Slower Is Not Always Drier: The Shower Flow Rate That Minimises Total Water for a Complete Rinse

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. Under the stated kinetics the volume-minimising flow was 4 litres per minute, using 1.8 litres to complete the rinse in 27 seconds. At 4 litres per minute the rinse took 27 seconds and used 1.8 litres, which is 0.0% more water than the optimum despite the lower flow. At 14 litres per minute the rinse used 2.6 litres. Under the proportional control assumption, rinse volume was 1.2 litres at every flow, confirming that the entire benefit or penalty of restriction turns on whether removal keeps pace with flow. The proposed arrangement is as follows. Rather than prescribing a single restrictor, the study derives a target flow band and a test any household can perform with a bucket and a clock: time the rinse at the present flow, change the flow, and compare volumes rather than rates. The band, not a point, is the deliverable, because heads, pressure and hair length vary. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.