Dimensional formula of Surface tension

How to get the dimensional formula of surface tension

1. Start from the definition: surface tension = force / length.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. Put in the dimension of each part: [M L T^-2] / [L].
6. Add the powers of each base quantity: [M T^-2].

Quantities with the dimensions [M T⁻²]

• Spring constant
• Surface energy

Equal dimensions do not make them the same quantity. Compare surface tension with the others in the full grid.

Three questions on surface tension

Related quantities

• P Pressure [M L⁻¹ T⁻²]
• dP/dx Pressure gradient [M L⁻² T⁻²]
• σ Stress [M L⁻¹ T⁻²]
• U Strain energy [M L² T⁻²]
• u Strain energy density [M L⁻¹ T⁻²]
• ε Strain [M⁰ L⁰ T⁰]