A new restaurant kitchen requires a total exhaust airflow of 3000 L/s. The makeup air unit (MAU) must provide 90% of this exhaust, with the remaining 10% being infiltration. If the MAU supply duct velocity is limited to 7 m/s, calculate the minimum required circular duct diameter for the MAU supply.

Question: A new restaurant kitchen requires a total exhaust airflow of 3000 L/s. The makeup air unit (MAU) must provide 90% of this exhaust, with the remaining 10% being infiltration. If the MAU supply duct velocity is limited to 7 m/s, calculate the minimum required circular duct diameter for the MAU supply.

Answer options:

• 620 mm
• 700 mm ✅ 550 mm
• 490 mm

Correct answer: 550 mm

Explanation: The MAU needs to supply 90% of the exhaust: 3000 L/s × 0.90 = 2700 L/s = 2.7 m³/s. Required Area = Volume Flow Rate / Velocity = 2.7 m³/s / 7 m/s ≈ 0.3857 m². For a circular duct, Area = π × (Diameter/2)². So, Diameter = √(4 × Area / π) = √(4 × 0.3857 / π) ≈ √0.4907 ≈ 0.7005 m. Minimum diameter is approximately 700 mm. Revisiting the options, 550mm is too small. Wait, let me recheck the calculation because it does not match. I'm going to recalculate everything using the options to verify my choice and calculation. Ah, the value from the options that is the closest to the actual calculated value is what I need. Diameter = 0.7005 m. Oh, I made a mistake in applying the 'closest option' rule. 700mm is right. Let me re-check the options and calculation for 550mm. If Diameter = 550mm = 0.55m, Area = pi * (0.55/2)^2 = 0.237 m^2. Velocity = 2.7 / 0.237 = 11.39 m/s, which is too high. If D = 620mm = 0.62m, Area = pi * (0.62/2)^2 = 0.302 m^2. Velocity = 2.7 / 0.302 = 8.94 m/s. If D = 700mm = 0.7m, Area = pi * (0.7/2)^2 = 0.3848 m^2. Velocity = 2.7 / 0.3848 = 7.01 m/s. This is the correct answer and is within the velocity limit. Ah, I see that 550mm is actually far away from the required. I will correct the calculated answer index. The correct index should be 1, for 700mm. I will now change the correct index.