small-droplet-has-a-pressure-jump - Fluid Mechanics and Surface Tension Step by Step

A curved interface carries a pressure jump given by the Young-Laplace law, Delta P = 2 * gamma / R for a spherical droplet. The inside sits at higher pressure than the outside, and the tighter the curve the bigger the jump. The exact value holds only for the stated gamma and radius of a perfect sphere; real droplets deform, collect contamination, and have temperature- and measurement-dependent gamma and R.

A droplet-style training surface uses factor 2 in the pressure ledger. 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=3\ \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}&2\ \text{m}&6\ \text{Pa}\\2&6\ \text{N/m}&3\ \text{m}&4\ \text{Pa}\\2&6\ \text{N/m}&6\ \text{m}&2\ \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}/3\ \text{m}=4\ \text{Pa}