Zerdly

Slurry Solids Fraction Calculator

Convert between slurry (pulp) density and the solids fraction — by weight and by volume — from the slurry SG, the water SG and the solids/ore SG. It is the quick plant check for any grinding, flotation, thickening, pumping or tailings stream, and it works both ways: enter the slurry density to get % solids, or enter % solids by weight to get the slurry density.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the solids / ore specific gravity (SG) — e.g. ~2.65 for quartz/silicate gangue, ~5.0 for magnetite or pyrite.
  2. Enter EITHER the measured slurry density (SG, numerically the same as t/m³) OR, if you don't have it, the % solids by weight — fill in just one of those two.
  3. Set the water SG if it isn't fresh water (1.00) — raise it for saline or process water, or a dense medium.
  4. Read the solids fraction by weight (Cw) and by volume (Cv), plus the slurry density, water fractions, dry solids per m³ and the water-to-solids dilution ratio.

How it works

Specific gravity is density relative to water, so it is numerically equal to density in t/m³. The volume fraction of solids is Cv = (ρ_slurry − ρ_water) / (ρ_solids − ρ_water), the lever rule between the water and solids densities. The mass (weight) fraction is then Cw = Cv · ρ_solids / ρ_slurry.

Going the other way, if you know the % solids by weight the slurry density is ρ_slurry = 1 / (Cw/ρ_solids + (1 − Cw)/ρ_water), which just adds the specific volumes of the solids and water in one kilogram of slurry.

Because SG equals t/m³, one cubic metre of slurry carries Cv · ρ_solids tonnes of dry solids and the rest as water. The dilution ratio — mass of water per mass of solids — is (1 − Cw)/Cw, the number liberation and reagent dosing are usually quoted against.

Worked example

Typical grinding/flotation slurry. A slurry measures 1.5 SG (1.5 t/m³) with quartz-type solids at SG 2.65 in fresh water (SG 1.0). Cv = (1.5 − 1.0)/(2.65 − 1.0) = 0.303 → 30.30% solids by volume. Cw = 0.303 × 2.65/1.5 = 0.5354 → 53.54% solids by weight. Each cubic metre holds 0.303 × 2.65 = 0.803 t of dry solids and 0.697 t of water, a dilution of 0.87 tonnes of water per tonne of solids.

Common mistakes

  • Mixing up solids by WEIGHT and by VOLUME — they are very different numbers (53.5% by weight is only 30.3% by volume for SG-2.65 solids); metallurgical accounting normally uses % solids by weight (Cw).
  • Using the default solids SG of 2.65 for a heavy ore — magnetite (~5.0), chromite (~4.2) or galena (~7.5) give very different results, so use the real ore SG.
  • Leaving the water SG at 1.00 for saline or process water, or for a dense-medium suspension, which shifts the fractions.
  • Entering a slurry density below the water SG or above the solids SG — that is physically impossible and the tool will flag it.

Frequently asked questions

What is the difference between % solids by weight and by volume?

By weight (Cw) is the mass of dry solids divided by the mass of the whole slurry; by volume (Cv) is the volume of solids divided by the total slurry volume. Because solids are denser than water, the weight fraction is always the larger number. Plant grade and mass balances use % solids by weight; pump, pipe and settling calculations often use % solids by volume.

How do I measure slurry density on the plant?

Weigh a known volume — a Marcy pulp-density scale, a pulp-density balance, or simply a 1-litre measuring cylinder on a scale — and divide mass by volume to get t/m³ (which equals SG). Enter that as the slurry density here.

What solids SG should I use?

Use the real value for your ore: roughly 2.65 for quartz/silicate gangue, 2.7–2.8 for many host rocks, 4.2 for chromite, ~5.0 for magnetite and pyrite, and ~7.5 for galena. Mixed mineralogy sits in between and changes with grade, so a lab SG (pycnometer) is best for accurate work.

Can I work backwards from a target % solids?

Yes. Leave the slurry density blank and enter the % solids by weight instead, together with the solids and water SG. The tool returns the slurry density you would need to hit that target, plus all the other fractions.

Does dissolved salt or entrained air affect the result?

Yes. Dissolved salts raise the carrier-water SG (set the water SG above 1.00), and entrained air lowers the measured slurry density, making the solids look lower than they are. De-aerate the sample or allow for it when the numbers matter.

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