Units in fluid mechanics – identifying the correct unit of surface tension In engineering practice, what is the correct S.I. unit for surface tension (also called surface energy per unit area or line force per unit length)?

Introduction / Context:
Surface tension quantifies the energetic or mechanical effect associated with liquid–gas or liquid–liquid interfaces. It can be viewed either as energy per unit area (how much energy is needed to create new surface) or as an equivalent line force acting tangentially along a boundary. This question asks you to recall its correct S.I. unit and to distinguish it from commonly confused units such as pressure, viscosity, or torque.

Given Data / Assumptions:

• S.I. base dimensions and units are used.
• Surface tension symbol: typically sigma or γ_s (not to be confused with specific weight).
• No numerical calculation is required; unit recognition is the focus.

Concept / Approach:
Two equivalent definitions are standard: (1) mechanical definition as line force per unit length acting at an interface, and (2) thermodynamic definition as surface energy per unit area. From the mechanical viewpoint, the unit is newton per metre. From the thermodynamic viewpoint, the unit newton metre per square metre reduces to newton per metre as well.

Step-by-Step Solution:
Step 1: Mechanical view → surface tension = force / length, so unit = N/m.Step 2: Thermodynamic view → surface energy / area = (N·m) / m^2 = N/m.Step 3: Compare with distractors: pressure is N/m^2 (Pa), viscosity is Pa·s, torque is N·m.Step 4: Conclude that the only correct S.I. unit consistent with both views is N/m.

Verification / Alternative check:
Typical values confirm the unit: water at about 20 °C has surface tension near 0.072 N/m; mercury is roughly 0.48–0.49 N/m. Expressing these in N/m is standard in handbooks and lab reports.

Why Other Options Are Wrong:

• N/m^2 (Pa): unit of pressure or stress, not surface tension.
• N/m^3: no common fluid property uses this unit.
• N·m: unit of energy or torque; per area would reduce to N/m.
• Pa·s: unit of dynamic viscosity, unrelated to interfacial phenomena.

Common Pitfalls:
Confusing surface tension with pressure at a curved surface; while pressure jump across a meniscus depends on surface tension (Laplace equation), their units are different.

Final Answer:
N/m