How to use it
- Choose what to find: the height, the surface tension or the tube diameter.
- Enter the known values. Surface tension is in mN/m (the same number as dyn/cm); 72.8 mN/m is water at about 20 °C.
- Enter the contact angle (0° for a liquid that wets the tube fully), the density and, if needed, a different gravity.
- Read the height in mm and cm and whether the liquid rises or drops.
Formula
- Jurin’s law: h = 4 γ cos θ ÷ (ρ g d)
- Surface tension from a height: γ = h ρ g d ÷ (4 cos θ)
- Diameter for a height: d = 4 γ cos θ ÷ (ρ g h)
- SI units: γ in N/m, ρ in kg/m³, g in m/s², d and h in metres
Worked example
Water (γ = 72.8 mN/m, θ = 0°, ρ = 998 kg/m³) in a glass tube of 1 mm inner diameter:
h = 4 × 0.0728 × 1 ÷ (998 × 9.80665 × 0.001) = 0.2912 ÷ 9.787 = 0.02975 m = 29.75 mm.
Mercury (485 mN/m, 140°, 13,534 kg/m³) in the same tube: h = −11.2 mm, the level drops.
A measured rise of 30 mm in a 1 mm tube with the density of water gives γ = 0.03 × 998 × 9.80665 × 0.001 ÷ 4 = 73.4 mN/m.
Tips
- Clean glass matters. Grease raises the contact angle and lowers the rise.
- Use the inner diameter, not the outer one of the tube.
- Surface tension falls as the temperature rises, so warm water climbs a little less.