Reference ID: MET-0AE4 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Slurry density is the bulk mass per unit volume of a liquid-solid mixture.
Accurate knowledge of this property is essential for sizing pumps, pipelines,
mixers, and settlers in mineral processing, wastewater treatment, starch
handling, and catalyst suspension loops. A quick estimate is obtained from
the volumetric fraction of solids and the true densities of the two phases,
assuming additive volumes and no excess mixing effects.
Methodology & Formulas
Phase densities
Denote the true density of the liquid phase by \( \rho_{\text{liquid}} \)
and of the solid phase by \( \rho_{\text{solid}} \).
Volume fraction
Let \( X_{\text{v}} \) be the volume fraction of solids in the slurry,
expressed on a 0–1 basis.
Linear mixing rule
Under the assumption of volume additivity, the slurry density
\( \rho_{\text{slurry}} \) is
\[
\rho_{\text{slurry}} = (1 - X_{\text{v}})\, \rho_{\text{liquid}}
+ X_{\text{v}}\, \rho_{\text{solid}}
\]
Regime
Validity Condition
Remarks
Linear rule applicable
\( 0 \le X_{\text{v}} \le X_{\text{v,max}} \)
Accuracy within a few percent; no hindered settling or non-Newtonian effects.
Accuracy degraded
\( X_{\text{v}} > X_{\text{v,max}} \)
Particle interactions, non-Newtonian viscosity, and hindered settling invalidate simple additivity.
Weigh a precisely known volume.
Fill a 1 L stainless-steel container to the brim, knock out trapped air, and weigh on a 0.1 g scale.
Subtract the tare mass; the remainder is the slurry mass in kg.
Density = mass / 1 L → read directly in kg L⁻¹ or multiply by 1000 for kg m⁻³.
Use the two-component mass balance.
Let ρm = slurry density, ρs = solids density, ρl = liquid density, and Cw = solids fraction by mass.
1/ρm = Cw/ρs + (1–Cw)/ρl.
Solve for any unknown once the other three values are known.
Nucleonic or vibrating-tube meters are standard.
Nucleonic (gamma) gauges: non-contact, 0.5% accuracy, good for abrasive lines.
Vibrating-tube (Coriolis) meters: 0.1% accuracy, also gives mass flow, but needs wear-resistant liners for coarse slurries.
Both give 4–20 mA signals for DCS density loops.
Temperature changes the liquid phase volume.
Water density drops 0.2% per °C around 20 °C; slurries follow the same trend.
Correct for every 5 °C change if your target accuracy is ±0.5%.
Apply ρT = ρref / [1 + β(T – Tref)] with β ≈ 2 × 10⁻⁴ °C⁻¹ for water-based slurries.
Worked Example – Slurry Density of a Starch–Water Mix
A snack-food plant prepares a pre-gelatinised starch slurry that is pumped to a drum dryer. To size the pump and check heat-transfer coefficients, the production engineer needs the exact slurry density when the starch volume fraction is 25%.
Knowns
Density of water at 25 °C: \( \rho_{\text{water}} \) = 1000 kg/m³
Density of starch granules: \( \rho_{\text{starch}} \) = 1500 kg/m³
Starch volume fraction: \( X_v \) = 0.25
Step-by-step calculation
Write the volume-fraction mixing rule for a two-phase slurry:
\[
\rho_{\text{slurry}} = X_v \rho_{\text{starch}} + (1 - X_v) \rho_{\text{water}}
\]
Insert the known values:
\[
\rho_{\text{slurry}} = 0.25 \times 1500 + (1 - 0.25) \times 1000
\]
