What is Stokes law for settling velocity?

For a discrete particle in laminar flow (Reynolds number < 1), the terminal settling velocity is vs = g(ρs − ρ)d² / (18μ), where d is particle diameter, ρs and ρ are particle and fluid densities, and μ is dynamic viscosity. Velocity rises with the square of diameter, so fine particles settle very slowly.

When does Stokes law stop applying?

Stokes law holds for particle Reynolds number Re 1000 Newton's law applies: vs ≈ 1.74·√(g(Ss − 1)d). Coarse sand and gravel fall in the transition/Newton range.

What is the surface overflow rate?

The surface overflow rate (surface loading rate) is the design discharge divided by the basin surface area, vo = Q/As, with units of velocity (e.g., gpd/ft² or m/h). In ideal Type I settling, any particle with settling velocity vs ≥ vo is fully removed, independent of basin depth — so surface area, not volume, governs removal.

What is Type I settling?

Type I (discrete) settling describes dilute suspensions of non-flocculating particles that settle independently at constant velocity — grit chambers, sand, and the coarse fraction of stormwater sediment. Type II is flocculent settling; Types III and IV are hindered and compression settling at high concentrations.

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Stokes Settling Velocity — Reference

Q: When does Stokes law stop applying?

Stokes law holds for particle Reynolds number Re 1000 Newton's law applies: vs ≈ 1.74·√(g(Ss − 1)d). Coarse sand and gravel fall in the transition/Newton range.

Q: What is the surface overflow rate?

The surface overflow rate (surface loading rate) is the design discharge divided by the basin surface area, vo = Q/As, with units of velocity (e.g., gpd/ft² or m/h). In ideal Type I settling, any particle with settling velocity vs ≥ vo is fully removed, independent of basin depth — so surface area, not volume, governs removal.

Q: What is Type I settling?

Type I (discrete) settling describes dilute suspensions of non-flocculating particles that settle independently at constant velocity — grit chambers, sand, and the coarse fraction of stormwater sediment. Type II is flocculent settling; Types III and IV are hindered and compression settling at high concentrations.

By Michael Flynn, PE · water resources & dam safety engineer · Last updated Oct 18, 2026

Terminal settling velocity of discrete particles, and the surface-overflow-rate basis for sedimentation basins, forebays, and grit chambers.

Settling Velocity by Regime

Stokes (Re < 1): v_s = g(ρ_s − ρ)d² / (18μ)

Newton (Re > 1000): v_s ≈ 1.74·√( g(S_s − 1)d )

Regime	Particle Re	Applies to
Stokes (laminar)	< 1	Silt, clay, fine sand
Transition	1–1000	Medium–coarse sand
Newton (turbulent)	> 1000	Gravel, large grit

Sizing a sediment basin, not one particle? HydroComplete runs a seven-bin PSD through the basin and reports trap efficiency.

Particle Re = ρ·v_s·d/μ. S_s = ρ_s/ρ (quartz sand ≈ 2.65). Water at 20°C: μ = 1.00×10⁻³ Pa·s, ρ = 998 kg/m³.

Typical Settling Velocities (quartz, 20°C water)

Particle	Diameter	v_s (approx.)
Coarse sand	1.0 mm	~100 mm/s
Medium sand	0.5 mm	~50 mm/s
Fine sand	0.1 mm	~6–8 mm/s
Very fine sand	0.05 mm	~2 mm/s
Silt	0.01 mm	~0.08 mm/s
Clay	0.001 mm	~0.0008 mm/s

Fine silt/clay settle far too slowly for practical basins — they require flocculation or filtration. The d² dependence is why removing the fine fraction is so hard.

Surface overflow rate governs removal.

v_o = Q / A_s

In ideal Type I settling, every particle with v_s ≥ v_o is fully captured — removal depends on surface area, not depth. Size sedimentation basins and forebays by overflow rate, then check detention time and short-circuiting.

Sources: Camp, T.R. (1946), "Sedimentation and the Design of Settling Tanks," Trans. ASCE. Metcalf & Eddy, Wastewater Engineering. Reynolds & Richards, Unit Operations and Processes in Environmental Engineering.

Sizing a basin or forebay? Open the settling velocity calculator → · Detention time? Detention time. · Want the whole set? Print all 38 cards →

Worked example: sizing a basin for a target particle

Sediment basin, Q = 2.0 cfs (0.0566 m³/s), quartz particles, water at 20°C

Given ρ_s = 2,650 kg/m³, ρ = 998 kg/m³, μ = 1.00×10⁻³ Pa·s

Find surface area needed to capture 0.05 mm and 0.01 mm particles

0.05 mm: v_s = 9.81 × (2,650 − 998) × (5×10⁻⁵)² / (18 × 10⁻³) = 2.25 mm/s

Check Stokes: Re = 998 × 0.00225 × 5×10⁻⁵ / 10⁻³ = 0.11 < 1, so the Stokes form is valid

A_s = Q/v_s = 0.0566 / 0.00225 = 25.2 m² ≈ 271 ft²

0.01 mm: v_s = 0.090 mm/s, A_s = 629 m² ≈ 6,770 ft², 25 times the area for a particle one-fifth the size

Same 0.05 mm particle in 5°C water (μ = 1.52×10⁻³): v_s = 1.48 mm/s, 34% slower

The d² term drives most basin decisions. A basin sized for fine sand is reasonable. One sized for fine silt is usually not, and clay will not settle in any practical footprint. Below roughly 0.01–0.02 mm the realistic options are flocculants, filtration, or accepting the turbidity. Design for the cold-weather viscosity if the basin has to perform in winter.

Common mistakes

Sizing by depth or detention time alone. In ideal discrete settling, removal depends on surface overflow rate, not depth. Depth adds sludge storage and protects against scour, but it does not capture finer particles.
Using Stokes’ law for sand coarser than about 0.1 mm. Above that, particle Re exceeds 1 and Stokes overpredicts velocity. Use the transitional drag relation instead.
Assuming the ideal basin. Short-circuiting, wind and inlet jets mean a real basin performs like one with a fraction of its area. Baffles and length-to-width ratio exist to recover that fraction.
Treating flocculent or hindered settling as discrete. Activated sludge, chemical floc and high-concentration slurries settle by different mechanisms and need column tests.

When this card doesn’t apply

Stokes’ law assumes isolated, spherical, rigid particles in still water. Platy clay minerals, organic flocs and aggregates depart from it, often by an order of magnitude. Regulatory sediment-basin sizing, such as state erosion-control manuals with fixed surface areas per acre or per cfs, may override the overflow-rate calculation. Use the governing manual where one applies.

Related cheat sheets and tools

Use v_s with the settling velocity tool and check detention time for the basin. Protect the basin inlet/outlet with riprap. For full RUSLE sediment load and BMP/forebay sizing across a watershed, see HydroComplete. Fluid properties for these calculations are in the water viscosity & density table.