curvature-pressure-ceiling-three-row-scan - Fluid Mechanics and Surface Tension Step by Step

A curvature-pressure-ceiling scan decreases radius or raises surface tension across three rows, checking when the Laplace pressure crosses the stated ceiling. The arithmetic is exact only for the stated surface tension, curvature radius, pressure ceiling, and rows in the ideal spherical-interface model. Real measurements add wetting/contact-angle variation, contamination, curvature departures, temperature, instrument calibration, finite precision, and measurement uncertainty.

Radius is scanned through a pressure ceiling. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 2 m so the checked pressure jump is 6 Pa. This row is above boundary relative to the 4 Pa ceiling.

\Delta P=k\gamma/R=2\times6\ \text{N/m}/2\ \text{m}=6\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 3 m so the checked pressure jump is 4 Pa. This row is on boundary relative to the 4 Pa ceiling.

\Delta P=k\gamma/R=2\times6\ \text{N/m}/3\ \text{m}=4\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 6 m so the checked pressure jump is 2 Pa. This row is below boundary relative to the 4 Pa ceiling.

\Delta P=k\gamma/R=2\times6\ \text{N/m}/6\ \text{m}=2\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}