capillarity

Question

Rise of water (γ=0.072 N/m, θ≈0°, ρ=1000 kg/m³, g=10) in tube radius 0.5 mm?

RankGuru · Accepted Answer

1. **Capillary Rise Formula**: $h = \frac{2 \gamma \cos 	heta}{ho g r}$.
2. **Identify Given Data**:
   - Surface Tension $\gamma = 0.072$ N/m
   - $	heta = 0^\circ$ (pure water) $\implies \cos 0^\circ = 1$
   - Density $ho = 1000 	ext{ kg/m}^3$
   - Radius $r = 0.5 	ext{ mm} = 5 	imes 10^{-4}$ m
   - Gravity $g = 10 	ext{ m/s}^2$
3. **Calculate**:
   - $h = \frac{2 	imes 0.072 	imes 1}{1000 	imes 10 	imes 5 	imes 10^{-4}}$
   - $h = \frac{0.144}{10000 	imes 5 	imes 10^{-4}} = \frac{0.144}{5}$
   - $h = 0.0288$ m.
4. **Converter**: $0.0288$ m $= **2.88$ cm**.

Rank Guru

capillarity

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