Question Bank • QB_APE_SIZE_005 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Particle size analysis for comminuted solids

Question Statement:

A $100.0\text{ g}$ sample of ground poultry feed is sieved through a standard Tyler sieve series (comprising 3/8", #4, #8, #14, #28, #48, #100, and pan). The cumulative mass percentage retained on each of the 7 standard sieves is determined as follows: 3/8" ($0.0\%$), #4 ($2.0\%$), #8 ($16.0\%$), #14 ($40.0\%$), #28 ($66.0\%$), #48 ($84.0\%$), #100 ($96.0\%$). The Fineness Modulus ($FM$) of the ground feed is ________ (round off to two decimal places).

Answer Key:

3.04

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Standard Definition of Fineness Modulus** Fineness Modulus ($FM$) is defined as the sum of the cumulative mass percentages retained on the standard set of 7 Tyler sieves divided by 100: $FM = \frac{\sum (\text{Cumulative } \% \text{ retained})}{100}$ $\sum = 0.0 + 2.0 + 16.0 + 40.0 + 66.0 + 84.0 + 96.0 = 304.0\%$ $FM = \frac{304.0}{100} = 3.04$ **Method 2: Average Particle Size Relation** According to ASAE Standard S319, average particle diameter $D_{\text{avg}}$ correlates with $FM$ via $D_{\text{avg}} = 0.10414 \times (2)^{FM}\text{ mm}$. For $FM = 3.04$, $D_{\text{avg}} \approx 0.10414 \times 8.225 = 0.856\text{ mm}$.
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