Illustrative wastewater case
This read-only example uses assumed wastewater inputs and Watterson starting values. It is not a customer performance record or a final equipment selection. The nested plate-pack geometry and the combined-area credit are model assumptions; the area credit still needs justification for the actual DAF.
1. Establish the feed and solids load
Total suspended solids (TSS) is the concentration of suspended solids in the wastewater, stated here in mg/L.
| Input | Value |
|---|---|
| Daily wastewater volume | 240 m³/day |
| DAF operating hours | 24 h/day |
| Laboratory wastewater TSS | 2,000 mg/L |
| Additional chemical-treatment solids | 500 mg/L, assumed for this example |
| Wastewater temperature | 26°C |
| Operating DAF tanks | One; width 2.0 m |
Feed flow: 240 ÷ 24 = 10.00 m³/h, with no additional flow allowance.
Solids entering: 2,000 + 500 = 2,500 mg/L.
Solids load: 10 × 2,500 ÷ 1,000 = 25.00 kg/h. In a project, the chemical solids are recalculated from the jar-test doses; the 500 mg/L here is an illustrative input.
2. Calculate the recycle flow
The example uses an air-to-solids ratio (A/S) of 0.035 kg air/kg solids: the required air mass per unit mass of solids. It also uses 5 bar gauge, a dissolved-air factor f = 0.65, and an air-solubility value of 18.7 mL/L at 26°C. These values define this calculation model.
Pressure ratio = (500 + 101.35) ÷ 101.35 = 5.9334
Model air capacity = 1.3 × 18.7 × (0.65 × pressure ratio − 1) = 69.447 mg/L
Recycle flow = 2,500 × 10 × 0.035 ÷ model air capacity = 12.60 m³/h
The pressure ratio uses absolute pressure relative to the model atmosphere of 101.35 kPa. The 1.3 conversion coefficient and air-solubility input are retained from Watterson’s sizing model; this guide does not independently validate their source basis.
Recycle is 126.0% of the feed. The total flow used for hydraulic and retention checks is 10 + 12.60 = 22.60 m³/h.
3. Check separation area and water volume
Hydraulic loading rate (HLR) is the water flow per unit separation area, expressed in m³/m²·h. These checks include both the wastewater feed and recycle flow.
| Check | Calculation | Result |
|---|---|---|
| HLR separation area | Total flow ÷ 4.5 | 5.022 m² |
| Rise-velocity area | 1.25 × total flow ÷ 10 | 2.825 m² |
| Required separation area | Larger of the two area checks | 5.022 m² |
| Minimum flotation water volume | Total flow × 10 minutes ÷ 60 | 3.767 m³ |
| Physical area for retention | Minimum water volume ÷ 1.5 m depth | 2.511 m² |
| Contact-zone area | Total flow ÷ 100 | 0.226 m² |
| Contact-zone water volume | Total flow × 1.5 minutes ÷ 60 | 0.565 m³ |
The rise check retains the factor of 1.25 used in Watterson’s sizing model. Retention time needs physical water volume; projected plate area does not add water volume. The contact-zone results are minimum area and volume checks, not finished chamber dimensions.
4. Explore the nested plate-pack assumption
This example uses 55° from horizontal, a 50 mm perpendicular gap, at least 0.3 m bottom clearance and no plate-thickness allowance. Watterson’s sizing model assumes that the plates nest against the sloping baffle, so the water-line pack length contains the horizontal pitches without adding the plate projection again.
- Plate length: (1.5 − 0.3) ÷ sin 55°, rounded down to 0.01 m = 1.46 m.
- Horizontal pitch: 0.05 ÷ sin 55° = 0.06104 m.
- Reference zone length: larger of retention area ÷ width and 1.0 m = 1.2555 m.
- Default plate count in this model: floor(reference length ÷ pitch) − 1 = 19 plates.
- Nested water-line pack length: (19 + 1) × pitch = 1.221 m. This convention includes one pitch at each end.
One plate has a horizontal projected area of 1.46 × cos 55° × 2.0 = 1.675 m². For 19 plates, the projected-area sum is 31.822 m².
A candidate flotation zone, with limits clearly stated
Model physical-area requirement = max(max(required separation area − projected plate area, 1.0 m²), retention area) = 2.511 m². The provisional zone length is the largest of that area divided by width, 1.0 m minimum length and the nested pack length.
Following the model area subtraction, retention floor, minimum length and nested-pack fit, then rounding the zone length up to the next 100 mm, gives an illustrative candidate of 2.0 m wide × 1.3 m long × 1.5 m water depth. This is the flotation zone only; it excludes the contact, sludge and clear-water compartments, freeboard and air space.
| Quantity | Result |
|---|---|
| Physical plan area | 2.60 m² |
| Water volume | 3.90 m³ |
| Actual retention time | 10.35 minutes |
| Physical-area HLR | 8.692 m³/m²·h |
| Tank area + projected plate area, arithmetic sum only | 34.422 m² |
| HLR if both areas are credited, unvalidated | 0.657 m³/m²·h |
Geometry and retention do not establish flotation capacity
The nested pack fits this candidate and its retention time exceeds 10 minutes. However, its physical-area HLR exceeds the selected 4.5 m³/m²·h input. The lower conditional HLR relies on crediting both tank area and projected plate area. That credit remains unvalidated for this DAF, so this example does not establish that the candidate meets the separation requirement or is ready for fabrication.
5. Size the ADT water volume and air supply
At a 1-minute recycle-water retention time, ADT water volume = recycle flow ÷ 60 = 0.210 m³. At 0.3 m internal diameter, the equivalent empty-cylinder water-filled length is 2.97 m.
The real tube is L-shaped, with additional air space above the water. This equivalent length is not a finished fabrication length or a packing-volume calculation.
Required useful air = 25 × 0.035 = 0.875 kg/h
Injected-air supply at an assumed 80% useful-air fraction = required air ÷ 0.80 = 1.0938 kg/h
Free-air flow = supply mass ÷ 1.204 = 0.908 m³/h, or 15.14 L/min
The free-air reference is dry air at 20°C and 101.325 kPa absolute. It is not the compressed-line volume. The 80% factor means the assumed fraction of injected air becoming useful microbubbles for this example; it is separate from f = 0.65 in the dissolved-air model. Neither factor is a measured result for this illustrative case.
Before selecting an actual unit
Confirm the wastewater and jar-test inputs, the dissolved-air model, the nested geometry and the separation-area credit. Then recheck final fabrication dimensions, contact-zone geometry, operating pressure and the complete treatment train. The DAF buyer checklist sets out the questions to ask.