Units and Definitions — What Quantity Has Units of Force per Unit Length? In fluid mechanics, which property has the dimension/unit of force per unit length (e.g., N/m)?

Introduction:
Dimensional awareness helps identify fluid properties quickly. Recognizing which property is measured as force per unit length is useful in problems involving interfaces, droplets, jets, and capillary tubes.

Given Data / Assumptions:

• Standard SI units; typical fluid-mechanics definitions.
• Interface between immiscible phases (e.g., water–air).

Concept / Approach:
Surface tension represents the tangential force per unit length acting along a line in the interface, equivalently the energy per unit area required to increase the surface. Its SI unit can be written as N/m (or J/m^2). Other listed properties have different units (e.g., viscosity is Pa·s).

Step-by-Step Solution:
Recall definition: surface tension sigma = force / length.Check dimensional equivalence: N/m equals J/m^2, matching the energetic interpretation.Therefore the correct choice is surface tension.

Verification / Alternative check:
Capillary-rise formulas include sigma with units N/m, reinforcing this identification.

Why Other Options Are Wrong:
Compressibility is fractional volume change per pressure (1/Pa).
Capillarity is a phenomenon caused by surface tension and wetting; it is not a property with N/m units.
Viscosity has units Pa·s (N·s/m^2).

Common Pitfalls:
Confusing the phenomenon (capillarity) with the property (surface tension); mixing dynamic viscosity with kinematic viscosity units.

Final Answer:
surface tension