Project ForgeFluid Mechanics
Mechanical Operations
GATE 2016
Hard
A rigid sphere falls at constant velocity: μ=0.1 Pa·s, g=10 m/s², ρparticle=1180, ρfluid=1000 kg/m³. The diameter (mm) of the largest sphere settling in the Stokes' law regime (Re≤0.1), rounded to 2 decimal places, is
2.15 mm(± 0.15 accepted)
Explanation
At the Re=0.1 boundary: d³=1.8μ²/(ρf·g·Δρ)=1.8×0.01/(1000×10×180)=1×10⁻⁸ m³. d=(10⁻⁸)^(1/3)=2.15×10⁻³m=2.15mm.
Source: GATE CH 2016 (2016)
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