Question Bank • QB_APE_EXP_037 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Particle size analysis for comminuted solids

Question Statement:

The Fineness Modulus ($FM$) of a ground grain sample is $3.50$. The average particle diameter $D_p$ in millimeters calculated using the empirical equation $D_p = 0.135 (1.366)^{FM}$ is ________ (round off to 2 decimal places).

Answer Key:

0.4

Step-by-Step Solution & Explanation

Empirical formula for average particle diameter from fineness modulus: $D_p = 0.135 (1.366)^{FM}$ Given $FM = 3.50$: $(1.366)^{3.50} = \exp(3.50 \times \ln 1.366) = \exp(3.50 \times 0.31189) = \exp(1.0916) \approx 2.979$ $D_p = 0.135 \times 2.979 \approx 0.402\text{ mm} \approx 0.40\text{ mm}$
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