ToolnozaInputs and measurement basis
Choose two particle sizes whose recoveries to underflow bracket the desired 50% partition. Enter recoveries as percentages of the feed solids in each size class reporting to underflow, not the underflow size distribution. Set bypass to zero for raw d50 or enter the assumed water bypass for d50c.
Lower particle size (µm); Raw underflow recovery at lower size (%); Upper particle size (µm); Raw underflow recovery at upper size (%); Assumed water bypass to underflow (%, 0 = raw d50).
Formula and calculation
Ei,c = 100(Ei − B)/(100 − B); a = (50 − E1,c)/(E2,c − E1,c); d50,c = exp[ln(d1) + a(ln(d2) − ln(d1))].
Find d50 or corrected d50c by log-size interpolation between measured hydrocyclone partition points.
Worked example
d1 = 40 µm; E1 = 40%; d2 = 80 µm; E2 = 80%; B = 20% → E1,c = 25%; E2,c = 75%; d50c = 56.57 µm.
How to interpret the result
At d50, half the feed particles in that size class report to the underflow. A corrected cut removes an assumed bypass fraction before locating the midpoint. These are different metrics and should be labeled separately.
The tool interpolates in log particle size and linear recovery. Use nearby size classes around the midpoint; widely separated points give a less reliable estimate. No cut size is inferred from cyclone diameter alone.
Assumptions and limits
Measured-data interpolation, not equipment sizing. Corrected recovery = (raw recovery − bypass)/(100 − bypass) × 100. Both corrected recoveries must bracket 50% and increase with size. Water bypass is an approximation; fish-hook curves require fuller analysis.
Frequently asked questions
What if both recoveries lie below 50%? Choose a larger size class until the selected points bracket the midpoint after correction. The tool rejects extrapolation.