← Back to Important Links

CE-211 · Capillarity

🍿 Capillary Climb

A narrow tube dips into liquid. Adhesion pulls wetting liquids up; cohesion pushes mercury down. Tune the tube bore and liquid so the meniscus lands exactly on the target line. Narrower tube = bigger effect (h ∝ 1/r).

Target mm Your h mm Score 0 Round 1/8
θ < 90° rises · θ > 90° depresses

The physics behind the game

h = 2σ·cosθ / (w·r)   (w = ρg, the specific weight)

Balancing the upward vertical pull of surface tension around the contact circle against the weight of the raised column gives the capillary rise. For water in glass θ ≈ 0 so cosθ ≈ 1 and it rises; for mercury θ ≈ 130° so cosθ < 0 and it is depressed. Because h ∝ 1/r, a 1 mm tube lifts water ~30 mm while a 0.1 mm tube would lift ~300 mm. Above 6 mm diameter the effect is negligible — which is why manometer tubes are made ≥ 6 mm. Values are illustrative.