Answer:
Time to Reach Saturation = 0.0146 day
Explanation:
In order to solve this problem, we first need to calculate the dust filtered by the filter per cubic meter of air:
Filtered Dust per m³ = Dust Particles Entering per m³ - Dust Particles Leaving per m³
Filtered Dust per m³ = 225 μg/m³ - 15 μg/m³
Filtered Dust per m³ = 210 μg/m³ = 210 x 10⁻³ mg/m³
Now, we find volume flow rate of air through filter:
Volume Flow Rate of Air = (400 ft³/min)(0.3048 m/1 ft)³
Volume Flow Rate of Air = 11.33 m³/min
Now, we calculate rate of dust filtered:
Rate of Dust Filtered = (Filtered Dust per m³)(Volume Flow Rate of Dust)
Rate of Dust Filtered = (210 x 10⁻³ mg/m³)(11.33 m³/min)
Rate of Dust Filtered = 2.38 mg/min
Now, for the time required to reach saturation:
Time to Reach Saturation = (Saturation Capacity)/(Rate of Dust Filtered)
Time to Reach Saturation = (50 mg)/(2.38 mg/min)
Time to Reach Saturation = (21.02 min)(1 day/24 h)(1 h/60 min)
<u>Time to Reach Saturation = 0.0146 day</u>
