Reference ID: MET-2581 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The Hausner ratio is a dimensionless number that compares the tapped bulk density to the loose bulk density of a particulate solid. It is widely used in process engineering to quantify powder flowability: a low ratio indicates that the particles can rearrange into a denser packing with little energy (free-flowing), whereas a high ratio reveals strong inter-particle forces that resist densification (cohesive). Typical applications include hopper and silo design, tablet formulation, pneumatic conveying, and any solids handling step where reliable flow is critical.
Methodology & Formulas
Convert practical bulk-density units to SI units:
\[ \rho_{\text{loose}} = \rho_{\text{loose,g cm}^{-3}} \cdot 1000 \]
\[ \rho_{\text{tapped}} = \rho_{\text{tapped,g cm}^{-3}} \cdot 1000 \]
where the factor 1000 changes g cm-3 to kg m-3.
Compute the Hausner ratio:
\[ H_{\text{R}} = \frac{\rho_{\text{tapped,g cm}^{-3}}}{\rho_{\text{loose,g cm}^{-3}}} \]
(The ratio is dimensionless, so any consistent pair of density units may be used.)
Assess flow regime from the calculated ratio:
Condition
Hausner Ratio Range
Flow Behaviour
\( H_{\text{R}} \le 1.25 \)
Free-flowing
Particles rearrange easily; low risk of arching or ratholing.
\( 1.25 < H_{\text{R}} < 1.5 \)
Moderate cohesion
Some resistance to flow; may require flow-aid devices.
\( H_{\text{R}} \ge 1.5 \)
Cohesive, prone to bridging
Strong inter-particle forces; high likelihood of flow stoppages.
The Hausner Ratio is the quotient of tapped density divided by bulk (loose) density of the same powder sample. A value near 1 indicates free-flowing, low-cohesion material; values above ~1.25 flag poor flow and potential segregation or compaction issues in bins, hoppers, and tablet dies.
Pour powder through a standardized funnel into a 100 mL stainless cylinder until it overflows; level off with a straight edge and weigh for bulk density.
Drop the same cylinder 500–750 times (ASTM B527/ISO 3953) from 3 mm height; reweigh for tapped density.
Keep sample mass identical for both tests and record temperature/humidity to ensure repeatability.
Yes—fill a 250 mL graduated cylinder to 200 mL, tap it vertically by hand against a benchtop 100 times, read the new volume, and calculate the ratio. While not ASTM-compliant, a ratio >1.35 still signals flow problems and justifies sending a sample to the lab for formal testing.
Blending with a free-flowing excipient or glidant to lower cohesion.
Installing bin activators or vibration pads to prevent ratholing and bridging.
Re-screening or milling to narrow particle-size distribution and reduce interlocking.
Running shear-cell tests to set correct hopper angles and discharge rates.
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Worked Example: Hausner Ratio for a New Catalyst Support
A process engineer at a petrochemical plant needs to qualify a fresh batch of alumina micro-spheres that will be loaded into a fixed-bed reactor. To predict how the solids will flow through the loading chute and pack inside the 2 m ID vessel, the engineer measures loose and tapped bulk densities in the lab and computes the Hausner ratio.
Loose (aerated) bulk density, \(\rho_{\text{loose}}\) = 0.38 g cm⁻³
Tapped (consolidated) bulk density, \(\rho_{\text{tapped}}\) = 0.50 g cm⁻³
Convert both densities to kg m⁻³ for consistency with plant units:
\[
\rho_{\text{loose}} = 0.38 \times 1000 = 380\ \text{kg m}^{-3}
\]
\[
\rho_{\text{tapped}} = 0.50 \times 1000 = 500\ \text{kg m}^{-3}
\]
Final Answer: The alumina support has a Hausner ratio of 1.32, indicating moderate cohesion; the solids should flow with mild assistance (e.g., gentle vibration) during reactor loading.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
