GATE 2022 AG – Question 45

Agricultural Process Engineering · Engineering Properties of Agricultural Produce · 2 marks · Multiple choice

Mass fraction on sieve i is $x_i$, and $\bar D_{pi}$ is the average opening of sieves i and i−1. Find volume–surface mean diameter over n fractions.

$1/\sum_{i=1}^n(x_i/\bar D_{pi})$
$\sum_{i=1}^n x_i\bar D_{pi}$
$[1/\sum_{i=1}^n(x_i/\bar D_{pi}^3)]^{1/3}$
$[1/\sum_{i=1}^n(x_i/\bar D_{pi}^3)]^{2/3}$

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Correct answer: (A) $1/\sum_{i=1}^n(x_i/\bar D_{pi})$

Explanation

For equal-density similarly shaped particles, surface per mass is proportional to 1/D. Summing fraction contributions gives total surface per mass proportional to $\sum x_i/D_i$. Inverting defines the volume–surface (Sauter) mean: **A**. A simple arithmetic mass average does not preserve surface.

GATE 2022 AG – Question 45

Explanation

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