🧪 Fluid Mechanics & Interfacial Surface Tension
Capillary Action & Jurin's Law Calculator
Compute liquid column capillary rise height ($h = \frac{2\gamma \cos\theta}{\rho g r}$), meniscus contact angle ($\theta$), surface tension ($\gamma$), and mercury capillary depression.
💧 Water in Glass (Rise, θ = 0°)
🌡️ Mercury in Glass (Depression, θ = 140°)
🧪 Ethanol Alcohol (Rise)
🔬 Benzene in Glass
Fluid & Tube Parameters
N/m (Water = 0.0728)
kg/m³
degrees (°)
mm (millimeter)
Capillary Column Height (h)
+29.69 mm (Rise)
Meniscus Type
Concave (Wetting)
Laplace Pressure
291.2 Pa
Tube Diameter
1.00 mm
💡 Jurin's Law Formulation:
$$h = \frac{2\gamma \cos\theta}{\rho g r} = \frac{2(0.0728)\cos(0^\circ)}{(1000)(9.81)(0.0005)} = +0.02969\text{ m} = +29.69\text{ mm}$$
Jurin's Law & Capillary Action
James Jurin formulated the mathematical description of capillary height in 1718:
- Jurin's Law: $$h = \frac{2\gamma \cos\theta}{\rho g r}$$
- Wetting vs Non-Wetting: If $\theta < 90^\circ$ ($\cos\theta > 0$), adhesive forces dominate and liquid rises (concave meniscus). If $\theta > 90^\circ$ (e.g. mercury $\theta \approx 140^\circ$), cohesive forces dominate and liquid is depressed ($h < 0$, convex meniscus).
- Young-Laplace Pressure Jump: $$\Delta P = \frac{2\gamma \cos\theta}{r} = \rho g h$$