Surface Environment, Mine Ventilation and Underground Hazards · Surface Environment · 2 marks · Numerical answer
A 50 μm dust particle enters a dry settling chamber 0.5 m above the floor at horizontal speed 1 m/s. Density is 2000 kg/m³, air viscosity 1.8×10⁻⁵ kg/(m s). Neglect air density and use Stokes settling. Find minimum chamber length in m, to two decimals.
Settling speed is v=ρgd²/(18μ)≈0.15139 m/s. Time to fall 0.5 m is 0.5/v≈3.3028 s. At horizontal speed 1 m/s, the required travel length is 3.3028 m, or 3.30. Convert 50 μm to 50×10⁻⁶ m before squaring.
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