Estimating the terminal settling velocity of spherical silicon particles in water involves using the Stokes' Law formula, which relates the settling velocity to particle properties and fluid characteristics. Here's how you can calculate it:
1. Calculate the density of water at 15°C:
Density of water (ρ) = 999 kg/m³
2. Determine the dynamic viscosity of water at 15°C:
Dynamic viscosity of water (µ) = 0.00113 Ns/m²
3. Calculate the density of the silicon particles:
Specific gravity = 2.5
Density of silicon particles = Specific gravity * Density of water
Density of silicon particles = 2.5 * 999 kg/m³
4. Convert the average diameter of the particles to meters:
(a) Diameter of particles = 0.07 mm = 0.07 * 10^-3 m
(b) Diameter of particles = 1.2 mm = 1.2 * 10^-3 m
5. Substitute the values into Stokes' Law equation:
Terminal settling velocity (v) = (2/9) * (ρp - ρ) * g * (d^2) / µ
where:
- v is the terminal settling velocity
- ρp is the density of the silicon particles
- ρ is the density of water
- g is the acceleration due to gravity
- d is the diameter of the particles
- µ is the dynamic viscosity of water
6. Calculate the terminal settling velocities for both particle sizes using the provided data and formulas.
Remember, this is an estimation, and actual settling velocities may vary due to factors like particle shape and flow conditions.
