A food powder has an aerated (poured) bulk density of $\rho_b = 480\text{ kg/m}^3$ and a tapped bulk density of $\rho_t = 640\text{ kg/m}^3$. According to Carr's Compressibility Index ($CI$) and Hausner Ratio ($HR$), the powder flowability is classified as:
Options:
(A) Excellent ($CI \le 10\%$)
(B) Passable / Fair ($CI = 21\%\text{--}25\%$)
(C) Very poor ($CI > 35\%$)
(D) Free-flowing liquid-like ($CI = 0\%$)
Answer Key:
B
Step-by-Step Solution & Explanation
1. Carr's Compressibility Index ($CI$):
$CI = \left(\frac{\rho_t - \rho_b}{\rho_t}\right) \times 100\% = \left(\frac{640 - 480}{640}\right) \times 100\% = \left(\frac{160}{640}\right) \times 100\% = 25.0\%$
2. Hausner Ratio ($HR$):
$HR = \frac{\rho_t}{\rho_b} = \frac{640}{480} = 1.333$
Standard Carr's classification:
- $CI \le 10\%$: Excellent
- $CI = 11\text{--}15\%$: Good
- $CI = 16\text{--}20\%$: Fair
- $CI = 21\text{--}25\%$: Passable / Fair
- $CI = 26\text{--}31\%$: Poor
- $CI > 35\%$: Very poor
At $CI = 25.0\%$, the powder is classified as Passable / Fair.