Revisiting the Gage–Bidwell Law of Dilution in relation to the effectiveness of swimming pool filtration and the risk to swimming pool users from Cryptosporidium

The transfer of water from a swimming pool to the treatment location is key in determining the effectiveness of water treatment by filtration in removing turbidity and managing the risk from particulate material, including microbial pathogens, such as Cryptosporidium spp. A key recommendation for pool operators when dealing with an accidental faecal release (the likely main source of high Cryptosporidium oocyst concentrations in pools) is that the pool water should be filtered for at least six turnover cycles prior to use. This paper briefly outlines the theoretical basis of what has become known as the Gage–Bidwell Law of Dilution, which provides a basis for this recommendation, and extends the idea to account for the impact of filter efficiency. The Gage–Bidwell Law reveals that for each pool turnover 63% of the water resident in the pool at the start of the turnover period will have been recirculated. Building on this, we demonstrate that both filter efficiency and water-turnover time are important in determining filtration effectiveness and can be combined through a single parameter we term ‘particle-turnover’. We consider the implications of the Gage–Bidwell Law (as referred to in the original 1926 paper) for the dynamics of the ‘dirt’ content of pool water, whether in terms of a specific particle size range (e.g., Cryptosporidium oocysts) or turbidity.