larger-radius-lowers-the-pressure-jump - Surface Tension and Capillarity Step by Step

Keeping gamma fixed while doubling radius halves the pressure jump. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Curvature pressure starts with radius and factor

The radius marker and curvature factor are both checked inputs. Neither is a caption-only explanation.

k=2\qquad R=6\ \text{m}

The pressure jump follows the exact product over radius

The table keeps every row exact. Changing radius or factor changes only the pressure value predicted by the ledger.

\begin{array}{c|c|c|c}k&\gamma&R&\Delta P\\2&6\ \text{N/m}&3\ \text{m}&4\ \text{Pa}\\2&6\ \text{N/m}&6\ \text{m}&2\ \text{Pa}\\2&6\ \text{N/m}&12\ \text{m}&1\ \text{Pa}\\\end{array}

Curvature pressure is an exact gamma over radius ledger

The diagram's radius marker, curvature factor, and pressure jump all come from the same checked source.

\Delta P=k{\gamma\over R}=2\cdot6\ \text{N/m}/6\ \text{m}=2\ \text{Pa}