Particle Settling Velocity
Terminal settling velocity of a discrete spherical particle in still fluid. Auto-detects flow regime (Stokes, transition, or Newton) by iterating on Reynolds number and the drag coefficient. Used for grit-chamber design, primary clarifier sizing, sediment basin analysis, and lab particle settling.
Defaults: 0.2 mm sand grain (SG = 2.65) at 20°C — common grit-chamber design particle. Stokes is valid only for Re < 1; Newton's law for Re > 1000. Transition zone uses CD = 24/Re + 3/√Re + 0.34.
Pick a regime, then check Re
The most common error is using Stokes for a particle that's actually outside its valid range. Stokes assumes laminar flow around the particle (Re < 1), which limits diameter to about 0.06 mm for sand at 20°C. Anything coarser than fine silt sits in the transition or Newton regime, where Stokes overpredicts settling velocity by 2× to 5×.
This calculator iterates: it assumes a regime, computes vs, computes Re from vs, and re-checks which formula's range it lands in. The reported velocity always corresponds to the regime that satisfies the consistency check.
Why settling velocity matters
- Grit chamber design. Aerated grit chambers are sized so the smallest particle to be captured (typically 0.21 mm sand) settles to the bottom before the flow exits. Surface loading rate must be ≤ vs for that particle.
- Primary clarifier. Overflow rate (gpd/ft² or m³/m²/d) must be less than the settling velocity of the design particle. Typical primary clarifier OFR: 600 to 1200 gpd/ft² (24 to 49 m³/m²/d) for plain sedimentation.
- Sediment basin (construction stormwater). NRCS / EPA Phase II requires a 0.02 mm silt particle as the design particle for construction site sediment basins. Stokes' law applies (laminar regime).
- Stokes' Pond & sediment forebay. Particle removal efficiency depends on basin surface area, not depth — for ideal sedimentation. Doubling depth doesn't help; doubling surface area doubles capacity (Hazen 1904).
Real particles aren't spheres
The drag coefficient assumes a smooth sphere. Real silt and sand are angular, leading to 20% to 40% lower settling velocity than the formula predicts. For sludge flocs, the discrepancy is larger because flocs are porous, irregular, and grow / break apart with shear. Hindered settling at high concentration (greater than ~3000 mg/L) further reduces vs by interaction effects.
Temperature dependence
Kinematic viscosity of water roughly halves between 0°C and 30°C. Cold water (winter) doubles the laminar drag, halving Stokes settling velocity for fine particles. Warm water settles faster. Design typically uses winter temperature for size-conservative design.
Reference: Davis, M.L. (2010). Introduction to Environmental Engineering, 4th ed., McGraw-Hill, ch. 6. Crittenden, J.C., et al. (2012). MWH's Water Treatment, 3rd ed., Wiley, ch. 9.