Carr Index ⃒ Hausner Ratio

1. Powder flowability characterization : Carr Index and Hausner Ratio

The Carr Index and the Hausner Ratio are both meant as being indicators of the flowability of bulk solids. The flowability of solids is complex and linked to many parameters, it is thus not always obvious to characterize the solid flowability with the few set of data that Engineers usually have in hand during design or troubleshooting.

Both Carr and Hausner attempted just that : assuming that the compressibility of a solid is related to its flowability, they proposed to measure the bulk and tapped density of bulk materials and calculate a ratio in order to estimate how the material will flow.

The lower the Carr Index or Hausner Ratio, the more flowable is a material.

2. Calculation formula of Carr Index

How to calculate the Carr Index ? What is Carr's index formula ?

The Carr's Index of a material is calculated with the following formula :

Carr's Index Formula

Carr_Index = (ρ_tapped-ρ_bulk)/ρ_tapped*100

With

ρ_tapped : the tapped bulk density of the material (kg/m³)
ρ_bulk : the loose bulk density of the material (kg/m³)

It is possible to relate the Carr's Index and the Hausner ratio with the following formula :

H = 100/(100-Carr_Index)

3. Calculation formula of the Hausner Ratio

How to calculate the Hausner Ratio ? What is the Hausner Ratio formula ?

The Hausner Ratio of a material is calculated with the following formula :

Hausner ratio formula

H = ρ_tapped/ρ_bulk

With

H : Hausner Ratio
ρ_tapped : the tapped bulk density of the material (kg/m³)
ρ_bulk : the loose bulk density of the material (kg/m³)

There are other methods to define the flowability of powders or granules (click for more infos) :

Angle of repose Powder rheometer Shear cells testing

4. Interpretation and relation to flowability of Carr index and Hausner Ratio

The flowability of a bulk solids is estimated by 1^st calculating the ratio, then referring to the table below to determine in which class is the powder studied :

Flowability expected	Hausner Ratio	Carr's Index
Excellent / Very Free Flow	1.00 - 1.11	<10
Good / Free Flow	1.12 - 1.18	11-15
Fair	1.19 - 1.25	16-20
Passable	1.26 - 1.34	21-25
Poor Flow / Cohesive	1.35 - 1.45	26-31
Very Poor Flow / Very Cohesive	1.46 - 1.59	32-37
Approximatively no flow	> 1.60	> 38

The table was determined by the authors of the method, by testing different material flowability, and calculating the compressibility ratio associated.

Note that Carr's Index and Hausner Ratio are approximate methods, the characterization of the flowability and the determination of physical parameters allowing the design of hoppers would require more measurement using powder rheometers or full shear cell testing.

Example of calculation of Carr Index

An Engineer wishes to have an idea of the probable flowability of a powder. He measures the bulk loose density as 600 kg/m³ and the tapped density as 660 kg/m3. He can then calculate the Carr Index :

Carr_Index = (ρ_tapped-ρ_bulk)/ρ_tapped*100 = (660-600)/660*100 = 9.1

Refering to the table above, the Engineer concludes the powder is probably free flowing.

Example of calculation of Hausner Ratio

With the data above, the Engineer also wishes to define the Hausner ratio, he then makes the following calculation :

H = ρ_tapped/ρ_bulk = 660/600 = 1.1

The table above is also used, the powder is indeed probably free flowing.

5. Carr Index and Hausner ratio Excel calculation tool

Please access here the Free Excel calculator for Carr Index and Hausner ratio : calculator download (click here)