How thick would be the cake on an AC filter with the size of 25in x 30in that fi

Question

How thick would be the cake on an AC filter with the size of 25in x 30in that filters the entire air volume in a house with area of 164 m^2 and room height of 2.2m with 98% efficiency if it operates long enough to cycle the entire volume of air in the house through the filter only once? Consider that the AC unit operates at a flow of 100L/s; the density of the cake is 2.5 g/mL; and the concentration of the particles is 800 micrograms/m^3 because the owners left the window open after a dust storm. Assume 10% of the particles settled after the storm and are not available for filtering.      I really need to see how this is worked out

Explanation / Answer

The volume of the house would give us the actual volume of the air available that needs to be filtered. For this we have to use the area of the house and the height provided, hence the volume would be as follows.

Volume = area X height

=164x2.2=360 m3

Now let’s find out the total amount of dust particles in the house which can be calculated as follows using the filtration speed and the concentration of the dust particles in the house.

Amount of dust in the air is 720microgrrams/ mcube this value is achieved by reducing the 10% dust that has settled.

So the amount of dust that has settled on the filter should be

720 X 360 = 259200 micrograms= 0.2592 gm

But the AC functions on 98% efficiency hence the amount of dust captured would be

0.2592 x 0.98=0.25401 gm

Now the density of the cake on the filter is given to be 2.5 g/ ml

DENSITY =MASS/VOLUME

2.5= 0.25401/25 x 30 x thickness

Thickness of the cake on AC filter

=0.25401/750x2.5

=0.25401/1875

=0.00013547inch

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