Cyclone Separator Cut Size and Pressure Drop

The Lapple cut size d50 is the particle diameter the cyclone captures with 50% efficiency; larger particles are caught more efficiently, smaller ones less, and the efficiency curve is smooth -- a cyclone does not have a sharp cutoff and never will. Every term in the numerator hurts and every term in the denominator helps, and reading them tells you how cyclones are designed. A NARROWER inlet improves the cut because particles have less distance to migrate to the wall; HIGHER velocity improves it, and so do MORE turns, which is why cyclones are tall and slender rather than squat; denser particles are easier. And that is the whole trade, because everything that improves the cut also raises the pressure drop, which goes as velocity SQUARED. A standard-proportion cyclone with a 0.25 ft inlet, 5 turns, and 50 ft/s on 90 lb/cubic ft wood dust cuts at 4.28 microns and costs 4.48 in w.g. Push the velocity to 70 ft/s chasing a finer cut and the cut size improves only to 3.62 microns, a 15% gain, while the pressure drop nearly doubles to 8.78 in w.g. That asymmetry is why cyclones are almost always followed by a filter rather than pushed harder: the last few microns cost more in fan power than a baghouse does. Cut size and pressure drop only. This is the classical Lapple relation with an assumed effective number of turns, and real collection efficiency depends on the full cyclone geometry, the inlet loading, particle shape and agglomeration, re-entrainment from the wall and the dust hopper, and the vortex finder -- none of which is a formula. It does not size the cyclone body, the hopper, or the airlock, and it takes NO position on combustible dust hazard management, which NFPA 652, NFPA 664 for wood, and NFPA 68 and 69 govern. Manufacturer test data and NFPA govern.

d50 = sqrt(9 mu W / (2 pi N V (rho_p - rho_g))); microns = d50_ft x 304800; dP = K rho_g V^2 / (2 gc), gc = 32.174; in w.g. = psf / 5.202; fan hp = dP_psf x cfm / 33,000.

The classical Lapple cut-size relation and cyclone pressure drop counted in inlet velocity heads (K commonly 8), by name. Cut size and pressure drop only -- collection efficiency also depends on full geometry, inlet loading, particle shape, re-entrainment, and the vortex finder. NO position on combustible dust hazard management, which NFPA 652, 664, 68, and 69 govern. Manufacturer test data and NFPA govern.

The Lapple relation and the velocity-head pressure drop are public; viscosity, densities, geometry, and the number of effective turns are user-entered.

Estimate. AHJ and licensed professional govern.

Field names used by the API: inlet_width_ft, inlet_velocity_fps, turns, gas_viscosity_lb_ft_s, gas_density_pcf, particle_density_pcf, k_velocity_heads, airflow_cfm, second_velocity_fps, d50_micron, pressure_drop_psf, pressure_drop_inwg, alt_d50_micron, alt_drop_inwg, fan_hp

• No sharp cutoff d50 is the 50% capture diameter on a smooth efficiency curve, not a thresholdLapple cyclone theory
• Velocity squared everything that improves the cut raises the pressure drop faster than it improves the cutLapple cyclone theory
• No dust-hazard position combustible dust management is governed by NFPA 652, 664, 68, and 69NFPA 652 / 664 / 68 / 69