Sedimentation Tank Design for Municipal Wastewater Treatment in Portland, OR

Scenario

A municipal wastewater treatment plant upgrade in Portland, Oregon required redesigning primary clarifiers to handle increased influent flow and improve removal of fine suspended solids (e.g., silt and organic flocs). Constraints included limited footprint expansion, strict discharge limits for total suspended solids (TSS < 30 mg/L), and seasonal temperature variation (4–18°C), affecting fluid viscosity. Regulatory approval mandated verification of settling velocity assumptions using empirically validated methods.

Given Data

• Acceleration due to gravity: 9.81 m/s²
• Particle density: 2650 kg/m³ (typical for mineral-laden biosolids flocs)
• Fluid density: 998 kg/m³ (at 15°C)
• Particle diameter: 85 µm = 0.000085 m
• Dynamic viscosity: 0.00114 Pa·s (measured at 15°C)
• Drag coefficient (turbulent): 0.44 (assumed for irregular flocs in transitional regime)

Calculation

The tool computes two settling velocities:

Laminar (Stokes’ law) velocity: [ v_s^{\text{laminar}} = \frac{(\rho_p - \rho_f) g d^2}{18 \mu} = \frac{(2650 - 998)(9.81)(0.000085)^2}{18 \times 0.00114} ] = (\frac{1652 \times 9.81 \times 7.225 \times 10^{-9}}{0.02052}) ≈ 0.005782 m/s

Turbulent (Newton’s law) velocity: [ v_s^{\text{turbulent}} = \sqrt{\frac{4 (\rho_p - \rho_f) g d}{3 C_d \rho_f}} = \sqrt{\frac{4 (2650 - 998)(9.81)(0.000085)}{3 \times 0.44 \times 998}} ] = (\sqrt{\frac{4 \times 1652 \times 9.81 \times 8.5 \times 10^{-5}}{1317.36}}) ≈ 0.062143 m/s

Reynolds number check (using laminar result): (Re = \frac{\rho_f v_s^{\text{laminar}} d}{\mu} = \frac{998 \times 0.005782 \times 8.5 \times 10^{-5}}{0.00114} \approx 0.44) → confirms laminar regime is appropriate.

Result and Decision

The verified laminar settling velocity of 0.00578 m/s was adopted for hydraulic design. This yielded a required surface overflow rate (SOR) of ≤ 25 m³/m²·d (≈ 0.00029 m/s) — well below the calculated settling rate, ensuring >90% removal of particles ≥85 µm. The team retained existing tank dimensions but added low-turbulence inlet baffles to minimize short-circuiting.

Lesson

Always validate the flow regime a posteriori using the computed velocity — here, assuming turbulent flow would have overestimated settling by >10× and led to undersized tanks and noncompliant effluent.