A prototype fan has a \(20-\mathrm{ft}\) diameter, an inlet pressure of \(14.40 \mathrm{psia}\), an inlet temperature of \(70^{\circ} \mathrm{F}\), and a speed of \(90 \mathrm{rpm}\). A \(\frac{1}{10}\)-scale model of the fan has the same inlet pressure and temperature, an inlet power of \(1.24 \mathrm{hp}\), a flow rate of \(220 \mathrm{ft}^{3} / \mathrm{min}\), and a speed of \(1800 \mathrm{rpm}\). Find the corresponding input power and flow rate of the prototype fan. Neglect Reynolds number effects.