Cyclone Cut Size D50

Remove supplied water bypass from measured increasing partition curve and linearly interpolate corrected d50 in size; no extrapolation.

Description

A hydrocyclone partition curve records the fraction of each size class reporting to underflow.

A hydrocyclone partition curve records the fraction of each size class reporting to underflow. Removing a supplied water bypass yields a corrected curve whose 50% crossing defines corrected d50.^[1]

The tool returns correctedD50Micrometers, correctedPartitionFractions. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Cyclone Cut Size D50

Use this for the following task: Remove supplied water bypass from measured increasing partition curve and linearly interpolate corrected d50 in size; no extrapolation. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Cyclone Cut Size D50 and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter sizeMicrometers, underflowPartitionFractions, waterBypassFraction according to the field table, then run the tool.
Read correctedD50Micrometers, correctedPartitionFractions. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
sizeMicrometers	Size micrometers	list of number	Required
underflowPartitionFractions	Underflow partition fractions	list of number	Required
waterBypassFraction	Water bypass fraction	number	Required

Use increasing positive sizes and aligned partition fractions, with bypass in [0,1). Corrected fractions must lie in [0,1], strictly increase, and bracket 0.5.

corrected partition = (measured partition−bypass)/(1−bypass); d50 = linear size interpolation at corrected partition 0.5

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
correctedD50Micrometers	Corrected d50 micrometers	number
correctedPartitionFractions	Corrected partition fractions	list of number

json

{
  "input": {
    "sizeMicrometers": [
      10,
      20,
      40
    ],
    "underflowPartitionFractions": [
      0.1,
      0.5,
      0.9
    ],
    "waterBypassFraction": 0.1
  },
  "output": {
    "correctedD50Micrometers": 22.5,
    "correctedPartitionFractions": [
      0,
      0.4444444444444445,
      0.888888888888889
    ]
  }
}

Limitations and assumptions

Interpolation is linear in size, not logarithmic size. No extrapolation, fitted partition model or independent bypass estimate is provided.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Cyclone Efficiency when you need its operation: Audit fine-overflow and coarse-underflow recovery from size-class flows and cut flags; distinct from corrected d50. Choose Cyclone Pressure Drop for the complementary operation: Estimate hydrocyclone inlet pressure loss with caller-calibrated dynamic-head coefficient; no universal geometry correlation.

Background reference: Introduction to Mineral Processing.

References

Introduction to Mineral Processing — NPTEL, Indian Institute of Technology Kharagpur

Similar or alternative tools

Cyclone Efficiency
Audit fine-overflow and coarse-underflow recovery from size-class flows and cut flags; distinct from corrected d50.
Cyclone Pressure Drop
Estimate hydrocyclone inlet pressure loss with caller-calibrated dynamic-head coefficient; no universal geometry correlation.