Flow and Load Calculations - Design Basis

Flow and load calculations establish the hydraulic and pollutant loading basis for wastewater treatment plant design. This guide covers population equivalent (PE), dry weather flow (DWF), Formula A, and diurnal variations following UK PS201 standards and UK operator guidelines.

Population Equivalent (PE)

Population Equivalent converts all wastewater sources to an equivalent population for design purposes.

UK Standards

UK definition:

1 PE = 60 g BOD/person/day

EU directive (alternative):

1 PE = 54 g BOD/person/day (less conservative)

UK operator and most UK water companies use 60 g BOD/person/day

PE Components

Total PE calculation:

Total_PE = Domestic_PE + Non-Residential_PE + Commercial_PE + Trade_Equivalent

Domestic PE

From actual population:

Domestic_PE = Population (persons)

Assumes standard 60 g BOD/person/day

From housing:

Domestic_PE = Number_of_dwellings × Occupancy_rate

Where typical occupancy = 2.3-2.5 persons/dwelling (UK average 2.4)

Non-Residential PE

Schools, offices, light commercial:

Non_Residential_PE = BOD_load (kg/d) / 0.060 (kg/PE/d)

Typical values:

• Schools: 0.02-0.03 PE/pupil/day
• Offices: 0.01-0.02 PE/employee/day
• Small shops: 0.05-0.10 PE/employee/day

Commercial PE

Restaurants, pubs, hotels:

Commercial_PE = BOD_load (kg/d) / 0.060

Typical values:

• Restaurants: 0.3-0.5 PE/meal served
• Pubs: 0.2-0.4 PE/customer/day
• Hotels: 0.8-1.2 PE/bed

Trade Equivalent

Industrial discharges:

Trade_Equivalent = Trade_BOD_load (kg/d) / 0.060

Must be calculated from actual trade effluent data (consent conditions).

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Dry Weather Flow (DWF)

DWF is the baseline flow for plant sizing.

DWF Formula

Standard formula:

DWF = P × PCC + I + E

Where:

• DWF = Dry Weather Flow (m³/d or L/d)
• P = Population or PE (persons)
• PCC = Per Capita Consumption (m³/hd/d or L/hd/d)
• I = Infiltration (m³/d or L/d)
• E = Trade Effluent (m³/d or L/d)

Unit consistency: Use either all m³/d or all L/d. Common practice: calculate in L/d, convert to m³/d.

Per Capita Consumption (PCC)

Typical UK domestic values:

• Urban areas: 130-150 L/hd/d
• Rural areas: 100-120 L/hd/d
• UK operator typical: 120-140 L/hd/d
• Future planning: 150 L/hd/d (allows for growth)

Non-domestic allowances:

PCC_total = PCC_domestic + PCC_non-domestic

Infiltration (I)

Groundwater ingress into sewers.

Typical values:

• Modern sewers: 1,000-3,000 L/d/km
• Older sewers: 3,000-10,000 L/d/km
• Combined sewers: 5,000-15,000 L/d/km

Calculation:

I = Sewer_length (km) × Infiltration_rate (L/d/km)

Example:

Sewer length = 10 km
Rate = 5,000 L/d/km

I = 10 × 5,000 = 50,000 L/d = 50 m³/d

Trade Effluent (E)

Industrial discharges.

Consented trade effluent:

E = Σ(Individual_consents)

Usually provided by water company or from trade effluent consent applications.

Example DWF Calculation

Design basis:

• Population: 5,000 persons
• PCC: 140 L/hd/d
• Infiltration: 50 m³/d
• Trade effluent: 100 m³/d

Calculation:

Domestic_flow = 5,000 × 140 / 1000 = 700 m³/d
Infiltration = 50 m³/d
Trade = 100 m³/d

DWF = 700 + 50 + 100 = 850 m³/d

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Average Daily Flow and Diurnal Variations

Average Daily Flow (Q_MEAN)

UK operator standard:

Q_MEAN = DWF × F_MEAN

Where F_MEAN = 1.6 (UK operator typical diurnal factor)

Physical meaning: Accounts for peak hour flows during the day vs overnight minimums.

Example:

DWF = 850 m³/d
F_MEAN = 1.6

Q_MEAN = 850 × 1.6 = 1,360 m³/d

Diurnal Flow Pattern

Typical domestic pattern:

• Minimum flow (02:00-04:00): 0.33 × average = 33% of daily average
• Morning peak (08:00-10:00): 1.8-2.0 × average
• Evening peak (18:00-20:00): 1.5-1.8 × average

Peak hour flow:

Q_peak = Q_MEAN × 1.5 to 2.5

Hourly variation important for:

• Pumping station sizing
• Storm tank design
• Dosing system control

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Storm Flows and Formula A

3 × DWF Threshold

Traditional UK storm flow threshold:

3DWF = DWF × 3

Flows above 3DWF are considered storm conditions.

Example:

DWF = 850 m³/d

3DWF = 850 × 3 = 2,550 m³/d

6 × DWF Maximum

Traditional maximum flow to full treatment:

6DWF = DWF × 6

Flows above 6DWF are diverted to storm tanks or overflow (after screening/settlement).

Example:

6DWF = 850 × 6 = 5,100 m³/d

Formula A (PS201)

Modern UK standard for calculating Full Flow to Treatment (FFT).

Formula:

FFT = DWF + 1.36 × P + 3.18 × √P

Where:

• FFT = Full Flow to Treatment (m³/d)
• DWF = Dry Weather Flow (m³/d)
• P = Population in thousands (not PE!)

Derivation: PS201 Formula A accounts for storm flow contribution based on catchment size. Larger populations have proportionally lower per-capita storm contribution (economies of scale).

Example:

DWF = 850 m³/d
Population = 5,000 (= 5.0 thousand)

FFT = 850 + 1.36 × 5.0 + 3.18 × √5.0
FFT = 850 + 6.8 + 7.11
FFT = 863.9 m³/d

Note: For small populations, Formula A often gives FFT ≈ DWF. For larger populations (> 20,000), storm component becomes more significant.

Determining FFT for Design

Formula:

FFT = minimum of (3DWF, 6DWF, Formula_A, Consented_FFT)

Hierarchy:

1. Consented limit (if specified in discharge permit)
2. Formula A (PS201 calculation)
3. 6 × DWF (traditional maximum)
4. 3 × DWF (conservative threshold)

Example:

DWF = 850 m³/d
3DWF = 2,550 m³/d
6DWF = 5,100 m³/d
Formula A = 863.9 m³/d
Consented FFT = Not specified

FFT = minimum(2550, 5100, 863.9) = 863.9 m³/d (Formula A controls)

For this small population, Formula A is very conservative. Common practice: Use 3DWF as minimum.

FFT = max(3DWF, Formula_A) = max(2550, 863.9) = 2,550 m³/d

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Pollutant Loads

BOD Load

Formula:

BOD_load = (PE × BOD_per_capita) + Trade_BOD

Where BOD_per_capita = 0.060 kg/PE/d (UK standard)

Concentration:

BOD_concentration = (BOD_load × 1000) / DWF

Example:

PE = 5,000
BOD_per_capita = 0.060 kg/PE/d
Trade_BOD = 10 kg/d (from consent)

BOD_load = 5,000 × 0.060 + 10 = 300 + 10 = 310 kgBOD/d

BOD_concentration = (310 × 1000) / 850 = 365 mg/L

TSS Load

Typical domestic ratio:

TSS_load = BOD_load × (TSS:BOD ratio)

Where UK typical TSS:BOD = 1.2 to 1.4

Example:

BOD_load = 310 kgBOD/d
Ratio = 1.3

TSS_load = 310 × 1.3 = 403 kgTSS/d

TSS_concentration = (403 × 1000) / 850 = 474 mg/L

Ammonia-N Load

Typical domestic:

NH₄-N_load = PE × 0.0125 kg NH₄-N/PE/d

UK typical: 12.5 g NH₄-N/person/day

Example:

PE = 5,000

NH₄_load = 5,000 × 0.0125 = 62.5 kgN/d

NH₄_concentration = (62.5 × 1000) / 850 = 73.5 mg/L

Total Phosphorus Load

Typical domestic:

TP_load = PE × 0.0025 kg TP/PE/d

UK typical: 2.5 g TP/person/day

Example:

PE = 5,000

TP_load = 5,000 × 0.0025 = 12.5 kg P/d

TP_concentration = (12.5 × 1000) / 850 = 14.7 mg/L

Chemical Oxygen Demand (COD)

Typical ratio:

COD_load = BOD_load × (COD:BOD ratio)

Where UK domestic typical COD:BOD = 2.0 to 2.5

Example:

BOD_load = 310 kgBOD/d
Ratio = 2.2

COD_load = 310 × 2.2 = 682 kgCOD/d

COD_concentration = (682 × 1000) / 850 = 802 mg/L

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Design Summary Table

Worked Example Summary

Parameter	Value	Units	Notes
Population	5,000	PE	Design population
PCC	140	L/hd/d	Per capita consumption
Infiltration	50	m³/d	Groundwater ingress
Trade effluent	100	m³/d	Industrial discharge
DWF	850	m³/d	Dry weather flow
Q_MEAN	1,360	m³/d	Average daily (F_MEAN = 1.6)
3 × DWF	2,550	m³/d	Storm threshold
6 × DWF	5,100	m³/d	Traditional maximum
Formula A	864	m³/d	PS201 calculation
FFT (design)	2,550	m³/d	Use 3DWF (conservative)
BOD load	310	kg/d	Including trade
BOD concentration	365	mg/L	At DWF
TSS load	403	kg/d	TSS:BOD = 1.3
TSS concentration	474	mg/L	At DWF
NH₄-N load	62.5	kg/d	12.5 g/PE/d
NH₄-N concentration	73.5	mg/L	At DWF
TP load	12.5	kg/d	2.5 g/PE/d
TP concentration	14.7	mg/L	At DWF
COD load	682	kg/d	COD:BOD = 2.2
COD concentration	802	mg/L	At DWF

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Growth and Design Horizon

Population Growth

Formula:

P_future = P_current × (1 + r)^n

Where:

• r = annual growth rate (decimal)
• n = number of years (design horizon)

Typical design horizons:

• Pumping stations: 10-15 years
• Treatment plants: 15-25 years (phased expansion common)
• Trunk sewers: 30-50 years

Example:

P_current = 5,000
Growth rate = 2% per year (r = 0.02)
Design horizon = 20 years

P_future = 5,000 × (1.02)^20 = 5,000 × 1.486 = 7,429 ≈ 7,500 PE

Future Flow

Account for:

1. Population growth
2. PCC increase (water use trends)
3. Infiltration increase (sewer deterioration)
4. New trade effluent

Example:

Future_PE = 7,500
PCC = 150 L/hd/d (increased from 140)
Infiltration = 75 m³/d (increased from 50)
Trade = 150 m³/d (new industry)

Future_DWF = 7,500 × 0.150 + 75 + 150 = 1,125 + 75 + 150 = 1,350 m³/d

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UK Water Company Variations

UK Industry Practice

• PE: 60 g BOD/person/day
• PCC: 120-140 L/hd/d typical (150 for future)
• F_MEAN: 1.6
• Use Formula A for FFT, minimum 3DWF
• NH₄-N: 12.5 g/PE/d
• TP: 2.5 g/PE/d

UK Industry Practice

• PE: 60 g BOD/person/day
• PCC: 140-160 L/hd/d (London higher)
• F_MEAN: 1.5-1.8 depending on catchment
• FFT: Often use 6DWF for older works

UK Industry Practice

• PE: 60 g BOD/person/day
• PCC: 130-150 L/hd/d
• F_MEAN: 1.6
• Use Formula A, verified against 3DWF

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Storm Tank Sizing

Traditional Method (68 L/hd)

Volume:

V_storm = P × 68 L/hd

Example:

P = 5,000

V_storm = 5,000 × 68 = 340,000 L = 340 m³

Modern Method (2-hour storm retention)

Volume:

V_storm = (Storm_flow - FFT) × Storm_duration

Where storm duration typically = 2 hours

Example:

Storm_flow = 6DWF = 5,100 m³/d = 212.5 m³/h
FFT = 2,550 m³/d = 106.25 m³/h
Storm_duration = 2 hours

V_storm = (212.5 - 106.25) × 2 = 212.5 m³

Modern method typically gives smaller tanks (cost-effective).

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Flow Measurement and Verification

Flow Monitoring

Required for:

• Consent compliance
• Infiltration assessment
• Treatment optimization
• Billing (trade effluent)

Measurement locations:

• Inlet works (total influent)
• Return streams (sludge liquor)
• Final effluent
• Individual trade effluent connections

Typical accuracy:

• Electromagnetic flowmeters: ±0.5%
• Ultrasonic flowmeters: ±1-2%
• Flumes/weirs: ±5-10%

Load Calculation from Flow and Concentration

Formula:

Load (kg/d) = (Flow (m³/d) × Concentration (mg/L)) / 1000

Example:

Flow = 850 m³/d
BOD = 365 mg/L

BOD_load = (850 × 365) / 1000 = 310.25 kg/d

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Sensitivity Analysis

Always test sensitivity to key assumptions.

Example Sensitivity

Base case:

• PE = 5,000
• PCC = 140 L/hd/d
• DWF = 850 m³/d

Scenario 1: High PCC (+20%)

PCC = 168 L/hd/d
DWF = 5,000 × 0.168 + 50 + 100 = 990 m³/d (+16%)

Scenario 2: Population growth (+50%)

PE = 7,500
DWF = 7,500 × 0.140 + 50 + 100 = 1,200 m³/d (+41%)

Scenario 3: High infiltration (double)

Infiltration = 100 m³/d
DWF = 700 + 100 + 100 = 900 m³/d (+6%)

Design recommendation: Size for worst-case combination or use phased expansion.

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Common Design Errors

Under-Estimating Infiltration

Problem: Actual flows exceed design, especially in wet weather.

Solution:

• CCTV survey of sewers
• Flow monitoring campaign (12 months)
• Allow 20-30% margin on infiltration estimate

Ignoring Future Growth

Problem: Plant undersized within 5 years.

Solution:

• Use realistic growth rates (1-3% typical UK)
• Design horizon 20-25 years
• Phased expansion strategy

Over-Reliance on Formula A for Small Populations

Problem: Formula A gives unrealistically low FFT for small works.

Solution:

• Use minimum of 3DWF for small works (< 10,000 PE)
• Formula A more appropriate for larger works

Neglecting Trade Effluent Variations

Problem: Trade loads vary significantly, overwhelming treatment.

Solution:

• Obtain actual trade effluent data (not just consent limits)
• Include trade effluent safety factor (1.2-1.5×)
• Monitor trade effluent contributions

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Related Calculations

• Primary Tanks: DWF and FFT used for tank sizing
• Biofilters: BOD and NH₄-N loads for media sizing
• Humus Tanks: Hydraulic loading based on FFT
• Chemical Dosing: TP load for chemical dose
• Alkalinity Balance: NH₄-N load for alkalinity consumption
• Sludge Production: TSS load for sludge calculations

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References

• UK Sewers for Adoption (7th Edition): Appendix PS201 - Flow and Load Calculations
• UK operator Design Standards: Population equivalent and flow determination
• CIRIA/WRc: Design flows for sewage treatment works
• BS EN 752: Drain and sewer systems outside buildings

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