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# 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. Involving velocity, pressure, density and temperature as functions of space and time.

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
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ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

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