GATE 2025 CE (CE2) – Question 63
A settling chamber is used for the removal of discrete particulate matter from air with following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = $2.1 \times 10^{-5}$ kg/m.s; Acceleration due to gravity (g) = 9.81 m/s$^2$; Density of air at 77°C = 1.0 kg/m$^3$; Assume the density of water as 1000 kg/m$^3$ and Laminar condition exists in the chamber.
The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in µm) is ______ (round off to one decimal place).
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Correct answer: 21.89 to 22.11
Explanation
A particle at the top of the inlet is removed if it settles the chamber height during the time the air takes to pass through. The required settling velocity is $v_s = \frac{Hv_h}{L} = \frac{2 \times 0.2}{12} = 0.0333$ m/s. For laminar settling (Stokes' law), $v_s = \frac{g(\rho_p - \rho)d^2}{18\mu}$, so $d^2 = \frac{18 \times 2.1 \times 10^{-5} \times 0.0333}{9.81 \times (2650 - 1.0)} = 4.85 \times 10^{-10}$ m² and $d = 2.20 \times 10^{-5}$ m $= 22.0$ µm. The Reynolds number of the particle is about 0.035, so the laminar assumption holds.