# Capillarity

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

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)

where

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.

LiquidSurface Tension
- σ -
N/mdynes/cm
Ethyl Alcohol 0.0223 22.3
Mercury 0.465 465
Water 20oC 0.0728 72.75
Water 100oC 0.0599

58.9

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):

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

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