Subtopic: Particle size analysis for comminuted solids
Question Statement:
The mass fraction retained on the iᵗʰ sieve is xᵢ and D̄pᵢ is the average opening size of iᵗʰ and (i-1)ᵗʰ sieves. The volume surface mean diameter (D̄s) of particles retained on n number of sieves is _________.
Options:
(A) D̄s = 1 / Σ(xᵢ/D̄pᵢ)
(B) D̄s = Σ xᵢ D̄pᵢ
(C) D̄s = [1/Σ(xᵢ/D̄pᵢ³)]^(1/3)
(D) D̄s = [1/Σ(xᵢ/D̄pᵢ³)]^(2/3)
Official Answer Key:
A, D
Step-by-Step Solution & Explanation
• The volume-surface mean diameter (Sauter mean diameter) is defined as the diameter of a sphere having the same volume-to-surface-area ratio as the particle population, and is computed as the reciprocal of the mass-weighted sum of reciprocal diameters:
• D̄s = 1/Σ(xᵢ/D̄pᵢ) — the standard, textbook Sauter mean diameter formula.
• Distractor logic: (B) is the arithmetic (length) mean diameter, not the surface-volume mean. (C) and (D) introduce cubic terms inconsistent with the standard Sauter-mean derivation.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.