A cyclone of diameter D_c of 2 ft, whose dimension ratios are as given in Figure 19.9, is being considered to remove dust from a cement kiln. The gas feed, at inlet velocity μ_i of 20 ft³/s, has 0.5 grain/ft³ of particles of average diameter d_p of 7 mm and density ρ_p of 175 lb/ft³, where 1 lb = 7,000 grains. At the operating conditions, air viscosity is 1.21 x 10^–5 lb/ft-s, and the air density is negligible compared to the particle density. The local air-pollution authority requires an effluent of less than 0.1 grain/ft³. Can this be achieved with the present cyclone? This can be determined by computing the fractional collection efficiency for the 7 mm particles from

where D_pcrit = the diameter of the smallest particle that is theoretically separated from the gas stream at a collection efficiency of 50%. From [28],

where N_t, the number of rotations made by the gas stream in the cyclone, is given by

with μ_i in ft/s.

0.5 Dcx0.2 Dc Collecting hopper diameter Dc 0.5 Dc Dcl 0.5 Dc 1.5 Dc 2.5 Dc 0.375 Dc Figure 19.9 Standard high-efficiency cyclone dimensions.