Solving for Minimum Duct Diameter in a Hospital Room Air Exchange System

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To determine the minimum duct diameter for a hospital room air exchange system, first calculate the room's volume, which is 120 cubic meters. The air must be replaced every 20 minutes, leading to a required volumetric flow rate of 6 cubic meters per minute. With a maximum air velocity of 5 m/s, the duct's cross-sectional area can be derived from the flow rate. Using the relationship between flow rate, area, and velocity, the minimum diameter of the duct can be calculated. This approach ensures efficient air exchange while adhering to the specified velocity limit.
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Q. The air in a 6m x 5m x 4m hospital room is to be completed replaced by conditioned air every 20 min. If the average air velocity in the circular air duct leading to the room is not to exceed 5 m/s, determine the minimum diameter of the duct.

We can figure out the volume of the room, knowing the dimensions then what.

time is given, what else can be done?
 
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think about volume flow rate...
 
Ok, found out volume flow rate what next
 
- You have the volume of the room that needs to be replaced every 20 minutes. That should tell you something about the volumetric flow rate needed to come out of the duct.

- If you have a flow rate, what equation also contains the duct's cross sectional area and it's velocity?

Those are two pretty big hints there.
 

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