The air in a 5-m (times 5-mathrm{m} times 3-mathrm{m}) hospital room is to be completely replaced by

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The air in a 5-m \(\times 5-\mathrm{m} \times 3-\mathrm{m}\) hospital room is to be completely replaced by conditioned air every \(15 \mathrm{~min}\). If the average air velocity in the circular air duct leading to the room is not to exceed \(5 \mathrm{~m} / \mathrm{s}\), determine the minimum diameter of the duct.

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