The inlet mass shares and assumed class efficiencies reproduce the article’s example: 13.5 kg/h collected and 6.5 kg/h escaping from a 20 kg/h inlet. These are teaching values, not predicted cyclone performance.
1. Ask what the laboratory actually measured
Before entering a particle-size distribution (PSD), identify whether the percentages describe mass, volume or particle count; whether the values are cumulative or interval fractions; and how the diameter was measured. A sieve opening, an optical equivalent diameter and an aerodynamic diameter describe different measurement conventions.
A count-based distribution can give strong emphasis to numerous fine particles while most mass sits in fewer coarse particles. Do not enter count percentages into a mass-weighted efficiency calculation. Volume fractions only equal mass fractions when the relevant particle density is constant across the size classes.
Also distinguish particle density from bulk density. Bulk density includes spaces between particles in a pile. A cyclone model requiring particle density needs the density of the particles, with attention to porosity and the model’s definition.
2. Convert cumulative passing into interval fractions
Suppose a mass-based report says 10% passes 2 µm, 35% passes 5 µm and 70% passes 20 µm. Subtract adjacent cumulative values to obtain each interval. The table below is an invented example, not a measured material.
| Interval | Mass fraction calculation | Mass share |
|---|---|---|
| Below 2 µm | 10 − 0 | 10% |
| 2–5 µm | 35 − 10 | 25% |
| 5–20 µm | 70 − 35 | 35% |
| Above 20 µm | 100 − 70 | 30% |
Cumulative passing must not decrease as size increases. Interval shares must be non-negative and sum to 100% for a complete distribution. Check units too: 0.02 mm is 20 µm.
Each interval still needs a representative diameter for a discrete calculation. A geometric midpoint can be a starting approximation for a bounded positive interval, but it does not recover the actual within-bin distribution. Open-ended classes need additional data or an explicit assumption; zero cannot be used as a geometric endpoint.
3. Separate grade efficiency from total efficiency
Grade efficiency is collection efficiency at a particular size. Overall mass efficiency weights those efficiencies by the inlet mass shares. The US EPA’s cyclone overview identifies inlet size distribution as a key influence on collection performance.
Using the example shares above, assume class efficiencies of 10%, 40%, 80% and 95%. The total is 0.10 × 0.10 + 0.25 × 0.40 + 0.35 × 0.80 + 0.30 × 0.95 = 0.675, or 67.5%. These efficiencies are assumed solely to demonstrate arithmetic; they are not a cyclone performance curve.
4. Turn the percentage into a downstream duty
At an inlet dust rate of 20 kg/h, the illustrative efficiency leaves 6.5 kg/h in the gas. With an outlet flow of 5,000 actual m³/h, the outlet concentration is 1,300 mg per actual m³. That is a calculated loading, not an emissions compliance result.
A permit or test report may require normal conditions, a dry basis or an oxygen correction. Do not compare concentrations until the gas-volume and reporting bases match. A high overall efficiency also does not demonstrate effective fine-particle removal.
5. Keep missing information visible
If only 90% of the inlet mass is classified, keep the remaining 10% visible rather than silently redistributing it. For a sensitivity bound, calculate once assuming none of that missing mass is collected and once assuming all of it is collected. The resulting ten-percentage-point range shows how much uncertainty the missing fraction alone introduces.
Retain the original laboratory file, sampling location, process state, measurement method and any conversion assumptions. Use narrower classes near the steep part of the grade-efficiency curve where better data are available. Compare plausible PSD cases before committing to equipment.
Read the cyclone design guide for operating flow, pressure drop and discharge considerations.
Sources and scope
US EPA: Monitoring by Control Technique — Cyclone explains performance influences and monitoring parameters. All numbers in this article are illustrative. Laboratory data preparation and mass-balance calculations do not validate a particular separation correlation or guarantee equipment performance.