Engineering
Centrifuge / Separator Speed Calculator — Separation Factor (Σ)
Calculate separation factor (G-force) and Sigma value for dairy centrifuges and separators. Verify bowl speed for effective cream separation and clarification.
Formula
(bowlSpeed * bowlSpeed * (bowlDiameter / 2000)) / 895
bowlSpeed
Bowl Speed (n) (RPM)
bowlDiameter
Bowl Diameter (mm)
Worked Example
1
Given:
bowlDiameter = 300
bowlSpeed = 6000
2
Apply the formula:
(bowlSpeed * bowlSpeed * (bowlDiameter / 2000)) / 895
3
Result:6034 × g6034 m/s
Separation Factor (Z-Factor / G-Force)
The separation factor expresses how much stronger the centrifugal force in the bowl is compared to gravity. Higher G-force = faster and more effective separation.
Z = ω² × r / g = (π × n / 30)² × r / g
Simplified: Z = (n² × r) / 895
Where:
- n = bowl speed (RPM)
- r = bowl radius (m) — half the bowl diameter
- g = 9.81 m/s²
Sigma Value (Σ) — Equivalent Settling Area
Sigma represents the equivalent settling area of the centrifuge:
Σ (m²) = (Q × Z) / (2 × v_s)
Where:
- Q = flow rate (m³/s)
- Z = separation factor (dimensionless)
- v_s = Stokes settling velocity of the particle being separated
Typical Separation Factors in Dairy
| Equipment | Typical G-Force (Z) | Bowl Speed |
|---|---|---|
| Cream separator (small) | 3,000–5,000 G | 5,000–7,000 rpm |
| Cream separator (large industrial) | 5,000–8,000 G | 3,500–5,500 rpm |
| Milk clarifier | 5,000–8,000 G | Similar to separator |
| Cheese whey centrifuge | 3,000–6,000 G | 3,000–5,000 rpm |
| Bactofuge (bacteria removal) | 8,000–12,000 G | 8,000–10,000 rpm |
Bowl Speed Effect on Separation
Doubling the bowl speed increases the G-force by 4× (since Z ∝ n²). This is why bowl speed is the most critical operating parameter for dairy separators.
Cautions
- Never exceed the manufacturer’s rated maximum bowl speed — the bowl can fail catastrophically
- Check vibration spectrum regularly — increased vibration at bowl speed frequency indicates imbalance
- For Indian climate: increased feed temperature (38–42°C) reduces viscosity and improves separation efficiency, allowing the same result at lower speed