Question

In an industry, a cyclone collector with 80% efficiency is installed for air purification, followed by an electrostatic precipitator with 50% efficiency. The concentration of particles entering the cyclone collector is 10 mg/m\(^3\).

The concentration (in mg/m\(^3\)) of particles exiting the precipitator is (rounded off to two decimal places).

Hint:

Apply each device's efficiency one after another to the concentration entering it, or combine both efficiencies into a single overall removal fraction first.

Answer 1

Correct Answer: 1

Step 1: Combine the two devices into one overall efficiency.
Rather than tracking the concentration stage by stage, we can first find the single overall removal efficiency of the cyclone and ESP acting together in series. When two collectors sit in series, the fraction of particles that survives both equals the product of each device's own survival fraction.

Step 2: Find the combined survival fraction.
Cyclone survival fraction $= 1 - 0.80 = 0.20$.
ESP survival fraction $= 1 - 0.50 = 0.50$.
Combined survival fraction:
\[ (1-\eta_1)(1-\eta_2) = 0.20 \times 0.50 = 0.10 \] So only 10% of the original particles survive both devices, which means the overall system efficiency is $1 - 0.10 = 0.90$, or 90%.

Step 3: Apply this to the inlet concentration.
The inlet concentration entering the cyclone is $10$ mg/m$^3$. Since 90% of the particles get removed overall, only 10% remain in the air leaving the precipitator:
\[ C_{out} = 10 \times 0.10 = 1 \text{ mg/m}^3 \]
Step 4: Final Answer.
\[ \boxed{1.00 \text{ mg/m}^3} \]