An ambient air stream at a superficial velocity of 9.84 ft/min, containing an aerosol of 1-mm-diameter particles at an estimated concentration of 10⁴ particles/m³, is to be filtered through a bed of glass fibers, 19 mm in diameter, with a bed void fraction, ϵ_b, of 0.0033. An empirical equation for the particle-collection efficiency as a function of bed thickness for glass fibers of this type is given by [26]:

where L = bed depth in inches, rb = bed bulk density = 5.15 lb/ft³, and u μs = superficial air velocity in ft/min. The pressure drop across the filter per unit bed depth is given approximately in terms of a modified drag coefficient as

where r¼air density = 1.210^–3 g/cm³, dp¼glass fiber diameter 19 x 10^–4 cm, and the drag coefficient is given by CD = 50 = NRe, where NRe = d_pρμ_s/m and m = air viscosity = 1.8x 10^–4 g/cm-s.

Calculate: 

(a) Bed depths in cm for a series of particle-collection efficiencies over a range of 90 to 99.99%; and 

(b) Pressure drop per unit bed depth in kg/m²-m. Adapted from [25].

Transcribed Image Text:

Fractional efficiency = 1-10-0.075109 Puz0.4 (1)