Hydrocyclone Cut Size (d50c Plitt) & Capacity Calculator
Predict industrial hydrocyclone classification performance using the empirical Plitt model: corrected cut size d50c, slurry flow capacity, feed pressure drop, water recovery split, and discharge roping limits.
1. Hydrocyclone Internal Geometries
2. Slurry Operating Conditions
Classification & Hydraulic Results
Hydrocyclone Schematic & Vortex Core
5 Fatal Engineering Traps in Hydrocyclone Operation
1. Spigot Overload & The Sudden Roping Transition Disaster
When grinding circuits experience a surge in solids feed rate or a drop in water addition, apex volumetric capacity is overwhelmed. The central air core instantly collapses, transforming the healthy 25° conical spray flare into a solid cylindrical "rope". In roping mode, coarse oversize rocks bypass centrifugal classification and dump straight into the overflow launder, ruining downstream flotation recoveries.
2. Vortex Finder Pinhole Wear & Slurry Short-Circuit Jetting
Abrasive quartz particles spinning at sonic speeds erode the outer barrel wall of the cast-polyurethane or ceramic vortex finder. Once a through-wall groove develops, high-pressure raw feed slurry jets directly through the side of the vortex finder into the overflow pipe, totally bypassing the cyclone classification vortex.
3. Backpressure on Overflow Piping Suppressing the Vacuum Air Core
Hydrocyclones require an unrestricted atmospheric discharge or gravity launder on both overflow and underflow to sustain the high-velocity low-pressure central air core. Piping overflow lines uphill or submerging discharge headers creates hydraulic backpressure that floods the air core, spikes d50c, and causes massive flow oscillation.
4. Slurry Viscosity Surges from Smectite/Illite Clay Gelling
Ore bodies rich in ultrafine swelling clays transform slurry into non-Newtonian thixotropic mud. High apparent viscosity dampens tangential fluid velocity near the wall by up to 60%. Centrifugal forces collapse, causing d50c to surge from 75 μm to over 220 μm, sending unground coarse minerals into carbon-in-leach circuits where gold cannot be extracted.
5. Apex Tramp Oversize Choking & Upstream Screen Failure
Operating a cyclone cluster without an upstream trash guard screen allows worn mill scats, wood chips, and broken rubber trommel fragments to enter the feed distributor. A single wood splinter wedges across the apex spigot, damming coarse solids inside the cone until the entire cyclone packs solid with sand.
Mathematical Derivations & Plitt (1976) Formulation
The corrected cut size (d50c in micrometers) is given by the Plitt empirical correlation:
d50c = [ 50.5 · Dc0.46 · Di0.60 · Do1.21 · exp(0.063 · Cv) ] / [ Du0.71 · h0.38 · Q0.45 · (ρs - ρl)0.5 ]
Where dimensions Dc, Di, Do, Du, h are in cm, Q is in L/min, and Cv is % by volume.
Slurry volumetric throughput capacity Q (L/min) related to feed pressure drop ΔP (kPa):
Q = [ 4.75 · ΔP0.56 · Dc0.21 · Di0.53 · h0.16 · (Du² + Do²)0.49 ] · exp(-0.0063 · Cv)
Separation sharpness index α (slope of the reduced recovery curve):
α = 1.94 · exp[ - 1.58 · (Du / Do) ] · [ (Dc² · h) / Q ]0.15
Water volumetric split to underflow (recovery ratio Rw):
S = [ 18.62 · (Du / Do)3.31 · h0.54 · (Du² + Do²)0.36 · exp(0.0054 · Cv) ] / [ Dc1.11 · ΔP0.24 ]
Rw = S / (1 + S) × 100 %