Calculating Gauge Pressure Inside Bubbles

What is the gauge pressure inside bubbles of radius 10 m?

Considering the surface tension of water and the radius of the bubble, how can we determine the gauge pressure inside the bubbles?

Answer:

The gauge pressure inside the bubble is 14,000 N/m² or 14,000 Pa.

When a machine is used to form bubbles from pure water by mechanically foaming it, the surface tension of water plays a significant role in determining the gauge pressure inside the bubbles.

To calculate the gauge pressure, Laplace's law for pressure inside a curved liquid interface can be applied:

ΔP = 2σ/R

Where ΔP is the pressure difference across the curved interface, σ is the surface tension of water, and R is the radius of the bubble.

Given:

• Surface tension of water (σ) = 0.070 N/m
• Radius of the bubble (R) = 10 μm = 10 × 10^(-6) m

Substituting the values into the equation, we get:

ΔP = 2σ/R = 2 * 0.070 / (10 × 10^(-6)) = 14,000 N/m²

The gauge pressure inside the bubble is 14,000 N/m² or 14,000 Pa. This pressure difference accounts for the curvature of the bubble's surface.