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How fast does the air flow in the duct in this problem?

A 18-cm-radius air duct is used to replenish the air of a room 10.2 m x 5.0 m x 5.5 m every 18 minutes.  How fast does air flow in the duct?

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This is the Best answer to this question.

The volume of the room is:

V = (10.2m)(5.0m)(5.5m) = 280.5m^3

The amount of air flowing through the duct each minute is:

280.5m^3/18m = 15.5833m^3/min

The area of the duct times the velocity of airflow must equal 15.5833m^3/min.

Area = Pi(r^2) = Pi(0.18m)^2 = 0.1018m^2

Velocity x 0.1018m^2 = 15.5833m^3/min.

Velocity = (15.5833m^3/min) / (0.1018m^2)

Velocity = 153.0962m/min, or

Velocity = (153.0962m/min)/ 60s/min = 2.5516m/s

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You could ask this question a thousand times, and get a thousand different answers, depending on individual's roundings of decimals, and values for pi. Are you going to ask a thousand times? Looks like it....

This is the correct answer for A 18-cm-radius air duct is used to replenish the air of a room 10.2 m x 5.0 m x 5.5 m every 18 minutes.  How fast does air flow in the duct?
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