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: Understand the setup.
Particle-laden air first passes through a cyclone collector (80% efficiency), and whatever leaves the cyclone then passes through an electrostatic precipitator, ESP, (50% efficiency). Each device removes a fraction of the particles that enter it, so the two devices act one after another on a shrinking stream of particles.

Step 2: Find the concentration leaving the cyclone.
Inlet concentration to the cyclone, \(C_0 = 10\) mg/m\(^3\).
Cyclone efficiency \(\eta_1 = 0.80\), so it removes 80% of the incoming particles and lets the other 20% through:
\[ C_1 = C_0 (1 - \eta_1) = 10 \times (1 - 0.80) = 10 \times 0.20 = 2 \text{ mg/m}^3 \]
Step 3: Find the concentration leaving the precipitator.
This 2 mg/m\(^3\) stream now enters the ESP, which removes 50% of what enters it and lets the other 50% through:
\[ C_2 = C_1 (1 - \eta_2) = 2 \times (1 - 0.50) = 2 \times 0.50 = 1 \text{ mg/m}^3 \]
Step 4: Final Answer.
The concentration of particles exiting the precipitator is:
\[ \boxed{1.00 \text{ mg/m}^3} \]