Young-Laplace Equation Calculator
Calculate capillary pressure, meniscus curvature, and liquid column height using the Young-Laplace equation
Calculate Young-Laplace Equation
Surface tension in J/m² (N/m)
Inner radius of the capillary tube
Contact angle in degrees (0° = perfect wetting)
R = a / cos(θ)
Pressure in the external phase (typically atmospheric)
Density of the liquid in kg/m³
Gravitational acceleration in m/s² (Earth: 9.807)
Young-Laplace Equation Results
Young-Laplace Equation: Δp = 2γ/R
Formula: Δp = (2 × 0.07294) / 1.0642 mm = 137.08 Pa
Analysis: Balanced adhesion-cohesion forces - Moderate capillary rise
Common Fluid Examples
Water (20°C)
γ: 0.07294 J/m², ρ: 1000 kg/m³, θ: 20°
Water (0°C)
γ: 0.07565 J/m², ρ: 999.8 kg/m³, θ: 20°
Mercury (20°C)
γ: 0.4865 J/m², ρ: 13534 kg/m³, θ: 140°
Ethanol (20°C)
γ: 0.02243 J/m², ρ: 789 kg/m³, θ: 13°
Glycerol (20°C)
γ: 0.0634 J/m², ρ: 1260 kg/m³, θ: 19°
Benzene (20°C)
γ: 0.02895 J/m², ρ: 876 kg/m³, θ: 9°
Olive Oil (20°C)
γ: 0.032 J/m², ρ: 915 kg/m³, θ: 23°
Surface Tension Values
Water (20°C)
0.0729 J/m²
Most common reference liquid
Mercury (20°C)
0.487 J/m²
Highest surface tension liquid
Ethanol (20°C)
0.0224 J/m²
Low surface tension solvent
Glycerol (20°C)
0.0634 J/m²
Viscous liquid with moderate γ
Key Formulas
Where: γ = surface tension, R = radius of curvature, θ = contact angle, a = tube radius
Contact Angle Guide
Understanding the Young-Laplace Equation
What is the Young-Laplace Equation?
The Young-Laplace equation describes the pressure difference across a curved interface between two immiscible fluids. It relates the capillary pressure to the surface tension and curvature of the interface, fundamental to understanding capillary phenomena.
Key Concepts
- •Capillary pressure drives fluid movement in narrow spaces
- •Surface tension creates curved interfaces (menisci)
- •Contact angle determines wetting behavior
- •Pressure difference is inversely related to curvature radius
Physical Significance
The equation explains why small droplets have higher internal pressure, why liquids rise in thin tubes (capillary action), and how surface tension affects fluid behavior in porous materials and microfluidic devices.
Mathematical Framework
Δp = 2γ/R (cylindrical interface)
R = a/cos(θ) (meniscus geometry)
h = 2γcos(θ)/(ρga) (capillary height)
Parameters
- Δp: Pressure difference across interface (Pa)
- γ: Surface tension (J/m² or N/m)
- R: Radius of curvature (m)
- θ: Contact angle (degrees)
- a: Tube radius (m)
- h: Capillary height (m)
Note: The general form Δp = γ(1/R₁ + 1/R₂) applies to surfaces with two principal radii of curvature.
Applications and Importance
Microfluidics
Design of lab-on-chip devices, droplet formation, and precise fluid control in microscale channels.
Petroleum Engineering
Understanding fluid behavior in porous rock, oil recovery processes, and reservoir characterization.
Materials Science
Wetting and coating processes, surface treatments, and design of hydrophobic/hydrophilic materials.