Appearance
Rectangular Primary Clarifier
Longitudinal flow primary sedimentation tank with chain-and-flight sludge collection mechanism for high-capacity installations.
Overview
The rectangular primary clarifier is preferred for large-capacity installations where multiple parallel tanks are required. The longitudinal flow pattern provides better hydraulic characteristics and the chain-and-flight mechanism offers reliable sludge removal.
When to Use
- Large municipal plants (>50,000 PE)
- Space-constrained sites (better land utilization)
- Multiple parallel tank requirements
- High-capacity industrial pretreatment
Advantages Over Circular
- Better space efficiency for multiple tanks
- Simpler common-wall construction
- More predictable hydraulics (plug flow tendency)
- Higher tanks-in-series equivalency (N=5-8 vs 3-5)
Settling Theory
Type I & II Settling
Rectangular clarifiers follow the same settling theory as circular:
Stokes' Law (Type I): $$V_s = \frac{g \times d^2 \times (\rho_s - \rho_w)}{18 \times \mu}$$
Camp Formula (Type II): $$\eta = 1 - \left(1 + \frac{n \times V_s \times t}{H}\right)^{-1/n}$$
Enhanced Plug Flow Behavior
Rectangular tanks approach plug flow behavior more closely:
$$E(\theta) = N^N \times \theta^{N-1} \times \frac{e^{-N\theta}}{(N-1)!}$$
Where:
- $E(\theta)$ = exit age distribution
- $\theta$ = dimensionless time (t/HRT)
- $N$ = tanks-in-series (5-8 for rectangular)
Design Equations
Surface Area
$$A = L \times W$$
Where:
- $L$ = tank length (m)
- $W$ = tank width (m)
Length-to-Width Ratio
Optimal L:W ratio ranges from 3:1 to 5:1:
$$\frac{L}{W} = 3 \text{ to } 5$$
Surface Overflow Rate
$$SOR = \frac{Q}{A} = \frac{Q}{L \times W \times N_{tanks}}$$
Horizontal Velocity
Critical for rectangular tanks to prevent scour:
$$v_h = \frac{Q}{W \times SWD}$$
Design limit: $v_h < 0.015$ m/s (to prevent settled solids resuspension)
Scour Velocity (Camp)
$$v_{scour} = \left(\frac{8 \times k \times (\rho_s - \rho_w) \times g \times d}{f \times \rho_w}\right)^{0.5}$$
Where:
- $k$ = 0.04 for unigranular particles
- $f$ = Darcy-Weisbach friction factor (0.02-0.03)
Short-Circuiting Model
Rectangular tanks have better hydraulic efficiency:
Tanks-in-Series Equivalency
| Configuration | N Value | Efficiency Factor |
|---|---|---|
| Circular (radial) | 3-5 | 0.75-0.83 |
| Rectangular (no baffles) | 5-8 | 0.83-0.89 |
| Rectangular (with baffles) | 8-12 | 0.89-0.92 |
Effective Removal
$$\eta_{eff} = \eta_{ideal} \times \frac{N}{N+1}$$
For N=6: efficiency factor = 0.857
Parameters
Geometric Parameters
| Parameter | Symbol | Unit | Range | Default | Description |
|---|---|---|---|---|---|
| Length | L | m | 20-80 | 40 | Tank length |
| Width | W | m | 5-20 | 10 | Tank width |
| Sidewater Depth | SWD | m | 2.5-5.0 | 3.0 | Min PS208: 2.5m |
| L:W Ratio | - | - | 3:1-5:1 | 4:1 | Optimal flow |
| Floor Slope | - | % | 1-2 | 1.5 | Longitudinal slope |
| Number of Tanks | N | - | 2-8 | 4 | For redundancy |
Mechanical Parameters
| Parameter | Unit | Range | Default | Description |
|---|---|---|---|---|
| Flight Speed | m/min | 0.5-1.5 | 1.0 | Chain-flight speed |
| Flight Spacing | m | 1.5-3.0 | 2.0 | Between flights |
| Scraper Type | - | chain/reciprocating | chain | Mechanism type |
Hydraulic Criteria (UK PS208)
| Parameter | Unit | DWF Limit | FFT Limit |
|---|---|---|---|
| Surface Overflow Rate | m³/m²/d | 28.8 | 48.0 |
| Upflow Velocity | m/h | 1.2 | 2.0 |
| HRT | hours | >2.0 | >2.0 |
| Horizontal Velocity | m/s | <0.015 | <0.025 |
| Weir Loading | m³/m/d | <300 | <500 |
Advanced Parameters
| Parameter | Unit | Default | Range | Description |
|---|---|---|---|---|
| shortCircuitFactor | - | 6 | 5-10 | Higher than circular |
| flocculationParameter | - | 0.35 | 0.2-0.5 | Camp n value |
| baffleConfiguration | - | none | none/transverse | Flow control |
| inletType | - | weir | weir/submerged | Entry distribution |
| outletType | - | weir | weir/launder | Exit collection |
Inlet and Outlet Design
Inlet Zone
Weir Inlet: $$q_{weir} = \frac{Q}{L_{weir}}$$
Distribute flow evenly across tank width.
Energy Dissipation:
- Baffle wall at 1-2m from inlet
- Perforated baffle (5-10% open area)
- Depth > 0.5 × SWD
Outlet Zone
V-Notch Weirs: $$Q = 1.38 \times H^{2.5}$$
Launders:
- Multiple parallel launders
- Spacing 2-4m
- Submerged orifices optional
Sludge Collection
Chain-and-Flight System
Components:
- Return flight (bottom) - collects sludge to hopper
- Forward flight (surface) - pushes scum to scum box
Sizing: $$P = k \times L \times W \times SWD$$
Where P = motor power (kW), k = 0.001-0.003
Hopper Design
Located at inlet end (counter-current to flow):
$$V_{hopper} = t_{storage} \times Q_{sludge}$$
Typical storage: 2-8 hours
Removal Efficiencies
Same as circular clarifiers (settling physics identical):
Without Chemical Dosing
| Parameter | Removal (%) |
|---|---|
| BOD | 25-35 |
| TSS | 50-65 |
| COD | 25-40 |
| NH₃-N | 0 |
| Total P | 10-20 |
With Chemical Dosing
| Parameter | Removal (%) |
|---|---|
| BOD | 35-45 |
| TSS | 60-75 |
| COD | 35-50 |
| NH₃-N | 0 |
| Total P | 60-85 |
Configuration
Step-by-Step Setup
Define Geometry
- Select tank type: Rectangular
- Enter length and width
- Verify L:W ratio (3:1 to 5:1)
- Set sidewater depth (min 2.5m)
- Define floor slope (1-2%)
Set Tank Count
- Calculate required total area
- Divide by practical single tank area
- Ensure N-1 compliance
Verify Hydraulics
- Check SOR < limits
- Verify horizontal velocity < 0.015 m/s
- Confirm HRT > 2 hours
Configure Mechanical
- Select collector mechanism
- Set flight speed
- Configure hopper capacity
Example Configuration
json
{
"type": "primaryClarifierRectangular",
"parameters": {
"length": 40,
"width": 10,
"sidewaterDepth": 3.0,
"floorSlope": 1.5,
"numberOfTanks": 4,
"chemicalDosing": false,
"calculationMode": "advanced",
"advancedParams": {
"shortCircuitFactor": 6,
"flocculationParameter": 0.35,
"baffleConfiguration": "transverse",
"flightSpeed": 1.0
}
}
}Worked Example
Given
- Population: 100,000 PE
- DWF: 25,000 m³/d
- FFT: 75,000 m³/d
- Influent TSS: 350 mg/L
Design
Step 1: Calculate Required Area
Target SOR at FFT = 40 m³/m²/d
$$A_{required} = \frac{75,000}{40} = 1,875 \text{ m}^2$$
Step 2: Select Configuration
Four tanks: 40m × 12m each
$$A_{actual} = 4 \times 40 \times 12 = 1,920 \text{ m}^2$$
L:W ratio = 40/12 = 3.33:1 ✓
Step 3: Check Upflow Velocities
At DWF: $$v_{up} = \frac{25,000}{1,920 \times 24} = 0.54 \text{ m/h}$$ ✓
At FFT: $$v_{up} = \frac{75,000}{1,920 \times 24} = 1.63 \text{ m/h}$$ ✓
Step 4: Check Horizontal Velocity
At FFT (per tank): $$v_h = \frac{75,000 / 4}{12 \times 3.0 \times 86,400} = 0.006 \text{ m/s}$$ ✓ (<0.015)
Step 5: Check HRT
Volume: $V = 1,920 \times 3.0 = 5,760$ m³
At DWF: $HRT = \frac{5,760}{25,000} \times 24 = 5.53$ hours ✓
At FFT: $HRT = \frac{5,760}{75,000} \times 24 = 1.84$ hours ⚠ (near limit)
Step 6: N-1 Check
With 3 tanks: $A_{N-1} = 1,440$ m²
At FFT: $v_{up} = \frac{75,000}{1,440 \times 24} = 2.17$ m/h ⚠ (slightly over)
Recommendation: Marginally acceptable for short-term N-1 operation.
Construction Considerations
Common-Wall Design
Multiple rectangular tanks share walls, reducing:
- Construction cost (20-30% savings)
- Land footprint
- Piping complexity
Floor Construction
- Longitudinal slope: 1-2%
- Cross slope to center channel: 5-10%
- Sludge hopper depth: 1.5-2.5m
Materials
| Component | Material | Notes |
|---|---|---|
| Walls | Reinforced concrete | Typical 300mm thick |
| Floor | Reinforced concrete | With slope |
| Flights | HDPE/Fiberglass | Corrosion resistant |
| Chains | Stainless steel | 316L grade |
| Weirs | Aluminum/FRP | Adjustable |
Troubleshooting
| Issue | Cause | Solution |
|---|---|---|
| Uneven flow distribution | Inlet design | Add distribution weir |
| Solids resuspension | High horizontal velocity | Reduce flow per tank |
| Poor sludge collection | Flight damage | Replace worn flights |
| Short-circuiting | Dead zones | Install baffles |
| Scum breakthrough | Weir issues | Install scum baffles |
Best Practices
- L:W Ratio: Maintain 3:1 to 5:1 for optimal hydraulics
- Inlet Design: Ensure even flow distribution
- Baffles: Consider transverse baffles for large tanks
- Flight Maintenance: Regular inspection of chain tension
- Hopper Capacity: Size for 4-8 hours storage minimum
- Parallel Operation: Maintain even flow split
Related Topics
- Circular-Primary-Clarifier
- Lamella-Primary-Clarifier
- Secondary-Clarifier
- Sludge-Handling
References
- Metcalf & Eddy (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th Ed.
- UK Water Industry (2020). Sewers for Adoption, 8th Ed. (PS208)
- WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8
- Camp, T.R. (1946). "Sedimentation and the Design of Settling Tanks"
- Hazen, A. (1904). "On Sedimentation". ASCE Transactions