A centrifugal air compressor has a rotor inner diameter of \(D_{1}=2.0\) in., a rotor outer diameter of \(D_{2}=6.5\) in., a rotor depth of \(10 \mathrm{in}\)., and a rotor rotational speed of \(3600 \mathrm{rpm}\). The fluid relative velocities \((W)\) are purely radial. The compressor delivers an air mass flow rate of \(1.0 \mathrm{lbm} / \mathrm{s}\) with \(T_{1}=70^{\circ} \mathrm{F}, p_{1}=14.7 \mathrm{psia}, T_{2}=\) \(240^{\circ} \mathrm{F}\), and \(p_{2}=33.1 \mathrm{psia}\). Find the power transferred by the rotor to the air and the inlet relative velocity \(W_{1}\).