Example 1 - Cyclones for removing PM (SiO2 and Na2CO3) particles Exhausts from two storage bins at a fiberglass plant are combined and passed through a cyclone that provides 95% particulate removal on a weight basis. The following measurements were made. Exhaust from bin A: flow rate3000 acfm (actual ft3/min) dry air loading15 grains of SiO2 per standard cubic foot (gr/scf) pressure16 pounds per square inch absolute (psia) temperature90 F Exhaust from bin B: flow rate2500 acfm dry air loading10 grains of Na2CO3 per scf pressure17 psia temperature110 F [assume standard P and T are: 1 atm and 77 F] Find the rate of solids discharge (collection of solids) from the cyclone, and the concentration of solids remaining in the air being exhausted from the cyclone. Solution Notes: 1 lb = 7000 grains. standard pressure and temperature: 1 atm = 14.7 psia, 77 oF or 25 oC

Balance envelope E F Feed , Cyclone exhaust Stream A 3000 acfm 15 gr/scf Stream B 16 psia 2500 acfm 90 F 10 gr/scf 17 psia 110 F Solids discharge Air balance: Solids balance: where Q = volumetric flow rate of air, in cubic feet per minute (cfm) p = density of air, lb/ft3 C = concentration of solids, in stream A or B (grains/ft3) A, B, F = subscripts identifying each stream Mar = mass flow rate of solids in stream F. Q, C, and p must have consistent units. That is, Q can be expressed in standard cubic feet per minute (scfm), C in grains/scf, and p in lb/scf; or Q can be expressed in actual cubic feet per minute (acfm), C in gr/act, and p in Ib/acf. Often, particulate matter (PM) measurements are reported as gr/scf, and regulations are written in terms of gr/scf. So, we will first convert the air flow rates to scfm