Reactive Wash-Off Dilution Series & Water Demand

The series assumes each bath reaches equilibrium before it drains, which is a fair description of a batch machine given a few minutes of circulation and a poor one of a continuous washing range, where counter-current flow does better than this model predicts and the right comparison is stages rather than baths. It also assumes the dye is free in the liquor: hydrolysed dye that has back-stained onto cellulose or, worse, onto an elastane or polyamide component is not governed by dilution at all and needs temperature, a soaping agent or a reduction clear, none of which appear here. Pick-up is the single most sensitive input and the one most often guessed - the difference between an efficiently squeezed 60 percent and a lazily drained 120 percent is a factor of two on every bath in the series, compounding. Take it from the machine by weighing fabric in and out rather than from a handbook. The single-bath comparison is a rhetorical device rather than a proposal; it is there to show the shape of the mathematics, and the practical readings are the bath count and the water figure beside it.