newton per metre

SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol

Name	Symbol	Quantity	Base units
newton per metre	N/m	surface tension	kg s⁻²
The newton per metre, symbol N/m, is the SI coherent derived unit of surface tension. One newton per metre is equal to the surface tension of a liquid that results in a force of one newton on a one metre line on its surface. The force being parallel to the surface and perpendicular to the line.
Definition			h c^-2 Δν_Cs³
$1 \mspace{4mu} \text{N} / \text{m} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^3} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^3}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{N} / \text{m} \mspace{6mu} \approx 1.746 \mspace{4mu} 086 \mspace{4mu} 621 \mspace{4mu} 278 \mspace{4mu} 988 \mspace{4mu} 563 \times10^{20} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^3$

Surface tension

Molecules in a liquid experience strong intermolecular attractive forces.

Within the body of a liquid, each molecule experiences intermolecular forces equally from all directions resulting in a net force of zero. However, molecules at the surface of a liquid are not surrounded by like molecules on all sides. They therefore experience a net force perpendicular to the surface, towards the bulk of the liquid. This net force is responsible for the phenomenon called surface tension.

In the absence of any other external force, surface tension acts on a body of liquid causing it to adopt the shape with the smallest surface area possible for its volume. A body of liquid acts as though it was wrapped in an invisible elastic membrane. Surface tension accounts for the spherical shape of soap bubbles and raindrops in freefall.

The strength of the surface tension depends on the liquid and its temperature.

The force acting on a line on a liquid surface is parallel to the surface and perpendicular to the line. The force, F, is directly proportional to the length of the line, d, and to the surface tension, γ, of the liquid:

$F \propto \gamma \mspace{2mu} d$

Using SI coherent units, the proportionality constant is 1. Thus:

$F = \gamma \mspace{2mu} d \\ \\ \\ \gamma = \dfrac{F}{d}$

where:

γ is the surface tension in newtons per metre, symbol N m^-1,
F is the net force applied in newtons, symbol N,
d is the length of the line in metres, symbol m.

Examples of the surface tension of liquids

Liquid	Surface tension / N m⁻¹
Water (20 °C)	0.073
Water (100 °C)	0.059
Ethanol	0.022
Mercury	0.513