Capillary Action Calculator
Capillary Action Calculator computes the height of liquid rise in a capillary tube using surface tension, contact angle, tube radius, and fluid properties.
Capillary Action Overview
Capillary action describes the rise or fall of a liquid in a narrow tube due to surface tension and adhesive forces. The height of liquid rise is given by:
Jurin’s Law: \\( h = \frac{2\sigma \cos\theta}{\rho g r} \\)
Where:
- \\(h\\): Height of liquid rise (m)
- \\(\sigma\\): Surface tension (N/m)
- \\(\theta\\): Contact angle (°)
- \\(\rho\\): Liquid density (kg/m³)
- \\(g\\): Acceleration due to gravity (m/s²)
- \\(r\\): Tube radius (m)
Example Calculations
Example 1: Water in Glass Tube
\\(\sigma = 0.0728 \, \text{N/m}\\), \\(\theta = 0^\circ\\), \\(r = 0.5 \, \text{mm}\\), \\(\rho = 1000 \, \text{kg/m}^3\\), \\(g = 9.81 \, \text{m/s}^2\\)
Height: \\( h = \frac{2 \times 0.0728 \times \cos(0)}{1000 \times 9.81 \times 0.0005} \approx 0.0297 \, \text{m} \approx 29.7 \, \text{mm} \\)
Example 2: Mercury in Glass Tube
\\(\sigma = 0.485 \, \text{N/m}\\), \\(\theta = 140^\circ\\), \\(r = 0.5 \, \text{mm}\\), \\(\rho = 13534 \, \text{kg/m}^3\\), \\(g = 9.81 \, \text{m/s}^2\\)
Height: \\( h = \frac{2 \times 0.485 \times \cos(140)}{13534 \times 9.81 \times 0.0005} \approx -0.0112 \, \text{m} \approx -11.2 \, \text{mm} \\)
Example 3: Ethanol in Glass Tube
\\(\sigma = 0.0223 \, \text{N/m}\\), \\(\theta = 0^\circ\\), \\(r = 0.3 \, \text{mm}\\), \\(\rho = 789 \, \text{kg/m}^3\\), \\(g = 9.81 \, \text{m/s}^2\\)
Height: \\( h = \frac{2 \times 0.0223 \times \cos(0)}{789 \times 9.81 \times 0.0003} \approx 0.0192 \, \text{m} \approx 19.2 \, \text{mm} \\)
Example 4: Water in Narrower Tube
\\(\sigma = 0.0728 \, \text{N/m}\\), \\(\theta = 0^\circ\\), \\(r = 0.1 \, \text{mm}\\), \\(\rho = 1000 \, \text{kg/m}^3\\), \\(g = 9.81 \, \text{m/s}^2\\)
Height: \\( h = \frac{2 \times 0.0728 \times \cos(0)}{1000 \times 9.81 \times 0.0001} \approx 0.1485 \, \text{m} \approx 148.5 \, \text{mm} \\)