Hydrocyclone Separation & Cut Size (d50) Sizing Calculator
Bradley & Rietema models, feed pressure drop, centrifugal G-force, and underflow spigot roping audit.
1. Slurry Feed Properties
2. Hydrocyclone Geometry & Standard
3. Hydraulics & Apex Sizing
Separation Cut Point & Hydraulic Results
Flow Split & Classification Telemetry
Hydrocyclone Double-Vortex Multiphase Separation Simulator
Interactive schematic: Tangential slurry entry, outer downward vortex carrying heavy coarse particles to apex spigot, inner upward vortex carrying fine particles to overflow, and low-pressure central air core.
5 Fatal Traps & Industrial Engineering Pitfalls
1. Apex Spigot Roping & Coarse Particle Overflow Contamination
When feed solids surge or when the apex spigot diameter ($D_u$) is undersized, the underflow transitions from a healthy 20-degree umbrella flare into a solid cylindrical rope. Roping chokes the apex discharge capacity, completely collapsing the low-pressure air core. Dense, coarse abrasive grit that should report to underflow backs up into the cyclone cone and exits out the top overflow nozzle, causing catastrophic downstream equipment erosion and ruining product grind targets.
2. Submerged Underflow Discharge & Air Core Destruction
A hydrocyclone requires an open atmospheric air core extending from the apex up through the vortex finder to establish the radial pressure gradient. If plant piping discharges the underflow spigot directly into a flooded sump or submerged pipe below the water line, backpressure destroys the air core. Separation efficiency plunges, water recovery into the underflow spikes from 15% to over 40%, and separation sharpness ($d_{50}$) becomes erratic.
3. Hindered Settling Viscosity Blindness in High-Density Slurries
Designing cyclone batteries based on clean-water cut size correlations ($d_{50}$) leads to massive classification failure when slurry solids exceed 20 vol% (over 40 wt% in mineral slurries). Apparent slurry viscosity escalates non-linearly, dampening centrifugal particle acceleration. The actual industrial cut size ($d_{50c}$) often doubles or triples compared to dilute laboratory data, resulting in severely under-ground ore recycled to ball mills.
4. Inlet Velocity Excessive Gouging Wear (>7 m/s)
Operating with excessive feed pressure drops (>250 kPa / 35 psi) drives inlet feed velocities above 7 to 9 m/s. High-velocity quartz or mineral particles impact the feed chamber and polyurethane or rubber liners with kinetic energy proportional to velocity squared ($v^2$). Abrasive gouging wears grooves through the liner within weeks. Once the liner wears unevenly, turbulence destroys laminar vortex rotation, causing unstable classification.
5. Asymmetric Radial Manifold Maldistribution in Clusters
In multi-cyclone clusters (e.g., 6 to 18 cyclones on a circular radial distributor), uneven slurry feed piping causes coarse particles to centrifuge to the outer wall of the feed header. Certain cyclones receive 30% higher solids loading than others, causing some units to rope while others run under-loaded in a flared spray. A central symmetric circular distributor with top axial feed entry is mandatory for uniform multi-cyclone performance.
Hydrodynamic Classification & Bradley Model Equations
The theoretical base cut size ($d_{50}$) in microns is modeled via the Bradley hydrodynamic equilibrium equation:
Where $K_B approx 38.5$ for Bradley geometry ($D_i / D_c = 0.14$, $D_o / D_c = 0.14$), with $D_c$ in meters, $Q$ in m3/h, and densities in kg/m3.
The corrected cut size ($d_{50c}$) accounting for hindered particle settling and volumetric solids concentration ($C_v$) is:
The Centrifugal G-Force Acceleration at the cyclone outer wall radius ($R_c = D_c / 2$) is: