surface-ledgers-share-one-gamma-source - Fluid Mechanics and Surface Tension Step by Step

Every capillary and wetting ledger at the same interface draws on one shared surface tension gamma, so the value must be consistent across the rise height, pressure jump, and contact-line pull. The consistency is exact only for the stated gamma and interface in the ideal model. Real interfaces add contamination, hysteresis, roughness, temperature dependence, meniscus geometry, calibration, and measurement/source uncertainty.

A shared gamma claim must be source identity, not same-valued text. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The line ledger owns the gamma source

The energy ledger may reuse gamma only by pointing to this source identity, not by copying the same number.

\gamma_{\text{line}}=3\ \text{N/m}\qquad F=12\ \text{N}

Shared values are listed with their bound source

The table is deliberately a source ledger. It keeps value and source identity visible at the same time.

\begin{array}{c|c|c}\text{ledger}&\text{value}&\text{source}\\\text{force}&12\ \text{N}&\text{bound}\\\text{energy}&24\ \text{J}&\text{bound}\\\text{gamma}&3\ \text{N/m}&\text{bound}\\\end{array}

A shared gamma claim needs source identity

The force and energy values can share gamma because the energy check points back to the exact line-force source.

12\ \text{N}\quad\text{and}\quad24\ \text{J}\quad\text{both cite}\quad3\ \text{N/m}