The head versus capacity curve for a certain fan may be approximated by the equation (H=30-10^{-7} Q^{2}),

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The head versus capacity curve for a certain fan may be approximated by the equation \(H=30-10^{-7} Q^{2}\), where \(H\) is the output static head in inches of water and \(Q\) is the air flow rate in \(\mathrm{ft}^{3} / \mathrm{min}\). The fan outlet dimensions are \(8 \times 16\) in. Determine the air flow rate delivered by the fan into a \(200 \mathrm{ft}\) straight length of \(8 \times 16 \mathrm{in}\). rectangular duct.

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