Surface tension represents force acting along a line at a liquid interface. What is the correct dimension of surface tension in terms of force F and length L?
-
AF L^-1
-
BF^-1 · L
-
CF · L^-2
-
DF^-2 · L
Answer
Correct Answer: F L^-1
Explanation
Introduction / Context:Surface tension appears in capillarity, bubble formation, and atomization. It is physically the force per unit length acting along a line in the surface, or equivalently energy per unit area. Getting its dimensions right is essential for correct use in correlations like Weber number and capillary rise equations.
Given Data / Assumptions:
- Surface tension symbol γ (or σ) with common units N/m (SI).
- Force denoted by F; length by L.
- Alternative energy interpretation: J/m^2 also equals N/m.
Concept / Approach:
By definition, surface tension = force per unit length. Hence its dimensions are force divided by length. This aligns with many interface mechanics derivations and balances at three-phase contact lines.
Step-by-Step Solution:
Define γ = force / length.Dimensional form → γ ~ F / L = F L^-1.Check with energy view: energy/area = (F·L)/(L^2) = F/L → consistent.Verification / Alternative check:
SI unit check: N/m corresponds exactly to the stated dimension. In base dimensions, γ = M T^-2 (since N = M L T^-2, divided by L → M T^-2), which agrees with F L^-1.
Why Other Options Are Wrong:
F^-1·L, F·L^-2, F^-2·L: These do not match the fundamental definition and lead to inconsistent units in capillarity balances.
Common Pitfalls:
Confusing surface tension with pressure (F L^-2) or elastic modulus; mixing up with interfacial energy units without the area relation.
Final Answer:
F L^-1