Young-Laplace Equation Calculator

The Young-Laplace Equation Calculator computes capillary pressure and liquid rise in a thin tube from surface tension, contact angle, tube radius, and fluid density. It applies the Young-Laplace relation used in fluid mechanics, chemistry, and porous media analysis.

Capillary pressure in a tube

For a curved meniscus in a capillary tube:

$$\Delta p = \frac{2 \gamma \cos \theta}{a}$$

where $\gamma$ is surface tension, $\theta$ is the contact angle, and $a$ is the inner tube radius. The meniscus radius is $R = a / \cos \theta$.

Capillary rise height

At equilibrium between capillary pressure and hydrostatic pressure:

$$h = \frac{2 \gamma \cos \theta}{\rho g a}$$

where $\rho$ is liquid density and $g$ is gravitational acceleration.

Frequently Asked Questions

What does the Young-Laplace equation calculate?

It relates pressure difference across a curved fluid interface to surface tension and curvature. In a capillary tube, it gives capillary pressure and liquid column height.

How is meniscus radius related to tube radius?

Meniscus radius $R$ equals tube radius $a$ divided by the cosine of the contact angle: $R = a / \cos \theta$.

What contact angle means wetting?

A contact angle below 90° indicates the liquid wets the solid surface. Smaller angles increase capillary rise and capillary pressure.

Why does a smaller tube produce higher capillary pressure?

Capillary pressure is inversely proportional to tube radius. Narrower tubes create sharper curvature, producing larger pressure differences across the interface.

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Young Laplace Equation Calculator