A room is to be ventilated using a centrifugal fan, mounted as shown in the figure. The fan discharge pipe has a cross-sectional area of \(150 \mathrm{~cm}^{2}\) while the ventilating duct cross-sectional area is \(500 \mathrm{~cm}^{2}\). If the fan capacity is \(0.40 \mathrm{~m}^{3} / \mathrm{s}\) and a minimum ventilating rate of \(\dot{V}_{\text {room }}=0.30 \mathrm{~m}^{3} / \mathrm{s}\) is required, determine the proper installation angle \(\beta\). Assume a local loss \(0.5 V_{1}^{2} / 2 g\) for the duct entering from the room.

FIGURE P6-44

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2 1 Room