# Powder Flow Rate Calculation Formula

Powder-flow rate is a critical attribute for pharmaceutical solid dosage form. It affects the mixing performance and uniformity of dosage units.

Some of the most commonly applied methods to measure the powder flow rate include:

• Carr’s index,
• Hausner ratio,
• Angle of repose (AOR),
• Flow through an orifice etc.

#### Carr’s index (Compressibility index) and Hausner ratio

The compressibility index and the closely related Hausner ratio have become the simple, fast, and popular methods of predicting powder flow characteristics.

The basic procedure is to measure the compressibility index and the Hausner ratio are calculated as follows:

Compressibility Index = 100 × [(Vo − Vf)/Vo]

Hausner Ratio = (Vo/Vf)

Where,

• the unsettled apparent volume, Vo, and
• the final tapped volume, Vf, of the powder after tapping the material until no further volume changes occur.

The compressibility index and Hausner ratio may also be calculated using measured values for bulk density (ρbulk) and tapped density (ρtapped) as follows:

#### Recommended Procedure for Compressibility Index and Hausner Ratio

Use a 250-mL volumetric cylinder with a test sample weight of 100 g. Smaller weights and volumes may be used, but variations in the method should be described with the results. An average of three determinations is recommended.

#### Angle of Repose

A variety of angle of repose test methods are described in the literature. The most common methods for determining the static angle of repose can be classified on the basis of the following two important experimental variables:

1. The height of the “funnel” through which the powder passes may be fixed relative to the base, or the height may be varied as the pile forms.

2. The base upon which the pile forms may be of fixed diameter or the diameter of the powder cone may be allowed to vary as the pile forms.

#### Angle of Repose

Although there is some variation in the qualitative description of powder flow using the angle of repose, much of the pharmaceutical literature appears to be consistent with the classification by Carr’s, which is shown in below Table. There are examples in the literature of formulations with an angle of repose in the range of 40° to 50° that were manufactured satisfactorily. When the angle of repose exceeds 50°, the flow is rarely acceptable for manufacturing purposes.

#### Flow through an Orifice

The flow rate through an orifice is generally measured as the mass per time flowing from any of a number of types of containers (cylinders, funnels, hoppers). Measurement of the flow rate can be in discrete increments or continuous.

Either mass flow rate or volume flow rate can be determined. Mass flow rate is the easier of the methods, but it biases the results in favor of high-density materials. Because die fill is volumetric, determining volume flow rate may be preferable. A vibrator is occasionally attached to facilitate flow from the container; however, this appears to complicate interpretation of the results. A moving orifice device has been proposed to more closely simulate rotary press conditions. The minimum diameter orifice through which powder flows can also be identified.

#### Recommended Procedure for Flow through an Orifice

Flow rate through an orifice can be used only for materials that have some capacity to flow. It is not useful for cohesive materials. Provided that the height of the powder bed (the “head” of the powder) is much greater than the diameter of the orifice, the flow rate is virtually independent of the powder head. Use a cylinder as the container because the cylinder material should have little effect on flow.

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Read also: Uniformity of Dosage Units Calculation

Reference: USP 〈1174〉