Washing a Wound from a Bottle on a Nail: Head Height, Hole Size, and the Volume a Stated Cleanliness Costs

A pierced plastic bottle hung above a wound is a common improvised way to wash a wound when no tap, syringe, or nurse is available. This study is a simulation from stated assumptions, not a measurement. Pressure at the wound is the hydrostatic pressure of the hanging height, flow follows the Torricelli relation with a stated discharge coefficient, and a stated contamination model assigns each litre a fixed fraction of loose surface contamination removed. At a hanging height of 1.0 m the pressure is 9.81 kPa (1.423 psi), just below the stated adequate-pressure threshold of 10.0 kPa (1.45 psi); at 1.2 m it is 11.772 kPa (1.707 psi). The theoretical minimum height for the threshold is 1.019 m. At adequate pressure the model needs 2.0 litres for a 99 percent reduction in loose contamination and 3.0 litres for a 99.9 percent reduction. Below the threshold the same reductions need 9.015 litres and 13.523 litres. A single hole of 1.0 mm at 1.2 m delivers 0.1418 litres per minute and needs 21.162 minutes for 3.0 litres, whereas four holes of 1.0 mm, or a single hole of 2.0 mm, deliver 0.5671 litres per minute and need 5.29 minutes for 3.0 litres. The sizing rule that follows is to hang the bottle at or above 1.019 m in theory and at 1.2 m among the stated heights, with a total hole area of 3.1416 square millimetres, so the stated volume arrives within the stated delivery time of 10.0 minutes at adequate pressure.