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Process Design

Slurry Density Calculator

This calculator computes slurry density and percent solids from the liquid density, the solids density and a solids loading entered as percent solids by mass, percent solids by volume or grams of solids per litre of slurry, using ideal two-phase mixture relations.

Slurry density is the bulk density of a two-phase mixture of solid particles suspended in a liquid. This hub calculator computes it from the liquid density, the solids (dry particle) density, and the solids loading entered four ways: percent solids by mass, percent solids by volume, solids concentration in g/L of slurry, or — in target-density lab-prep mode — by working backwards from a desired slurry density to the mixture proportions. It returns slurry density and all four phase fractions (mass and volume), converting between every basis. It is a preliminary two-phase estimate: it does not model entrained air, dissolved species, rheology, settling, or particle size effects.

TypeInteractive engineering calculator

Calculator

0–100 %

Result
Slurry density1229.7 kg/m³
Solids mass fraction0.3
Solids mass percent30 %
Solids volume fraction0.139211
Solids volume percent13.9211 %
Liquid mass fraction0.7
Liquid volume fraction0.860789

Formulas

Slurry density from mass fraction Xs
ρ_slurry = 1 / (Xs / ρ_solids + (1 − Xs) / ρ_liquid)
Slurry density from volume fraction Cv
ρ_slurry = Cv × ρ_solids + (1 − Cv) × ρ_liquid
Volume fraction from mass fraction
Cv = (Xs / ρ_solids) / (Xs / ρ_solids + (1 − Xs) / ρ_liquid)
Mass fraction from volume fraction
Xs = (Cv × ρ_solids) / ρ_slurry
g/L mode (per 1 m³ slurry, 1 g/L = 1 kg/m³)
ρ_slurry = C + (1 − C / ρ_solids) × ρ_liquid
Mass fraction in g/L mode
Xs = C / ρ_slurry, Cv = C / ρ_solids
Target-density lab-prep — volume fraction
Cv = (ρ_target − ρ_liquid) / (ρ_solids − ρ_liquid)
Target-density lab-prep — mass fraction
Xs = (Cv × ρ_solids) / ρ_target

Diagram

Slurry Density: Two-phase Mixtureliquidρ_L+solidsρ_S=slurryρ_slurryρ_slurry = 1 / (Xs/ρ_S + (1−Xs)/ρ_L)

Worked example

A mineral slurry has a liquid (water) density of 1000 kg/m³ and a solids density of 2650 kg/m³ (quartz-like) at 30% solids by mass. What is the slurry density and the volume fraction of solids?

  1. 01Xs = 0.30 (mass fraction)
  2. 02ρ_slurry = 1 / (0.30 / 2650 + 0.70 / 1000)
  3. 03ρ_slurry = 1 / (0.0001132 + 0.0007000) = 1 / 0.0008132
  4. 04ρ_slurry ≈ 1229.6 kg/m³
  5. 05Cv = (0.30 / 2650) / 0.0008132 ≈ 0.139
Result

Slurry density ≈ 1229.6 kg/m³; solids volume fraction ≈ 13.9% (Cv), versus 30% by mass.

FAQ

Why is the volume percent so much lower than the mass percent?
Because the solids are denser than the liquid. For quartz-like solids (2650 kg/m³) in water, 30% by mass corresponds to only about 14% by volume. The denser the solids relative to the liquid, the larger the gap. Mass percent and volume percent are never interchangeable without the densities.
Which percent-solids basis should I enter — mass or volume?
Use the basis your data is reported on. Plant assays and Marcy-cup readings are usually mass-based (Cw); some pumping and pipeline calculations use volume-based (Cv). This calculator converts between them once you supply both densities.
Does this account for dissolved salts or process chemistry?
Only indirectly. Dissolved species raise the liquid density. If your liquor is not plain water, enter the measured (corrected) liquid density rather than 1000 kg/m³. The calculator does not model chemistry itself.
Does this model entrained air or rheology?
No. Entrained air, foaming, yield stress, viscosity, settling, and particle size are all out of scope. This is a clean two-phase density estimate for preliminary work only.
Why is g/L not the same as weight percent (wt%)?
g/L (numerically equal to kg/m³) is a per-volume concentration: grams of solids per litre of slurry. Weight percent is a per-mass ratio: mass of solids divided by total slurry mass. They only coincide if the slurry density were exactly 1000 kg/m³, which it never is for a real slurry. For example, 300 g/L of quartz-like solids in water gives a slurry density of about 1187 kg/m³ and a mass percent of only ~25.3% — not 30%. The g/L mode reports the converted mass percent so the difference is explicit.
Why are the target-density (lab-prep) results only preliminary?
Lab-prep mode gives the ideal two-phase mixture proportions for a target density assuming the volumes add perfectly and the densities are exact. Real mixtures deviate: volume contraction or expansion on mixing, entrained air, dissolved species changing the liquid density, moisture in nominally dry solids, particle packing effects, settling and segregation, rheology, sampling error, and plant-scale mixing losses all shift the result. Treat the numbers as a starting point and confirm by measuring the actual mixed density.

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