Equations · equation

Capillary Rise

Fluid Dynamics · 1718

Equation
h = 2 γ cos θ / (ρ g r)
Field
Fluid Dynamics
Named After
James Jurin
Year
1718

Symbols

h height the liquid climbs in a narrow tube · γ surface tension · θ contact angle between liquid and wall · ρ liquid density · g gravitational acceleration · r tube radius

Significance

Liquid climbs a narrow gap when it wets the walls, and higher the narrower the gap — Jurin's law of 1718. It draws molten solder and brazing alloy into a joint that fits closely and refuses one that does not, lifts water through soil and up a plant, and wicks ink into paper. When the liquid does not wet, θ passes 90° and it is pushed out instead: mercury in glass.

Skills

Requires

Referenced by

equation
skill

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.