A cyclone separator like that in the figure is used to remove fine solid particl

Question

A cyclone separator like that in the figure is used to remove fine solid particles, such as fly ash, that are suspended in a gas stream. In the flue-gas system of an electrical power plant, the weight fraction of fly ash in the exhaust gases is approximately 0.00146.

Determine the mass flow rates at the two outlets (flue gas and fly ash) when 7.648 kg/s of flue gas and ash mixture enters this unit. Also determine the amount of fly ash collected per year mash = kg/s (Round to five decimal places) flue gas mash kg/s (Round to five decimal places) kg/year (Round to the nearest hundred)

Explanation / Answer

Let m1 = mass flow rate of inlet gas mixture

m flue gas = mass flow rate of outlet flue gas

m ash = mass flow rate of outlet ash

Given data

mass flow rate of flue gas and fly ash mixture at inlet

m1 = 7.648 kg/s

The weight fraction (mass) of the fly ash in the exhaust gas

m ash / m1 = 0.00146

m ash = 0.00146 x 7.648 = 0.01117 kg/s

Overall mass balance

m1 = m ash + m flue gas

m flue gas = m1 - m ash

= 7.648 - 0.01117

= 7.63683 kg/s

Amount of fly ash collected per year

m ash = (0.01117 kg/s) x (24h/day) x (3600s/h) x (365days/year)

= 352257.120 kg/year

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