Hi guys, I've been at this literally all day and am at the end of my rope. Please take a look and if you could give me any kind of guidance I'd be really grateful.
I'm supposed to design a centrifugal separator cyclone for removal of particles. However, when plugging into the equation, none of the numbers seem to come out right. Hoping one of you can find my mistake.
The info I'm given:
Flow rate (Q)= 1 m^3/s
Gas density (Pg) = 8.8 x 10^-4 g/cm^3
Gas viscosity (ug)= 0.000225 g/cm s
Particle density (Pp) = 1.5 g/cm^3
Ka = a/D = 0.5
Kb = b/D = 0.2
Equations to figure out diameter and Inlet velocity:
D = 0.0262 * ({[Q*Pg^2]/[ug*Pp]}*{[1-Kb]/[Ka*Kb^2.2]})^0.454 (Kalen and Zenz's equation)
Uin = Q/ab
I'm first supposed to find the diameter. So I need to use that first equation to do so. Pg and Pp need to be in Kg/m^3, and ug needs to be in Pa s. So after conversion I have these values at:
Pg = 8.8 x 10^-5 kg/m^3
Pp = 0.15 kg/m^3
Ug = 0.0000225 Pa s
Now when I plug all of my known values into the diameter equation, I come up with 0.0102531421 m for the cyclone diameter.
It tells me the next step is to use the diameter to figure out Uin. So I take the geometric ratios Ka and Kb and use D to find a and b:
a = 0.5 * 0.0102531421 = 0.0051265711
b = 0.2 * 0.0102531421 = 0.0020506284
Now when I take those values and plug them into the Uin equation, I'm getting a cyclone velocity of 94,861.48 m/s. The value of these cyclones is supposed to be between 15 and 30 m/s. I am going wrong somewhere in these first 2 steps, but can not for the life of me figure out where. What do you guys think?
My inspection immeadiately reveals that your density conversions for Pg and Pp are off, 1g/cm3 = 1000kg/m^3.
The correct values are:
Pg = 8.8 x 10^-4 * 10^3 = 8.8 x 10^-1 or .88 kg/m^3
Pp = 1.5 * 10^3 = 1.5 x 10^3 kg/m^3
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