Sedimentation Rate Calculator (Stoke's Law)
Calculation Results:
Terminal Velocity (v): m/s
Terminal Velocity (v): mm/s
*Calculated using Stoke's Law for laminar flow conditions.
Understanding Sedimentation Rate
Sedimentation rate, often referred to as terminal settling velocity, is the speed at which a particle falls through a viscous fluid due to gravity. This calculation is critical in fields such as wastewater treatment, geology, and chemical engineering to determine how quickly solids will settle out of a liquid suspension.
The Science Behind the Calculation: Stoke's Law
This calculator utilizes Stoke's Law, which is applicable for small particles moving through a fluid at low Reynolds numbers (laminar flow). The formula used is:
v = [g * d² * (ρp – ρf)] / (18 * μ)
- g: Acceleration due to gravity (9.81 m/s²)
- d: Particle diameter (converted to meters)
- ρp: Density of the particle (kg/m³)
- ρf: Density of the fluid (kg/m³)
- μ: Dynamic viscosity of the fluid (converted to Pa·s)
Practical Examples
| Material | Diameter | Approx. Rate |
|---|---|---|
| Fine Sand | 100 μm | ~8.98 mm/s |
| Silt | 20 μm | ~0.36 mm/s |
| Clay Particle | 2 μm | ~0.0036 mm/s |
Key Factors Affecting Sedimentation
Several variables can significantly alter the settling speed of particles in a real-world environment:
- Particle Size: As the diameter increases, the sedimentation rate increases exponentially (squared relationship).
- Fluid Viscosity: Higher viscosity (like oil vs. water) significantly slows down the settling process.
- Density Differential: The greater the difference between the particle density and the fluid density, the faster the particle will sink.
- Temperature: Temperature affects fluid viscosity. For instance, water becomes less viscous as it heats up, leading to faster sedimentation.