Problem Statement
The surface tension of mercury and water at 60°C are 0.47 N/m and 0.0662 N/m respectively. What capillary height change will occur in these two fluids when they are in contact with air in a glass tube of radius 0.30mm? Use θ = 130° for mercury and 0° for water.
Given Data
- Radius of tube (r) = 0.30 mm = 0.0003 m
- Surface tension for mercury (σₘ) = 0.47 N/m
- Surface tension for water (σw) = 0.0662 N/m
- Contact angle for mercury (θₘ) = 130°
- Contact angle for water (θw) = 0°
- Density of mercury (ρₘ) = 13600 kg/m³
- Density of water (ρw) = 1000 kg/m³
- g = 9.81 m/s²
Solution
Mercury Capillary Height
Using the formula: h = (2σ cos θ)/(ρgr)
hₘ = (2 × 0.47 × cos(130°))/(13600 × 9.81 × 0.0003)
hₘ = -0.0149 m = -14.9 mm
Negative value indicates mercury depression in the tube
Mercury Capillary Depression = 14.9 mm
Water Capillary Height
Using the formula: h = (2σ cos θ)/(ρgr)
hw = (2 × 0.0662 × cos(0°))/(1000 × 9.81 × 0.0003)
hw = 0.0445 m = 44.5 mm
Positive value indicates water rise in the tube
Water Capillary Rise = 44.5 mm
Key Points
- Mercury shows capillary depression (negative height) due to its large contact angle (> 90°)
- Water shows capillary rise (positive height) due to its zero contact angle
- The magnitude of height change depends on surface tension, contact angle, fluid density, and tube radius
