The power, \(\mathscr{P}\), required to drive a fan is assumed to depend on fluid density \(ho\), volume flow rate \(Q\), impeller diameter \(D\), and angular speed \(\omega\). If a fan with \(D_{1}=8\) in. delivers \(Q_{1}=15 \mathrm{ft}^{3} / \mathrm{s}\) of air at \(\omega_{1}=2500 \mathrm{rpm}\), what size diameter fan could be expected to deliver \(Q_{2}=88 \mathrm{ft}^{3} / \mathrm{s}\) of air at \(\omega_{2}=1800 \mathrm{rpm}\), provided they were geometrically and dynamically similar?