Hong Life CalculatorsUnderstanding the cyclone cut size and efficiency calculator — concept and principle
A cyclone separates dust from a gas stream by spinning it, with no moving parts and no filter media. It is used as a pre-cleaner ahead of bag filters, in grain handling, sawmills, dryers and cement plants. This calculator estimates the cut diameter d₅₀, the particle size collected with 50% efficiency, and the collection efficiency for one particle size, using the classic Lapple method.
How it is calculated
- Cut diameter: d₅₀ = √(9 μ W ÷ (2π Nₑ v ρₚ)), in metres, shown in µm.
- Fractional efficiency: η = 1 ÷ (1 + (d₅₀/d)²).
μ is the gas viscosity (Pa·s), W the inlet width (m), Nₑ the number of effective turns the gas makes inside the body, v the inlet velocity (m/s) and ρₚ the particle density (kg/m³).
The principle
In the spinning vortex each particle feels a centrifugal force that pushes it outward, while gas drag (Stokes' law) resists the motion. A particle is caught if it can cross the inlet width W during the time the gas spends making Nₑ turns. Lapple defined d₅₀ as the size that just manages to travel half that width, which gives the square-root formula. Faster gas, more turns and denser particles all shorten the required distance or time, so d₅₀ falls; a wider inlet or more viscous gas raises it. The efficiency curve is a smooth fit to Lapple's experimental curve: 50% at d = d₅₀, rising toward 100% for larger particles.
Worked example
- Defaults: W = 0.2 m, Nₑ = 6, v = 15 m/s, ρₚ = 2000 kg/m³, μ = 1.8 × 10⁻⁵ Pa·s, d = 10 µm.
- Numerator: 9 × 1.8 × 10⁻⁵ × 0.2 = 3.24 × 10⁻⁵.
- Denominator: 2π × 6 × 15 × 2000 = 1.131 × 10⁶.
- d₅₀ = √(2.865 × 10⁻¹¹) = 5.35 × 10⁻⁶ m = 5.35 µm.
- η = 1 ÷ (1 + (5.352/10)²) = 1 ÷ 1.2865 = 77.73%.
| Effective turns | Cut diameter d₅₀ (µm) |
|---|---|
| 1.5 | 10.7047447 |
| 3 | 7.569397566 |
| 4.5 | 6.180387232 |
| 6 | 5.352372348 |
| 7.5 | 4.787307365 |
| 9 | 4.370193722 |
| 12 | 3.784698783 |
How to read the result
Conventional cyclones are effective for particles larger than about 10 µm and poor for fine dust of a few micrometres. To estimate total collection, apply η to each size class of your dust's size distribution and weight by mass. A lower d₅₀ means better collection, but higher inlet velocity also increases pressure drop roughly with v², and too high a velocity can re-entrain collected dust.
Common mistakes
- Entering the particle size in metres or the viscosity of the wrong gas temperature; gas viscosity rises with temperature and hurts efficiency.
- Using Nₑ = 6 for a cyclone that is not of standard proportions.
- Treating the efficiency at one size as the overall efficiency.
Frequently asked questions
What is a typical inlet velocity?
Many designs work in the range of roughly 15 to 25 m/s, balancing efficiency against pressure drop and wear.
Does a smaller cyclone collect finer dust?
Yes. A smaller body has a narrower inlet, so d₅₀ falls; banks of small cyclones in parallel use this effect.
Why use a cyclone before a bag filter?
It removes most of the coarse dust cheaply, reducing the load and abrasion on the filter.
Sources: Cooper, C. D. & Alley, F. C. Air Pollution Control: A Design Approach. Waveland Press.