Disc Stack Centrifuge Sigma Factor & G-Force Calculator

Calculate equivalent clarifying area (Ambler Sigma factor Σ), bowl G-force, Stokes particle cut-off diameter, and maximum volumetric throughput for industrial disc stack separators.

Centrifuge Rotor Speed & Disc Stack Geometry

Rotational Speed N (RPM): Industrial: 4,000 - 12,000 RPM

Number of Discs in Stack (n): Standard: 80 - 180 discs

Outer Disc Radius r2 (mm):

Inner Disc Radius r1 (mm):

Disc Conical Half-Angle θ (degrees): Typically 40° to 50° (standard self-cleaning = 45°)

Fluid & Separation Target

Liquid Viscosity (cP): Water = 1.0, Dairy ~ 2.0

Density Difference Δρ (kg/m³): Yeast in broth ~ 80 - 150 kg/m³

Operating Feed Flow Rate Q (L/h):

Equivalent Settling Area & Performance

Ambler Sigma Factor (Σ)

-- m²

-- sq ft equivalent gravity settling area

Relative Centrifugal Force (RCF)

-- G

-- m/s bowl tip speed

Cut-Off Particle Size (d_cut)

-- µm

100% theoretical capture

Critical Settling Velocity (v_g): -- mm/s

Operating Flow in GPM: -- GPM

Specific Loading (Q / Σ): -- m/h

Scale-Up Comparison Factor: --

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Frequently Asked Questions

What is the Sigma (Σ) factor in centrifuge design?

The Ambler Sigma factor (Σ) represents the equivalent surface area of a gravity settling tank required to achieve the exact same clarifying performance as the centrifuge operating at that speed and geometry. A compact disc centrifuge with a bowl diameter of 400 mm often possesses an equivalent Sigma area of 5,000 to 25,000 m².

How does disc angle θ affect separation and discharge?

The conical angle θ (typically 40° to 50°) determines both settling area and solids sliding. As particles hit the underside of a disc, they agglomerate and slide down into the bowl periphery. If θ is too small (<40°), solids stick and foul the discs; if θ is too steep (>55°), the projected settling area cot(θ) drops drastically.

How do you scale up disc centrifuges using Q/Σ?

Under Ambler centrifuge scale-up theory, two centrifuges of different sizes or operating speeds will produce the same separation efficiency and effluent clarity if their specific loading rates (Q / Σ) are identical: Q1 / Σ1 = Q2 / Σ2.