Sedimentation Rate Calculator (Stokes' Law)
Kilograms per cubic meter (kg/m³) – Sand is approx 2650
Kilograms per cubic meter (kg/m³) – Water is 1000
Micrometers ($\mu m$)
Pascal-seconds (Pa·s) – Water at 20°C is 0.001
Meters per second squared (m/s²)
Calculation Results
Settling Velocity (m/s):
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Settling Velocity (cm/hr):
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Reynold's Number ($Re_p$):
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Flow Regime:
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*Results assume spherical particles and laminar flow (Stokes' Law validity).
How to Calculate Sedimentation Rate of Suspension
Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained and come to rest against a barrier. This process is fundamental in various industries, including wastewater treatment, pharmaceuticals, and geology.
The most common method to calculate the sedimentation rate (or terminal setting velocity) of spherical particles in a fluid is by using Stokes' Law. This law balances the gravitational force pulling the particle down against the drag force and buoyancy force pushing it up.
The Sedimentation Rate Formula
The formula for terminal settling velocity ($v$) is derived from Stokes' Law:
v = [g · (ρp – ρf) · D²] / (18 · μ)
Where:
- v = Sedimentation velocity (m/s)
- g = Gravitational acceleration (9.81 m/s²)
- ρp = Density of the particle (kg/m³)
- ρf = Density of the fluid (kg/m³)
- D = Diameter of the particle (meters)
- μ = Dynamic viscosity of the fluid (Pa·s)
Key Factors Affecting Sedimentation
- Particle Size: Because the diameter is squared ($D^2$) in the formula, doubling the particle size increases the sedimentation rate by a factor of four. This is the most influential variable.
- Density Difference: The speed depends on the difference between the particle density and fluid density ($(\rho_p – \rho_f)$). Heavier particles in lighter fluids settle faster. If the fluid is denser than the particle, the particle will float (negative velocity).
- Viscosity: Higher viscosity fluids (like oil or honey) exert more drag, significantly slowing down sedimentation compared to low viscosity fluids like water.
Example Calculation
Imagine a silt particle with a diameter of 50 micrometers ($50 \times 10^{-6}$ m) and a density of 2650 kg/m³ settling in water (density 1000 kg/m³, viscosity 0.001 Pa·s).
- Density Difference: 1650 kg/m³
- Diameter Squared: $(50 \times 10^{-6})^2 = 2.5 \times 10^{-9}$ m²
- Calculation: $(9.81 \times 1650 \times 2.5 \times 10^{-9}) / (18 \times 0.001)$
- Result: Approx 0.0022 m/s or 0.22 cm/s.
Validity of Stokes' Law
Stokes' Law is only valid for Laminar Flow, which typically occurs at a Reynolds number ($Re$) less than 0.1 (sometimes cited up to 1.0). If the calculator shows a Turbulent flow regime, the standard Stokes' formula becomes inaccurate, and drag coefficients for transitional or turbulent flow must be applied.