit area. Rearranging gives force as stress times area. In viscous flows near solid boundaries, tau = mu * (du/dy) for Newtonian fluids, and the net shear force follows directly.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional consistency: [tau] = N/m^2, [A] = m^2, so F = N, confirming the product relation.

Why Other Options Are Wrong:

Sum, different, ratio: These words do not reflect the physics or dimensional analysis; only product yields correct force units.

Common Pitfalls:

Confusing wall shear stress with average shear; neglecting non-Newtonian behavior where tau may not be proportional to du/dy, though F = tau * A still holds once tau is known.

Final Answer:

product