Chemegate

GATE 2024 Chemical Engineering, Q58 · Mechanical Operations

The correct answer is 14.3 to 14.6.

Question

A metallic spherical particle of density 7001kg/m37001 kg/m³ and diameter 1 mm is settling steadily due to gravity in a stagnant gas of density 1kg/m31 kg/m³ and viscosity 10510⁻⁵ kg/(m·s). Take g =9.8m/s2.= 9.8 m/s². Assume that the settling occurs in the regime where the drag coefficient CDC_{D} is independent of the Reynolds number, and equals 0.44. The terminal settling velocity of the particle, in m/s, rounded off to 2 decimal places, is ____

Official answer: 14.3 to 14.6

Why

GATE 2024 official key: 14.30 to 14.60. Newton's law regime: vt=[4gd(ρpρf)/(3CDρf)]=[4×9.8×0.001×7000/(3×0.44×1)]=207.914.42v_{t} = √[4gd(ρp−ρf)/(3C_{D}ρf)] = √[4 \times 9.8 \times 0.001 \times 7000/(3 \times 0.44 \times 1)] = \sqrt{207.9} \approx 14.42 m/s.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.