Industrial Hydrocyclone Sizing & Cut Size Calculator
Perform industrial sizing and classification modeling for mineral processing, closed-circuit grinding, and desanding hydrocyclones. Calculate corrected cut size (d50c), slurry pressure drop, volumetric split ratio, apex/vortex finder geometries, and evaluate spray vs roping discharge regimes.
1. Slurry Feed & Cyclone Geometry
2. Cut Point, Split & Discharge Sizing
Engineering Principles & Hydrocyclone Kinetic Derivations
Hydrocyclones are the dominant wet classification equipment in closed-circuit grinding, mineral beneficiation, and sand washing due to their high volumetric throughput and small footprint.
1. Slurry Density & Volume Concentration Conversion
From mass percent solids (C_w), dry mineral skeletal density ( ho_s), and carrier liquid density ( ho_L) ((1000, ext{kg/m}^3)):
2. Plitt Empirical Cut Size ($d_{50c}$) Equation
The corrected cut size (d_{50c}) in microns is modeled via the comprehensive Plitt equation:
Where (D_c, D_i, D_o, D_u, h) are in cm, (Q) is in L/min, and densities are in ( ext{g/cm}^3). As solids volume concentration (C_v) increases, (exp(0.063 C_v)) causes severe cut-point coarsening due to hindered settling.
3. Volumetric Split & Water Recovery
The volumetric split ratio (S = Q_u / Q_o) between underflow and overflow is dictated by orifice ratio (D_u / D_o):
The fraction of water reporting to underflow (R_f = rac{S}{1 + S}) defines the fine particle bypass percentage.
4. Apex Discharge Hydrodynamics: Spray vs. Roping
The apex discharge transitions from an umbrella cone spray to roping when the underflow volumetric solids concentration exceeds critical packing ((C_{v,uf} > 52% ext{ to }56%)):
5 Fatal Engineering Traps & Industrial Operating Hazards
1. Apex Roping Overload & Severe Coarse Misplacement
When mass solids feed surges without adjusting apex diameter, the underflow packing fraction exceeds 54 vol%. The central air core collapses, transforming the umbrella spray into a thick, cylindrical "rope". During roping, the apex cannot clear coarse particles, forcing rocks directly into the overflow stream where they destroy downstream flotation cells or leach tanks.
2. Siphoning & Air Core Collapse from Submerged Overflow Pipes
Piping the cyclone overflow discharge line directly below the water level in an open distributor tank creates an uncontrolled barometric siphon. Negative suction pressure draws air out of the cyclone core, collapsing the inner vortex. Classification sharpness ((alpha)) drops by 40%, and water short-circuits to the underflow.
3. High Slurry Viscosity Choking from Clay and Fines
Processing ores containing bentonite, smectite, or kaolinite clays creates high non-Newtonian plastic viscosity. At 40% solids, clay slimes damp out tangential swirl velocity, shifting (d_{50c}) from 75 µm to over 200 µm. Corrective action requires lowering cyclone feed solids to 30 wt% or adding chemical sodium silicate dispersants.
4. Polyurethane & Ceramic Apex Liner Gouging Wear
Centrifugal velocities exceed 15 m/s at the apex tip, where abrasive quartz and sulfide grains concentrate. Standard polyurethane liners erode within 4 to 8 weeks, enlarging the spigot diameter by 20% to 35%. This unchecked wear increases underflow water bypass, dropping underflow density and overloading downstream dewatering screens.
5. Manifold Flow Maldistribution in Radial Cyclone Clusters
Mounting multiple hydrocyclones on a radial cluster distributor requires uniform feed velocity. If the central inlet riser is undersized or operated below design pressure (<70 kPa), slurry separates in the manifold. Centrally located cyclones receive dense coarse solids, while peripheral units receive dilute slimes, destroying circuit efficiency.