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Important dimensionless numbers • Resistance coefficient = Euler number – Relates cyclone pressure drop to some characteristic velocity: Eu p ( f v 2 / 2) • Gives ratio to pressure forces to inertial forces • Constant for given cyclone geometry, important for scaleup • What characteristic velocity should we use? – One based on gas flow rate q/cross sectional area (D = cyclone diameter) 4q v D2 Stokes 50 number (Stk50) • Physical significance: Ratio of centrifugal force (less buoyancy) to the drag force acting on a particle of diameter x50 Stk50 2 x50 pv 18 D • - gas viscosity, density is particle density, D is cyclone body diam., char.velocity is same as previous. • x50 = Cut size… at this diameter, 50 percent of particles will be collected Cool rule of thumb: • For well-designed cyclones, there is a direct correlation between Eu and Stk50 12 Eu Stk50 • This is pretty neat because you could find x50 by knowing specifics about cyclone For hw problem 1, Rhodes 7.2 • Info about size distribution given in dFc/dx and dF/dx format Size range (microns) 6.6-9.4 Feed size 0.05 distribution, dF/dx Coarse product size 0.016 distribution, dFc/dx 9.4-13.3 13.3-18.7 18.7-27.0 27-37 37-53 0.2 0.35 0.25 0.1 0.05 0.139 0.366 0.3 0.12 0.06