Subtopic: Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers
Question Statement:
A very small particle of diameter dp and density ρp freely settles at constant velocity in a tank of depth L containing liquid of viscosity μl. The density of the liquid is ρl where ρl < ρp. The velocity of particle in the liquid can be expressed as
Options:
(A) gL
(B) g
(C) g
(D) g
Official Answer Key:
C
Step-by-Step Solution & Explanation
For a very small particle settling under laminar (Stokes-regime) conditions, Stokes' Law gives the terminal settling velocity: v_t = g(ρp−ρl)d_p²/(18μ_l) — this is the standard closed-form result and depends on d_p², not on the tank depth L → option (C). Options (A)/(B)/(D) incorrectly introduce the (irrelevant) tank depth L into the terminal-velocity expression, or use the wrong power of d_p.
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