line-force-gamma-length-cross-scan - Surface Tension and Capillarity Step by Step

Line force is scanned across gamma and contact length with exact rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Line force starts from one checked contact edge

The contact edge supplies the measured line length. Gamma and length are both shown before the force number is accepted.

F=n\gamma L=1\cdot3\ \text{N/m}\cdot4\ \text{m}=12\ \text{N}

Changing gamma changes force one for one

Hold the surface count and contact length fixed. Three gamma rows show the force scaling without needing a paragraph.

\begin{array}{c|c|c|c}n&\gamma&L&F\\1&2\ \text{N/m}&4\ \text{m}&8\ \text{N}\\1&3\ \text{N/m}&4\ \text{m}&12\ \text{N}\\1&4\ \text{N/m}&4\ \text{m}&16\ \text{N}\\\end{array}

Changing line length also changes force one for one

The second scan changes a different input. The same gamma source now pulls harder only because the checked edge is longer.

\begin{array}{c|c|c|c}n&\gamma&L&F\\1&3\ \text{N/m}&2\ \text{m}&6\ \text{N}\\1&3\ \text{N/m}&4\ \text{m}&12\ \text{N}\\1&3\ \text{N/m}&6\ \text{m}&18\ \text{N}\\\end{array}