h = 4σcosθ / (ρgd) — height of capillary rise (or depression if θ > 90°) in a circular tube driven by surface tension.
Fluid Mechanics IIθ > 90° → capillary depression (e.g. mercury in glass).
Jurin's law (capillary rise):
h > 0 (rise) when θ < 90°. h < 0 (depression) when θ > 90° (e.g. mercury in glass).
Capillary length λ:
λ is the length scale at which surface tension and gravity are comparable. Tubes with d << λ show strong capillarity. For water: λ ≈ 2.7 mm (so a 1 mm tube gives ~29 mm rise).
Typical capillary rise for water at 20°C (θ = 0°):
| Tube d | Rise h |
|---|---|
| 0.1 mm | ~295 mm |
| 0.5 mm | ~59 mm |
| 1 mm | ~29 mm |
| 2 mm | ~15 mm |
| 5 mm | ~6 mm |
| 10 mm | ~3 mm |
Where: