Question

A smoking lounge is to accommodate 15 heavy smokers. The minimum fresh air requirement for smoking lounges is specified to be \(30 \mathrm{L} / \mathrm{s}\) per person (ASHRAE, Standard 62,1989 ). Determine the minimum required flow rate of fresh air that needs to be supplied to the lounge, and the diameter of the duct if the air velocity is not to exceed \(8 \mathrm{m} / \mathrm{s}\)

Short answer

Answer: The minimum required flow rate of fresh air for 15 heavy smokers is 450 L/s and the diameter of the duct should be approximately 26.75 cm.

Step-by-step solution

Find the minimum required flow rate of fresh air

First, we need to calculate the total fresh air requirement for 15 heavy smokers. The fresh air requirement per person is 30 L/s. To find the total requirement, multiply this by the number of people: Total fresh air requirement = requirement per person × number of people Total fresh air requirement = 30 L/s × 15 Total fresh air requirement = 450 L/s

Convert the flow rate to cubic meters per second

To calculate the diameter of the duct, we need the flow rate in cubic meters per second (m³/s). To convert from liters per second (L/s) to cubic meters per second (m³/s), divide the flow rate by 1000: Flow rate (m³/s) = Total fresh air requirement / 1000 Flow rate (m³/s) = 450 L/s / 1000 Flow rate (m³/s) = 0.45 m³/s

Calculate the cross-sectional area of the duct

Now, we will use the flow rate and the maximum air velocity (8 m/s) to calculate the cross-sectional area (A) of the duct. Use the formula: Area (m²) = Flow rate (m³/s) / Air velocity (m/s) Area (m²) = 0.45 m³/s / 8 m/s Area (m²) ≈ 0.05625 m²

Calculate the diameter of the duct

Since the duct is circular, we can use the formula for the area of a circle to find its diameter. The formula for the area of a circle is: Area (m²) = π × (diameter/2)² Now, we will solve for the diameter: Diameter = 2 × √(Area / π) Plugging in the calculated area: Diameter = 2 × √(0.05625 m² / π) Diameter ≈ 0.2675 m

Convert the diameter to its appropriate unit

The diameter is calculated in meters. To convert it into a more commonly used unit, like centimeters, multiply the diameter by 100: Diameter (cm) = Diameter (m) × 100 Diameter (cm) = 0.2675 m × 100 Diameter (cm) ≈ 26.75 cm So, the minimum required flow rate of fresh air that needs to be supplied to the lounge is 450 L/s, and the diameter of the duct should be approximately 26.75 cm for the air velocity not to exceed 8 m/s.