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Hydrometallurgy

Thickener Underflow Density Calculator

Thickener underflow density is the slurry density of the thickened solids leaving the underflow. This calculator estimates it from the dry solids rate, the target underflow wt% solids, and the solids and liquid densities — building the slurry and liquid mass flows, the solids and liquid volume flows, and the total slurry volume to get the underflow slurry density. It is a preliminary density and flow estimate only: it is not a thickener sizing model, rheology model, or settling test.

TypeInteractive engineering calculator

Calculator

t/h

dry solids basis

wt%

0–100 wt% solids by mass

kg/m³

dry solids particle density

kg/m³

liquor density

Result
Underflow slurry mass flow181.818 t/h
Liquid mass flow81.8182 t/h
Solids volume flow37.037 m³/h
Liquid volume flow81.8182 m³/h
Total slurry volume flow118.855 m³/h
Slurry density1529.75 kg/m³
  • !Preliminary density and flow estimate only — not a thickener sizing model, rheology model, or settling test.

Formulas

Slurry mass flow
ṁ_slurry = ṁ_solids / (wt% / 100)
Liquid mass flow
ṁ_liquid = ṁ_slurry − ṁ_solids
Solids volume flow
Q_solids = ṁ_solids × 1000 / ρ_solids
Liquid volume flow
Q_liquid = ṁ_liquid × 1000 / ρ_liquid
Slurry volume flow
Q_slurry = Q_solids + Q_liquid
Slurry density
ρ_slurry = ṁ_slurry × 1000 / Q_slurry

Diagram

Thickener underflow density — ρ_slurry = ṁ_slurry / Q_slurryfeed slurryoverflow (clear)dense underflowρ_slurry = ṁ_slurry / (Q_solids + Q_liquid)

Worked example

A thickener underflow carries 100 t/h dry solids at 55 wt% solids. Solids density 2700 kg/m³, liquid density 1000 kg/m³. Estimate the underflow slurry density.

  1. 01Slurry mass: 100 / (55 / 100) = 181.82 t/h
  2. 02Liquid mass: 181.82 − 100 = 81.82 t/h
  3. 03Solids volume: 100 × 1000 / 2700 = 37.04 m³/h
  4. 04Liquid volume: 81.82 × 1000 / 1000 = 81.82 m³/h
  5. 05Slurry volume: 37.04 + 81.82 = 118.86 m³/h
  6. 06Slurry density: 181.82 × 1000 / 118.86 ≈ 1529 kg/m³
Result

Slurry mass 181.82 t/h, liquid mass 81.82 t/h, solids volume 37.04 m³/h, liquid volume 81.82 m³/h, slurry volume 118.86 m³/h, slurry density ≈ 1529 kg/m³.

FAQ

Is this a thickener sizing calculator?
No. It estimates the underflow slurry density and component flows from the solids rate and target wt% solids. Thickener area, rake torque, flocculant dose, and rise rate require settling testwork and vendor data.
Why do I need both solids and liquid densities?
The slurry density depends on how solids and liquid volumes combine. The solids density converts the solids mass to a volume; the liquid density converts the liquor mass to a volume. Together they give the total slurry volume and hence the density.
How does underflow wt% solids change the density?
A higher wt% solids means less liquor per tonne of solids, a smaller slurry volume, and a higher slurry density. The relationship is non-linear because it runs through the phase volumes.
Does this predict whether the thickener will reach this density?
No. It tells you the density that corresponds to a target wt% solids. Whether the thickener actually achieves that underflow depends on settling behaviour, flocculant, bed depth, and rake design — all from testwork.

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