🌪️ Cyclone Separator Calculator

Calculate the cut size (d50) of a cyclone separator using Lapple model.

Inputs

Cyclone Diameter (D)

Inlet Width (W)

Inlet Velocity (Vi)

ft/s

Particle Density (ρp)

lb/ft³

Gas Density (ρg)

lb/ft³

Gas Viscosity (μ)

lb/(ft·s)

Results

Cut Size (d50)

0.00 µm

Particles larger than 0.0 µm are collected with >50% efficiency.

Cyclone Cut Size Chart

Calculator Description

A cyclone separator uses the centrifugal force of a swirling gas stream to separate and collect solid particles or liquid droplets suspended in the gas. Because it has no consumable parts like a filter, is mechanically simple, and tolerates high temperature and pressure, it is one of the most widely used devices for dust collection and gas pre-cleaning in industry.

What this calculator finds: the Cut Size (d₅₀)

Cyclone performance is usually expressed by its cut size (d₅₀): the particle diameter that is collected with exactly 50% efficiency. Particles larger than d₅₀ are mostly captured, while smaller ones mostly escape. A smaller d₅₀ therefore means a higher-performance cyclone that can capture finer particles.

Why it matters

Checking whether a dust-collection system can meet emission limits before building it
Sizing a pre-cleaning cyclone to reduce the load on downstream bag filters or ESPs
Quantitatively comparing how changes in inlet velocity or geometry affect performance

Formula

Lapple Cut-Size Model

The most widely used semi-empirical relation is the Lapple (1951) model. It derives d₅₀ from the balance between the centrifugal force on a particle and the (Stokes) drag force opposing it.

d_{50} = \sqrt{\dfrac{9\,\mu W}{2\pi N_e V_i\left(\rho_p - \rho_g\right)}}

d₅₀ — Cut size — particle diameter collected at 50% efficiency [m or µm]
μ — Gas dynamic viscosity [kg/(m·s)]
W — Inlet width [m]
V_i — Inlet gas velocity [m/s]
Nₑ — Effective number of turns (typically ≈ 5 for a standard cyclone)
ρ_p, ρ_g — Particle density and gas density respectively [kg/m³]

How the formula works

Higher inlet velocity V_i increases centrifugal force, lowering d₅₀ → finer particles captured.
A larger particle–gas density difference (ρ_p − ρ_g) makes separation easier, lowering d₅₀.
Higher gas viscosity μ or a wider inlet W raises drag / travel distance, increasing d₅₀ → poorer performance.

Grade-efficiency curve (chart)

The collection efficiency for an individual particle size dp is approximated by η(dp) = 1 / (1 + (d₅₀/dp)²). The S-shaped curve in the chart above is exactly this relation, and you can see that efficiency is precisely 50% at dp = d₅₀.

Worked example

For 1000 kg/m³ particles in air (μ ≈ 1.8×10⁻⁵ kg/(m·s), ρ_g ≈ 1.2 kg/m³) with an inlet width of 0.125 m, inlet velocity 15 m/s and Nₑ = 5, the result is d₅₀ ≈ 5 µm — meaning particles larger than about 5 µm are collected with more than 50% efficiency.

Useful Tips

Practical tips

Raising inlet velocity lowers d₅₀ but pressure drop rises with the square of velocity. 15–25 m/s is usually the economical range.
Using many small cyclones in parallel (multiclones) reduces each body diameter and improves fine-particle capture.
Sticky or hygroscopic dusts foul the walls and degrade performance — consider material, cone angle and rapping.

Limitations & cautions

The Lapple model assumes standard geometry ratios; real efficiency can deviate by ±10–20%.
Accuracy drops for sub-5 µm particles, so precise cleaning needs a downstream filter stage.
At very high loadings, particle-to-particle interaction can make real efficiency higher than predicted.