One Full Push Is Too Much: The Smallest Pump Dose That Still Covers Both Hands

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. The ideal film volume before losses is 1.36 mL, and 1.36 mL must actually reach the skin after the modelled losses. A dose of 2.0 mL per push was the smallest tabulated dose reaching at least 95.4% coverage, while the common 3.0 mL push reached 99.0% coverage and used 50.0% more soap than the recommended dose for a gain of only a few percentage points of coverage. Over a year at twelve washes a day the recommended dose consumes 8.76 litres against 13.14 litres, saving USD 17.52 per wash point per year at the stated price. Halving a large push by instruction alone, with realistic variation between users, delivered coverage as low as 75.1% for the least careful quartile in the model. The proposed arrangement is as follows. The proposed design is a pump head delivering the computed dose in one full push, so that correct use requires no judgement from the user. Where replacing the head is impractical, the fallback rule is a marked partial push, but the modelling shows why the full-push design is preferred: partial pushes vary between users far more than the dose itself does. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.