Surface Tension Force — Dependence on Line of Contact Is the following statement correct? “Surface tension force equals the product of surface tension per unit length and the cross-sectional area of flow.”

Introduction:
Surface tension arises at interfaces and manifests as a force acting along lines (perimeters) of contact, not over cross-sectional areas like pressure forces. Clarifying this distinction prevents dimensional and conceptual mistakes in capillarity problems.

Given Data / Assumptions:

• Clean liquid–gas or liquid–liquid interface.
• Contact angle alpha defined at the solid–liquid interface where relevant.
• Quasi-static conditions.

Concept / Approach:
The magnitude of surface tension force is F = sigma * L * cos(alpha_component) where sigma is surface tension (N/m) and L is the length of contact (e.g., tube inner perimeter). This already shows that multiplying by an area would give wrong units and an incorrect physical interpretation.

Step-by-Step Solution:
Identify units: sigma has units N/m.Multiply by a length L (m): sigma * L gives N, a force.Multiplying by area (m^2) would produce N*m, not a force, hence the statement is false.

Verification / Alternative check:
Capillary rise formula h = (4 * sigma * cos(alpha)) / (w * d) derives from balancing sigma * perimeter against the weight of the column, again confirming perimeter (length), not area.

Why Other Options Are Wrong:
Choosing “Correct” ignores the fundamental line-force nature of surface tension and leads to dimensional inconsistency.

Common Pitfalls:
Confusing surface tension (line force) with surface energy (J/m^2) and with pressure forces (which act over area).

Final Answer:
Incorrect