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Capillary rise: how high does a liquid climb in a thin tube?

Calculate the height a liquid rises, or falls, in a capillary tube from its surface tension, contact angle, density and the tube radius, with Jurin's law.

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Results

Capillary rise (negative: depression)

29.75

The liquid wets the tube and climbs above the outside surface
Capillary length √(γ ÷ ρg)
2.727
Rise × radius (constant for a given liquid)
14.88 mm²

Liquids that climb

Dip a thin glass tube into water and the water climbs inside it, above the level of the surrounding liquid. Dip the same tube into mercury and the level inside drops instead. Both effects come from surface tension and from how well the liquid wets the tube. The English physician James Jurin described the rule in 1718.

Jurin’s law

h = 2γ cos θ ÷ (ρ g r)

  • γ: surface tension of the liquid, in N/m
  • θ: contact angle between the liquid and the tube wall
  • ρ: density of the liquid
  • g: gravity, 9.81 m/s²
  • r: inner radius of the tube

A contact angle below 90° means the liquid wets the wall and rises; above 90°, it does not wet the wall and is pushed down. The height is inversely proportional to the radius, so the product h × r is constant for a given liquid and surface.

Example

Clean water at 20 °C, with a surface tension of 72.8 mN/m and a contact angle of 0°, in a glass tube with a 0.5 mm radius:

  • h = 2 × 0.0728 × 1 ÷ (998 × 9.81 × 0.0005) = 29.75 mm
  • In a tube ten times narrower, 0.05 mm, it would rise about 30 cm

Typical properties

Liquid γ (mN/m) ρ (kg/m³) θ on glass
Water, 20 °C 72.8 998 about 0°
Ethanol 22.3 789 about 0°
Glycerol 63.4 1,261 about 0°
Mercury 485 13,534 about 140°

Surface tension falls as temperature rises, and soap or other surfactants lower it sharply, so soapy water rises much less.

The capillary length

The capillary length, √(γ ÷ ρg), is about 2.7 mm for water. Below this scale, surface tension dominates gravity: drops stay round, insects walk on water and liquids climb in narrow gaps. Above it, gravity wins and puddles spread flat.

Capillarity in everyday life

  • Rising damp: water climbs through the fine pores of brick and stone walls, which is why old houses without a damp-proof course show damp at the base of their walls.
  • Soils: water rises from the water table into fine soils, more in clay than in sand.
  • Wicks, paper towels and sponges draw liquids through narrow channels.
  • Plants: capillarity helps, but the cohesion of water pulled by evaporation from the leaves does most of the work of raising sap.

Frequently asked questions

What is Jurin's law?

The height a liquid climbs in a narrow tube is h = 2γ cos θ ÷ (ρ g r), where γ is the surface tension, θ the contact angle, ρ the density, g gravity and r the tube radius. James Jurin published it in 1718.

Why does mercury go down instead of up?

Mercury does not wet glass: its contact angle is about 140°, so cos θ is negative and the level inside the tube sits below the outside surface. That is called capillary depression.

How high does water rise in a 1 mm tube?

In a tube with a 0.5 mm radius, clean water at 20 °C rises about 30 mm. Halving the radius doubles the rise, so in a 0.05 mm radius tube it reaches about 30 cm.

Where does capillary action matter?

In soils and plants, in paper towels and wicks, in rising damp in masonry walls and in microfluidics. In trees it helps, but transpiration and cohesion do most of the work of lifting sap.

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Results are estimates provided for information purposes. They do not replace professional advice.

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