Dust is generated continuously in a room by an industrial process at the rate of
ID: 3035682 • Letter: D
Question
Dust is generated continuously in a room by an industrial process at the rate of .02 Ibs/min. The volume of the room is 4000 cubic feet and you may assume that the air in the room is well mixed by fans. The air conditioning system draws air from the room at the rate of r = 800 cubic feet per minute, and the filtered air is returned to the room at the same rate. The filter reduces the concentration of dust in the air passing through it by a multiplicative factor of the form e^-2b where b is the thickness in inches of the filter material. Derive a differential equation which models the dynamical process described above. Solve the differential equation derived in part (a) if the initial concentration of dust in the room is 10^-5 pounds per cubic foot. What is the minimal acceptable thickness of the filter if the limiting concentration of dust in the room must not exceed 4.0 times 10^-5 pounds per cubic foot. Using the value for the minimal acceptable thickness of the filter found in part (c), simulate your model using Simulink.Explanation / Answer
Given here is the dust generated, a=0.02 lbs/min
Volume of the room, v=4000 cubic feet
Air drawn from the room r= 800 cubic ft
Concentration of dust multiplies by e-2b
Hence the differential equation is,
X(t)=av+(cv-av)e-2b
where c is the concentration of dust.
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