GATE 2020 CH – Question 26

Fluid Mechanics and Mechanical Operations · Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing · 1 mark · Multiple choice

A rigid sphere of diameter $2\times10^{-4}$ m and density 3000 kg/m³ settles freely in liquid of density 750 kg/m³ and viscosity $9.81\times10^{-3}$ Pa s. Assume Stokes law and g = 9.81 m/s². Find terminal speed in m/s.

$2\times10^{-3}$
$3\times10^{-3}$
$4\times10^{-3}$
$5\times10^{-3}$

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Correct answer: (D) $5\times10^{-3}$

Explanation

Stokes terminal velocity is $v_t=(\rho_p-\rho_f)gd^2/(18\mu)$. Substitute to get $v_t=(3000-750)(9.81)(2\times10^{-4})^2/[18(9.81\times10^{-3})]=0.005$ m/s. Thus D. The buoyant density difference, not particle density alone, enters the force balance.

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