Question Bank • QB_PARAMETRIC_APE_PHY_028NAT • 2 Marks
Section 6: Agricultural Process Engineering
Physical & Geometric Properties of Agro-Produce
Subtopic: Grain sphericity calculation
Question Statement:
The triaxial dimensions of a paddy grain are: major axis $a = 6.5\text{ mm}$, intermediate axis $b = 3.2\text{ mm}$, and minor axis $c = 2.4\text{ mm}$. The sphericity ($\phi$) of the grain defined by $\phi = \frac{(a b c)^{1/3}}{a}$ is ________ (round off to two decimal places). (Variation QB_PARAMETRIC_APE_PHY_028)
Answer Key:
0.57
Step-by-Step Solution & Explanation
Geometric mean diameter is:
$D_g = (a b c)^{1/3} = (6.5 \times 3.2 \times 2.4)^{1/3} = (49.92)^{1/3} = 3.682\text{ mm}$
Sphericity is:
$\phi = \frac{D_g}{a} = \frac{3.682}{6.5} = 0.566$
Rounding to two decimal places: $0.57$.