Slurry density calculation: complete example at 40 wt% solids and 100 m³/h

Read the relationships and model conditions

Open the Minerallum calculator

This example manually verifies the main outputs of the Minerallum calculator.

All values are fictional and are used only to explain the method.

Starting data

Assume a simple two-phase slurry:

• solid particles;
• carrier liquid;
• no significant entrained air.

Inputs:

Solids by mass:

Slurry volumetric flow:

Step 1 - calculate slurry density

Substitute:

Terms:

Sum:

Therefore:

Result:

Step 2 - calculate solids by volume

Therefore:

This immediately shows why 40 wt% is not 40 vol%.

Step 3 - verify density using the volume-fraction form

Solid contribution:

Liquid contribution:

Total:

The same density is recovered.

Step 4 - total slurry mass flow

or:

Step 5 - dry-solids flow

or:

Step 6 - cross-check dry-solids flow from volume fraction

The independent form gives the same result.

This is a useful software invariant.

Step 7 - liquid mass flow

or:

Step 8 - mass closure

The total slurry mass flow closes.

Step 9 - phase volume flows

Solids:

Liquid:

Check:

Step 10 - dilution ratio

The example contains 1.5 units of liquid mass per unit dry-solids mass.

Results summary

Quantity	Result
Slurry density	1331.6583 kg/m³
Solids by mass	40.0000%
Solids by volume	20.1005%
Liquid by mass	60.0000%
Liquid by volume	79.8995%
Total slurry mass flow	133.1658 t/h
Dry-solids flow	53.2663 t/h
Liquid mass flow	79.8995 t/h
Solid volume flow	20.1005 m³/h
Liquid volume flow	79.8995 m³/h
Dilution ratio	1.5

Reverse check: recover 40 wt% from slurry density

Now assume we know:

• ρs = 2650 kg/m³
• ρl = 1000 kg/m³
• ρm = 1331.658291457 kg/m³

Use:

Substituting returns:

or:

The forward and inverse calculations are consistent.

Why this does not size a pump

The example provides:

• densities;
• concentration;
• volumetric flow.

It does not necessarily provide:

• viscosity;
• rheology;
• particle-size distribution;
• deposition velocity;
• pipe friction;
• pipe diameter/length;
• elevation;
• NPSH;
• entrained gas.

It would therefore be incorrect to convert this calculation into a pump or pipeline recommendation.

Minerallum deliberately keeps the tool limited to composition and derived flows.

Entrained-air warning

If the measured density contains a significant gas void fraction, it can be lower than the true solid-liquid slurry density.

This example contains no gas phase.

Do not blindly use an aerated bulk-density measurement as ρm in this two-phase calculation.

Privacy

The intended Minerallum implementation performs the calculation locally.

Technical input values are not stored by Minerallum or transmitted to analytics.

The contact CTA does not automatically carry the user’s calculation data.

References

1. Wills, B. A.; Finch, J. Wills’ Mineral Processing Technology, 8th edition, Chapter 3. https://doi.org/10.1016/C2010-0-65478-2
2. Scelzo, M. T. et al. (2021). Design and validation of a capacitance-based sensor for slurry density measurement. https://doi.org/10.1016/j.expthermflusci.2020.110299
3. Bamberger, J. A.; Greenwood, M. S. (2004). Using ultrasonic attenuation to monitor slurry mixing in real time. https://doi.org/10.1016/j.ultras.2004.02.016

Use the calculator

Enter your own phase densities and known concentration/density.

Open Show calculation to inspect every substitution.

This guide uses fictional values and is not equipment sizing, process validation or engineering approval.