Engineering calculators · Wastewater
Population equivalent, dry weather flow and loads calculator
Work out the design flows and loads for a sewage treatment works from the population served, from a BOD load, or from measured flow and influent concentrations. The calculator gives dry weather flow, Formula A, flow to full treatment on both the 3 DWF and 3PG + I + 3E bases, the storm flow to be stored, and daily BOD, COD, solids, nitrogen and phosphorus loads with the influent concentrations they imply at DWF. Per-capita loads are editable and default to the UK Flows and Loads code of practice values.
Inputs
Results
- Per-capita consumption is within the usual UK range (120 to 180 L/hd/d; 150 is the common default).
- Infiltration is 15% of DWF, within the usual range for a reasonably tight sewer.
- BOD at DWF is 340 mg/L, typical of medium-strength crude sewage.
- Formula A (88.9 L/s) exceeds 3 DWF (30.6 L/s). The difference must be stored in storm tanks or passed forward, so treat FFT as 3PG + I + 3E (27.6 L/s) and check the storm tank capacity.
Daily loads and influent concentrations at DWF
| Determinand | Per capita, g/hd/d | Load, kg/d | At DWF, mg/L | PE from this load |
|---|---|---|---|---|
| BOD5 | 60 | 300 | 340 | 5,000 |
| COD | 120 | 600 | 680 | 5,000 |
| Suspended solids | 70 | 350 | 397 | 5,000 |
| Total nitrogen (TKN) | 11 | 55.0 | 62.3 | 5,000 |
| Ammoniacal nitrogen | 8 | 40.0 | 45.3 | 5,000 |
| Total phosphorus | 1.8 | 9.00 | 10.2 | 5,000 |
PE from each load = load (g/d) ÷ per-capita load. In the population and BOD modes it equals the population by definition; in the measured mode it shows which determinand implies the largest population, which is the usual check for an unrecorded trade discharge.
Sensitivity to per-capita consumption
| Consumption, L/hd/d | DWF, m³/d | DWF, L/s | Formula A, L/s | 3PG + I + 3E, L/s | 3 DWF, L/s | BOD at DWF, mg/L |
|---|---|---|---|---|---|---|
| 100 | 588 | 6.81 | 85.5 | 18.4 | 20.4 | 510 |
| 120 | 706 | 8.17 | 86.9 | 22.1 | 24.5 | 425 |
| 150 | 882 | 10.2 | 88.9 | 27.6 | 30.6 | 340 |
| 180 | 1,059 | 12.3 | 91.0 | 33.1 | 36.8 | 283 |
| 200 | 1,176 | 13.6 | 92.3 | 36.8 | 40.8 | 255 |
How the calculation works
- Population equivalent. PE = BOD load (g/d) ÷ 60 g/PE/d [BW] [ATV]. With a population entered, PE = P.
- Domestic flow. PG = P × G, with G the per-capita consumption in L/hd/d.
- Dry weather flow. DWF = PG + I + E [EA]. When infiltration is given as a share f of DWF, DWF = (PG + E) ÷ (1 − f) and I = f × DWF.
- Formula A. Formula A = DWF + 1360P + 2E in L/d [EA]. This is the minimum pass-forward flow before a storm overflow may spill.
- Flow to full treatment. FFT = 3PG + I + 3E, the form the Environment Agency uses where infiltration is known, or 3 DWF as a traditional rule of thumb [EA]. Storm tank flow = Formula A − FFT.
- Loads. Load (kg/d) = P × per-capita load (g/hd/d) ÷ 1000 [BW]. Concentration at DWF (mg/L) = load (kg/d) × 1000 ÷ DWF (m³/d) [M&E].
Worked example with the default inputs
5,000 people at 150 L/hd/d give PG = 750,000 L/d = 750 m³/d. With infiltration at 15% of DWF and no trade effluent, DWF = 750 ÷ 0.85 = 882 m³/d (10.2 L/s), so I = 132 m³/d. Formula A = 882,353 + 1360 × 5,000 = 7,682,353 L/d = 88.9 L/s. FFT = 3 × 750,000 + 132,353 = 2,382,353 L/d = 27.6 L/s, and 3 DWF = 30.6 L/s. Storm tank flow = 88.9 − 27.6 = 61.3 L/s. BOD load = 5,000 × 60 ÷ 1000 = 300 kg/d, which at DWF is 300 × 1000 ÷ 882 = 340 mg/L.
What this cannot tell you. Per-capita figures are long-term averages for domestic sewage. They do not capture seasonal populations, catering and institutional loads, trade effluent strength, septic tank imports, or the diurnal shape of the flow, all of which Flows and Loads 4 handles with separate allowances. Measured DWF should be the Q90 of at least a year of daily flows. Formula A and FFT are permit matters agreed with the Environment Agency, and the values here are design estimates, not permit conditions.
Sources
- British Water, Code of Practice: Flows and Loads 4. Sizing criteria, treatment capacity for sewage treatment systems (per-capita flows and loads)
- Environment Agency: Water companies, environmental permits for storm overflows and emergency overflows (Formula A, DWF, flow to full treatment definitions)
- DWA (formerly ATV-DVWK), Standard ATV-DVWK-A 131E: Dimensioning of single-stage activated sludge plants (per-capita loads, 60 g BOD5/PE/d)
- Metcalf & Eddy / AECOM (2014) Wastewater Engineering: Treatment and Resource Recovery, 5th ed., ch. 3 (wastewater flowrates and constituent loads)
Frequently asked questions
What is a population equivalent (PE)?
One population equivalent is the organic load from one person, taken as 60 g of BOD5 a day in the UK and in the EU Urban Waste Water Treatment Directive. A works receiving 600 kg BOD/d therefore serves 10,000 PE whether that load comes from people, trade effluent or both. PE is the usual basis for sizing biological treatment and for permit thresholds.
What is dry weather flow and how is it measured?
Dry weather flow (DWF) is the average daily flow to the works during a period without rain. By the Environment Agency definition it is the sum of domestic flow (PG), infiltration (I) and trade effluent (E). Measured DWF is usually taken as the Q90 of daily flows, the flow exceeded on 90% of days, over a year or more.
What is Formula A and why is it different from 3 DWF?
Formula A = DWF + 1360P + 2E litres a day is the minimum flow a sewer system must pass forward to the works before a storm overflow may operate. It includes the whole of infiltration once but adds a storm allowance of 1360 L per person per day. Three times DWF triples the infiltration too, so when infiltration is high 3 DWF exceeds Formula A, and when infiltration is low Formula A can be the larger of the two. Flow to full treatment is often set at 3PG + I + 3E, which never triples infiltration.
Why do the loads use 60 g BOD, 120 g COD and 70 g solids per person per day?
These are the per-capita loads in British Water Code of Practice Flows and Loads 4 and are close to the ATV-DVWK-A 131E values used across Europe. They are averages for domestic sewage. Catering, schools, hospitals, hotels and holiday parks have their own per-head or per-unit allowances in the code, and trade effluents must be added from measured or consented loads.