Stokes' Law Settling Calculator
A 50 µm sand grain settles in 20 °C water at 2.24532 mm/s, well within the laminar range where Stokes' law holds.
Sand 2650, floc about 1050–1200, fly ash 2000–2500.
Water at 20 °C 998.2; air 1.2.
2.2453183175316 mm/s
Full answer, then cut to fewer decimals (not rounded):
- 2.2453183175316 mm/s
- 2.245318317531 mm/s
- 2.24531831753 mm/s
- 2.2453183175 mm/s
- 2.245318317 mm/s
- 2.24531831 mm/s
- 2.2453183 mm/s
- 2.245318 mm/s
- 2.24531 mm/s
- 2.2453 mm/s
- 2.245 mm/s
- 2.24 mm/s
- 2.2 mm/s
- In m/h
- 8.083145943 m/h
- Particle Reynolds number
- 0.1118401569
- Stokes law valid?
- yes (Re < 1, laminar)
- Overflow rate that removes it fully
- 193.9955026 m³/(m²·day)
Step-by-step solution
- vₛ = g(ρₚ − ρ_f)d² ÷ (18μ) = 9.80665 × 1651.8 × 0.00005² ÷ (18 × 0.001002)
- vₛ = 0.002245318318 m/s
- Re = ρ_f vₛ d ÷ μ = 0.1118401569
Stokes' Law Settling Formula
vₛ = g(ρₚ − ρ_f)d² / (18μ)
valid for particle Reynolds number below about 1 (laminar settling)
Worked Example
A 50 µm sand grain (2650 kg/m³) in water at 20 °C:
- vₛ = g(ρₚ − ρ_f)d² ÷ (18μ) = 9.80665 × 1651.8 × 0.00005² ÷ (18 × 0.001002)
- vₛ = 0.002245318318 m/s
- Re = ρ_f vₛ d ÷ μ = 0.1118401569
Particle Reynolds number: 0.1118401569 · Stokes law valid?: yes (Re < 1, laminar) · Overflow rate that removes it fully: 193.9955026 m³/(m²·day)
GATE tip
In an ideal (Camp) settling tank, any particle with vₛ ≥ v₀ = Q/A is removed completely and smaller ones in the proportion vₛ/v₀; depth does not matter.
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Frequently asked questions
Why does size matter so much?
Velocity grows with d²: a 100 µm grain settles four times faster than a 50 µm grain, which is why grit chambers remove sand but not fine silt.
How does temperature affect settling?
Viscosity falls as water warms (1.79 mPa·s at 0 °C, 1.00 at 20 °C), so particles settle almost twice as fast in summer.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Stokes' Law Settling Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/stokes-law-calculator/
IEEE
Scientific Converters, "Stokes' Law Settling Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/stokes-law-calculator/