Keeping Shared Water Honest: The Exchange Rate a Communal Bath Needs to Hold a Stated Load Limit

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. At six bathers per hour the exchange flow needed to hold the stated limit was 24 litres per hour, or 0.6% of the bath volume per hour. Stepped simulation reached a peak of 30000 units per litre, at the limit as designed. Session operation with a full change every 3 hours spent 74 minutes above the limit per session and used 8000 litres per operating day against 288 litres for continuous exchange. Heating the continuous exchange cost USD 1.0 per operating day. Continuous exchange became cheaper than session changes above 4 bathers per hour. The proposed arrangement is as follows. The proposed operating rule is a metered continuous exchange, set from the peak arrival rate by the derived formula and checked against a simple turbidity observation, rather than a calendar of full changes. A worked setting for the stated bath is given so an operator can adopt it directly and rescale it. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.