Capillary Rise in a Tube

Capillary rise in a circular tube

\( \displaystyle h = \frac{2\sigma \cos\theta}{\rho g r} \;=\; \frac{4\sigma \cos\theta}{\rho g D} \)

Symbols

\(h\) — capillary rise (+) or depression (−) (m)
\(\sigma\) — surface tension (N·m\(^{-1}\))
\(\theta\) — static contact angle (°), measured in the liquid
\(\rho\) — liquid density (kg·m\(^{-3}\))
\(r\), \(D\) — tube radius, inner diameter (m), with \(D=2r\)

Capillary tube schematic: meniscus, contact angle θ, rise h

Inputs

Preset

Pick a preset to lock \( \theta,\sigma,\rho \). Choose Custom… to edit them.

Surface tension, σ (N/m)

Density, ρ (kg/m³)

Contact angle, θ (°)

Tube inner diameter, D

Plot range: 0.20–2.00 mm. Use the slider or drag the red dot.

Current values

h (m)

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h (mm)

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\(g = 9.81\ \mathrm{m/s^2}\). With smaller \(D\), \(h\) grows like \(1/D\).

This tool uses \( h = \tfrac{4\sigma\cos\theta}{\rho g D} \) for circular tubes with \( D = 2r \). Choose a preset (or Custom…) and explore diameters from 0.20–2.00 mm.