Basis, datum and the art of not confusing yourself

Two conventions decide whether a balance stays self-consistent, and both are choices the engineer makes rather than facts the problem supplies: the basis and the datum. Neither is difficult, and both are skipped often enough that a large share of confused calculations trace back to one of them being unstated or quietly changed mid-working. Naming them and holding them fixed is the art of not confusing yourself.

Basis: the amount you build on

A basis is the fixed amount the calculation is built on — "per 100 kg of feed", "per hour", "per batch", "per tonne of product". A balance computes ratios and splits; the basis turns those ratios into definite quantities by anchoring them to one chosen amount. Choosing a convenient basis — often 100 units of a stream, so percentages become masses directly — can turn an awkward problem into arithmetic. The rule is that one basis governs the whole calculation: pick it at the start, state it plainly, and convert to the real production rate only at the end. Switching basis in the middle — computing one part per hour and another per batch — is a frequent and silent source of error.

Datum: the reference you measure from

A datum is the reference state from which a state property is measured. Energy and enthalpy have no absolute zero that matters to a process — only differences do — so an energy balance fixes a reference (a temperature, a phase, sometimes a pressure) at which enthalpy is taken as zero, and measures every stream’s enthalpy as a difference from there. Property tables do exactly this: steam tables, for instance, reference their enthalpies to a defined state, and the numbers are meaningful only relative to it. The rule mirrors the basis: one datum for the whole balance. Mixing enthalpies referenced to different datums adds numbers that do not belong on the same scale, and the result is wrong in a way the arithmetic cannot reveal.

The shared discipline

Basis and datum are the same habit applied to two different things — the amount and the reference — and the discipline is identical: choose it, state it, hold it. A number quoted without its basis ("the consumption is 12") or a property without its datum ("the enthalpy is 400") is ambiguous and cannot be safely combined with anything. Written down at the top of the working and carried unchanged to the end, the two conventions keep a balance honest. This page lands on no calculator because its content is a convention, not a computation — but it is the convention that makes every worked example in this path reproducible, and the reason each one states the amount and the reference its numbers are built on.