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
2. Materials and Methods
- Disinfection using chlorine gas (0.45 mg L−1 free chlorine in the pool water).
- pH adjustment (pH 7.0 in the pool water).
- Flocculant dosing approx. 0.05 mg L−1 Al as poly-aluminium chloride (PAC).
- Dual media filter (0.5 m sand depth, 0.7–1.2 mm grain size), (0.5 m anthracite depth, 1.4–2.5 mm grain size).
- Filtration velocity 35 m h−1.
3.1. The Gage–Bidwell Law of Dilution: Empirical Approach
3.2. The Gage–Bidwell Law of Dilution: Computational Approach
3.3. The Role of Filter Efficiency in Contaminant Removal
3.4. Application of the Gage–Bidwell Approach to Modelling the Peak Turbidity of Pool Water
- To establish the equilibrium turbidity likely to be achieved if a constant bathing load (in terms of numbers of bathers per hour) is maintained indefinitely.
- To establish the maximum turbidity likely to be achieved if a constant bathing load is sustained for a finite time that is too short for the equilibrium to be achieved.
3.4.1. Modelling the Maximum Turbidity Achievable If the Design Maximum Bathing Load for a Pool Is Sustained Indefinitely
3.4.2. Modelling the Maximum Turbidity Achievable If the Design Maximum Bathing Load for a Pool Is Sustained for a Finite Period
3.5. Modelling Observed Time Courses of NTU
3.6. Public Health Implications
- Prediction of the time it takes to achieve satisfactory removal of a contaminant (e.g., Cryptosporidium oocysts) following a single contamination event.
- Prediction of the maximum equilibrium concentration of a contaminant under conditions of a steady input of the contaminant (we considered the maximum turbidity achieved under conditions of a prolonged constant bathing load).
- Prediction of the amount of water that should be circulated per bather to ensure that water clarity remains excellent, even when there is a very prolonged period when bathers are entering the pool.
- Prediction of the peak turbidity likely to be achieved in practice from knowledge of the distribution of bathing load during the day.
- Depth ranging from 1–2 m (average depth 1.5 m).
- 4 m2 pool area allowed per bather at maximum bathing load following the UK guidelines , i.e., each bather occupies 6 m3 of water on average.
- 3 h water-turnover time.
- Average bathing time of 0.75 h.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|State||Cumulative Fraction of Pool Volume Removed||Average Concentration (C) in Pool Water after Mixing|
|Starting state||0||C = Co|
|After first container||1/3||C = (1 − 1/3) Co|
|After second container||2/3||C = (1 − 1/3) (1 − 1/3) Co|
|After third container||1||C = (1 − 1/3) (1 − 1/3) (1 − 1/3) Co|
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Simmonds, L.P.; Simmonds, G.E.; Wood, M.; Marjoribanks, T.I.; Amburgey, J.E. 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. Water 2021, 13, 2350. https://doi.org/10.3390/w13172350
Simmonds LP, Simmonds GE, Wood M, Marjoribanks TI, Amburgey JE. 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. Water. 2021; 13(17):2350. https://doi.org/10.3390/w13172350Chicago/Turabian Style
Simmonds, Lester P., Guy E. Simmonds, Martin Wood, Tim I. Marjoribanks, and James E. Amburgey. 2021. "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" Water 13, no. 17: 2350. https://doi.org/10.3390/w13172350