Hydrocyclone Cut-Size (d₅₀) & Plitt Model Calculator
Size and rate industrial classification hydrocyclones. Compute cut-size ($d_{50}$), pressure drop ($\Delta P$), volumetric recovery to underflow ($S$), apex spigot capacity, and separation efficiency using the Plitt empirical model.
1. Hydrocyclone Geometry
2. Slurry Operating Conditions
Hydrocyclone Cut-Point & Performance
Overflow & Underflow Mass Balance
Apex Discharge Regime Assessment
Interactive Hydrocyclone Dual-Vortex & Cut-Size Cross-Section
Dynamic visualizer showing tangential feed inlet, descending outer primary slurry vortex, ascending inner overflow vortex, central air core, vortex finder, and apex spigot flare.
In-Depth Mineral Processing: The Plitt Hydrocyclone Mathematical Model
The standard industrial methodology for predicting hydrocyclone classification performance is the Plitt Model (1976), extensively validated across thousands of operating industrial mineral grinding circuits:
1. Corrected Cut-Size ($d_{50c}$) Correlation
The corrected cut point $d_{50c}$ (particle size with a 50% probability of reporting to underflow due purely to centrifugal sedimentation rather than liquid bypass) is given by:
Where all linear dimensions ($D_c, D_i, D_o, D_u, h$) are in centimeters, $Q$ is slurry feed flow rate in L/min, $C_v$ is volumetric solids percent, and densities are in g/cm³.
2. Slurry Pressure Drop ($\Delta P$) Correlation
Pressure drop across the feed inlet nozzle and overflow discharge is modeled as:
3. Volumetric Flow Split Ratio ($S$) & Underflow Recovery
The volumetric split ratio $S = Q_u / Q_o$ dictates water distribution between streams:
5 Fatal Engineering Pitfalls in Hydrocyclone Operation
Under normal operation, underflow discharges in a hollow conical spray (20°–30° angle) with a central air core. If solids loading exceeds apex volumetric capacity, the air core collapses and discharge turns into a dense, cylindrical "rope". In roping mode, classification completely fails: coarse unground rocks short-circuit into the overflow, while classification efficiency plummets.
If the vortex finder does not extend sufficiently below the feed inlet centerline (minimum $0.8 \times D_i$), feed slurry sweeps directly across the top cover plate into the overflow without ever entering the downward separation vortex. This introduces unclassified coarse tramp particles directly into final flotation concentrate or leach circuits.
Operating below minimum design inlet pressure (< 50 kPa) results in insufficient centrifugal acceleration ($G < 50g$). The internal forced vortex fails to generate a stable low-pressure air core, causing violent pressure surging, surging overflow rates, and an uncontrolled coarsening of the $d_{50}$ cut point.
In multi-cyclone radial clusters, uneven slurry distribution due to improper distributor design or partially choked inlet valves creates differing inlet pressures across individual cyclones. Starved cyclones rope while over-fed cyclones deliver ultra-fine cuts, ruining overall circuit recovery and causing rapid localized liner gouging.
The apex spigot experiences the highest shear velocities and particle packing in the entire plant. A mere 5 mm increase in spigot diameter due to abrasive wear lowers underflow solids concentration, increases water bypass ($R_f$) from 15% to 35%, and dilutes grinding mill circulating load with excess water, reducing grinding efficiency.