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Surface Tension and Pressure for a Raindrop

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Prequisite Knowledge
Surface Tension

Problem
Estimate the excess pressure inside a raindrop having a temperature of 25°C and a diameter of 4 mm.

Solution

First, assume the droplet is spherical. Cut the spherical droplet in half. From the surface tension lesson, the force developed around the edge of the cut surface due to surface tension is:

2πrσ

This force is balanced by the force due to the pressure difference Δp. Then, for equilibrium:

2πrσ = Δpπr²

Rearranging the equation for Δp:

Δp = 2σ/r

The surface tension is σ and r is the radius of the droplet.

The surface tension can be found using the Surface Tension of Water in Contact with Air table (ext link), interpolating for the temperature of 25°C given in the problem statement.

Then σ = 0.072 N/m. Substituting the known values for the excess pressure:

Δp = [2*(0.072 N/m)] / 0.002 m

Δp = 72 Pa