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Capillarity - or capillary action - is the ability of a narrow tube to draw a liquid upwards against the force of gravity.

The height of liquid in a tube due to capillarity can be calculated

h = 2 σ cosθ / (ρ g r)                              (1)


h = height of liquid (ft, m)

σ = surface tension (lb/ft, N/m)

θ = contact angle ( θ = 0 for clean tube)

ρ = density of liquid (lb/ft3, kg/m3 )

g = acceleration of gravity (32.174 ft/s2, 9.81 m/s2)

r = radius of tube (ft, m)

Surface Tension

Surface tension is typically measured in dynes /cm or N/m .

Capillarity - Surface Tension vs. Liquid
LiquidSurface Tension
- σ -
N/m dynes/cm
Ethyl Alcohol 0.0223 22.3
Mercury 0.465 465
Water 20 oC 0.0728 72.75
Water 100 oC 0.0599


Capillarity, like surface tension, decreases with increasing temperature. The temperature variation, however, is small and insignificant in most problems.

Example - Water Capillarity Rise in Tube

The capillarity rise in a clean tube (θ = 0) with diameter 2 mm and water temperature 20 oC with density 1000 kg/m3 can be calculated as

h = 2 (0.0728 N/m) cos(0) / ((1000 kg/m3 ) (9.81 m/s2) (2 10-3 m))

= 0.0074 m

= 7.4 mm

Capillarity Rise in Tubes

Capillarity rise in clean circular glass tubes for distilled water, fresh water and mercury at temperature 20 oC (68 oF) :

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Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Surface Tension

Surface tension of liquids like water, mercury, oils and more.

Surface Tension - Water in contact with Air

Surface tension of water in contact with air for temperatures ranging 0 to 100 degC (32 to 212 degF) - in imperial units (BG units) and SI units.

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