Young-Laplace Equation Calculator
Use this Young-Laplace equation calculator to estimate capillary pressure difference and capillary rise in a tube from surface tension, fluid density, contact angle, and tube radius.
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Quick Answer: The Young-Laplace relation for capillary systems can be written as Δp = 2γ/R. With tube radius and contact angle, the meniscus radius becomes R = a / cos(θ), so Δp = 2γcos(θ)/a. The same pressure difference can also be written as Δp = ρgh.
How to Calculate
- Choose the fluid or enter custom values: Start with fluid density and surface tension either from a preset or from your own measurements.
- Enter tube radius and contact angle: These two inputs determine the meniscus radius when capillary geometry is known.
- Calculate pressure difference: The calculator applies Δp = 2γcos(θ)/a or the equivalent meniscus-radius form.
- Translate pressure to capillary rise: If density is known, the same pressure difference can be converted into a capillary rise height with Δp = ρgh.
Formula
Δp = 2γ / R = 2γcos(θ) / a = ρgh
| Variable | Meaning | Unit |
|---|---|---|
| Δp | Pressure difference across the curved interface | Pa |
| γ | Surface tension | N/m |
| R | Meniscus radius of curvature | m |
| a | Tube radius | m |
| θ | Contact angle | degrees |
| ρ | Fluid density | kg/m3 |
| h | Capillary rise or depression height | m |
Worked Examples
Water in a tube - 2 mm diameter tube
- Fluid: Water
- Tube radius: 1.0 mm
- Contact angle: 20°
- Surface tension: 0.07294 N/m
Result: Capillary pressure is about 137.1 Pa.
This matches the Omni example structure for water in a narrow tube.
Capillary rise - Pressure to height
- Pressure difference: 137.1 Pa
- Density: 1000 kg/m3
Result: Capillary rise is about 0.0140 m.
The pressure difference corresponds to about 1.4 cm of capillary rise in water under standard gravity.
Different fluid - Mercury comparison
- Fluid: Mercury
- Tube radius: 1.0 mm
- Contact angle: 140°
- Surface tension: 0.487 N/m
Result: The sign and size of the capillary effect differ strongly from water.
Wetting behavior matters because the cosine term changes the pressure difference and direction of the meniscus response.
Interpretation Table
| Range | Meaning | Action |
|---|---|---|
| Small tube radius | Stronger capillary pressure | Expect larger pressure differences and more noticeable capillary rise or depression. |
| Contact angle below 90° | Wetting fluid | Capillary rise is favored because cos(θ) is positive. |
| Contact angle above 90° | Non-wetting fluid | Capillary depression can occur because cos(θ) becomes negative. |
Frequently Asked Questions
Use the equivalent form Δp = 2γcos(θ)/a, where a is the tube radius and θ is the contact angle.
Capillary pressure comes from the interaction between surface tension, interface curvature, and wetting behavior at the solid boundary.
It matters in porous media, microfluidics, coatings, and reservoir engineering because it controls how fluids move through small passages.
For a static column, the same pressure difference can be written as Δp = ρgh, which lets you convert pressure into rise or depression height.
Note: This calculator uses an idealized capillary model. Real systems may deviate because of tube imperfections, contamination, temperature changes, and non-uniform wetting.
References
Last reviewed: March 14, 2026