What Is the Centrifugal Clarifier Sigma Factor & Cutoff Particle Calculator?
The Sigma factor represents the area of an ideal gravity sedimentation tank that would achieve identical solid-liquid clarification as the centrifuge.
How Does the Centrifugal Clarifier Sigma Factor & Cutoff Particle Calculator Work?
Combines bowl geometry and rotational speed to scale settling throughput via Q = 2 * v_g * Sigma, where v_g is terminal gravity settling velocity.
Centrifugal Clarifier Sigma Factor & Cutoff Particle Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Sigma = rac{pi omega^2 L R^2}{g}, quad G = rac{omega^2 R}{g}, quad d_{ ext{cut}} = sqrt{ rac{18 mu Q}{2 Delta
ho g Sigma}}
Ambler Sigma theory for centrifugal solid-liquid sedimentation scaling.
How to Use the Centrifugal Clarifier Sigma Factor & Cutoff Particle Calculator
- Input bowl speed in RPM, bowl radius and length in mm, and slurry feed rate in m³/h.
Step-by-Step Example Calculation
Solid Bowl Decanter Slurry Clarification
Input Values:
bowlSpeedRpm:4500
bowlRadiusMm:160
bowlLengthMm:650
feedFlowM3Hr:3.2
Worked Steps: Sigma area = 1,170 m², Centrifugal acceleration = 3,624 g, Cutoff particle d50 = 3.65 µm.
Understanding Your Result
Displays equivalent settling area Sigma in m², G-force number, and Stokes cutoff diameter d50 in microns.
Factors That Affect the Result
- Doubling rotational speed quadruples the Sigma clarification capacity (omega squared relationship).
When Should You Use This Calculator?
- Scaling laboratory disc-stack or decanter centrifuge test results to full-scale industrial separators, biopharma cell harvesting, and wastewater sludge dewatering.
Assumptions & Limitations
- Assumes laminar Stokes settling of dilute spherical particles without fluid turbulence or hindrance.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Ambler Sigma theory formulation.