Q.57 A sedimentation tank of height 100 cm is used in a conventional activated sludge
process to separate a suspension of spherical shaped granular sludge biomass of
0.5 mm diameter. The viscosity of the liquid is 1 cP. The difference in density
between the suspended biomass and the liquid is 0.1 g cm−3. If the
biomass reach their terminal velocity instantaneously, the biomass settling time
in min (rounded off to two decimal places) is _________.
Settling time in the sedimentation tank is calculated using Stokes’ law for terminal velocity, given the small particle size and low Reynolds number conditions. Biomass particles reach terminal velocity instantly, so settling time equals tank height divided by terminal settling velocity.
Correct Answer
3.79 min (rounded to two decimal places).
Problem Parameters
Convert all quantities to SI:
- Height H = 100 cm = 1 m
- Particle diameter d = 0.5 mm = 5 × 10-4 m
- Radius r = 2.5 × 10-4 m
- Viscosity μ = 1 cP = 10-3 Pa·s
- Density difference Δρ = 0.1 g/cm³ = 100 kg/m³
- Liquid density ρl ≈ 1000 kg/m³
- Gravity g = 9.81 m/s²
Terminal Velocity Calculation
For spherical particles in laminar flow (Stokes’ regime):
vt = 2r²Δρg / (9μ)
Substituting values:
vt ≈ 0.0044 m/s
Settling Time
Time to settle:
t = H / vt = 1 / 0.0044 ≈ 227 s ≈ 3.79 min
Why Stokes’ Law Applies
Reynolds number:
Re = ρl vt d / μ < 1
This confirms:
- Laminar settling
- Discrete particle sedimentation (Type I)
- No turbulence or hindered settling
Alternative high-Re models (Newton’s law, Allen’s regime) would overpredict velocity.
