Question

A baghouse filter has to treat 12 m\(^3\)/s of waste gas continuously. The baghouse is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m\(^3\)/min-m\(^2\) cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the baghouse is \(\underline{\hspace{1cm}}\).

Hint:

The total number of bags required can be calculated by dividing the total cloth area by the area of one bag.

Answer 1

Correct Answer: 30

To determine the total number of bags required in the baghouse, follow these steps:

1. First, calculate the cloth area required while one section is shut down for cleaning, leaving four sections operational. The total volumetric flow rate is 12 m³/s. When converted to m³/min, this becomes 720 m³/min (since 1 s = 1/60 min).
2. With an air-to-cloth ratio of 6.0 m³/min-m², the cloth area required for the 4 sections is:
   A = (720 m³/min) / (6.0 m³/min-m²) = 120 m².
3. Since each section should have the same area and there are 5 sections, the total cloth area for all five sections is:
   Total Cloth Area = 5/4 × 120 m² = 150 m².
4. Next, calculate the cloth area for each bag. The diameter of the bag is 32 cm = 0.32 m, and the length is 5 m. The surface area A of each cylindrical bag (not considering the ends) is given by:
   A_bag = π × d × h = π × 0.32 m × 5 m ≈ 5.024 m².
5. The total number of bags required is then:
   Number of Bags = Total Cloth Area / A_bag ≈ 150 m² / 5.024 m² ≈ 29.86.
6. Since the number of bags must be an integer, round 29.86 up to 30 to ensure adequate capacity.

The total number of bags required in the baghouse is 30.