Subtopic: Average particle diameter from fineness modulus
Question Statement:
A ground grain sample has a fineness modulus of $FM = 3.0$. Using Henderson's empirical equation $D = 0.0041 \times 2^{FM}$ where $D$ is average particle diameter in inches ($1\text{ inch} = 25.4\text{ mm}$), the average particle diameter in millimeters is ________ $\text{mm}$ (round off to two decimal places).
Answer Key:
0.83
Step-by-Step Solution & Explanation
Using Henderson's formula:
$D = 0.0041 \times 2^{FM} = 0.0041 \times 2^{3.0} = 0.0041 \times 8 = 0.0328\text{ inches}$
Converting to millimeters:
$D = 0.0328 \times 25.4 = 0.833\text{ mm}$
Rounding to two decimal places: $0.83\text{ mm}$.