Introduction
To calculate the settling velocity of grit particles in water, we can use Stokes’ Law, which applies to small spherical particles settling in a viscous fluid.
Given Data
- Specific gravity of grit (SG) = 2.7
- Size of grit particles (diameter) = 0.21 cm
- Viscosity of water (ν) = 1.0 × 10⁻² cm²/sec
Settling Velocity Calculation
The settling velocity (V) can be calculated using the formula derived from Stokes' Law:
V = (g * (SG - 1) * d²) / (18 * ν)
Where:
- g = acceleration due to gravity (approximately 980 cm/sec²)
- SG = specific gravity of the particle
- d = diameter of the particle in cm
- ν = kinematic viscosity of the fluid
Substituting Values
1. Calculate the buoyant force factor:
SG - 1 = 2.7 - 1 = 1.7
2. Substitute values into the equation:
V = (980 * 1.7 * (0.21)²) / (18 * 1.0 × 10⁻²)
3. Calculate the settling velocity:
- (0.21)² = 0.0441
- V = (980 * 1.7 * 0.0441) / 0.18
4. Final calculation yields:
V ≈ 104.37 cm/sec
Conclusion
The settling velocity of grit particles with the given parameters is approximately 104.37 cm/sec. This value indicates how quickly the grit will settle in water, which is crucial for various engineering applications, including sedimentation processes.