surface-audit-cites-every-source - Fluid Mechanics and Surface Tension Step by Step

A surface-tension audit traces every gamma, line length, and contact angle back to a named source, so no value enters the wetting ledger without a citation. The bookkeeping is exact only for the stated inputs and their cited origins in the ideal interface model. Real interfaces add contamination, hysteresis, roughness, temperature dependence, meniscus geometry, calibration, and measurement/source uncertainty that blur the audit.

The final surface ledger accepts only a coherent source-bound chain. 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 audit starts as a source map

Each source role is present before the accepted bit is trusted. A missing or cloned source would fail the check.

\text{sources}=5\qquad \text{accepted}=1

Every source contributes one checked value

The audit is not a new formula. It is a compact inventory of values that already came from earlier checked ledgers.

\begin{array}{c|c|c}\text{ledger}&\text{value}&\text{source}\\\text{line}&24\ \text{N}&\text{bound}\\\text{energy}&24\ \text{J}&\text{bound}\\\text{pressure}&4\ \text{Pa}&\text{bound}\\\text{capillary}&20\ \text{Pa}&\text{bound}\\\text{projected}&12\ \text{N}&\text{bound}\\\end{array}

The accepted surface claim cites every source

The capstone accepts only one coherent chain of line force, energy, curvature, capillary balance, and projected force.

\text{line}=24\ \text{N};\quad\text{energy}=24\ \text{J};\quad\Delta P=4\ \text{Pa};\quad\text{projected}=12\ \text{N}